Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 79.3% → 91.5%

Time: 24.3s

Alternatives: 21

Speedup: 0.9×

• 37.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.06 \cdot 10^{+61}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c\_m}, \mathsf{fma}\left(9, \frac{x}{c\_m} \cdot \frac{y}{z}, \frac{\frac{b}{c\_m}}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.06e+61)
    (/ (+ (* a (* -4.0 t)) (/ (- b (* y (* x -9.0))) z)) c_m)
    (fma
     -4.0
     (* a (/ t c_m))
     (fma 9.0 (* (/ x c_m) (/ y z)) (/ (/ b c_m) z))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.06e+61) {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	} else {
		tmp = fma(-4.0, (a * (t / c_m)), fma(9.0, ((x / c_m) * (y / z)), ((b / c_m) / z)));
	}
	return c_s * tmp;
}

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.06e+61)
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * t)) + Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z)) / c_m);
	else
		tmp = fma(-4.0, Float64(a * Float64(t / c_m)), fma(9.0, Float64(Float64(x / c_m) * Float64(y / z)), Float64(Float64(b / c_m) / z)));
	end
	return Float64(c_s * tmp)
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.06e+61], N[(N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.0599999999999999e61

   1. Initial program 82.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 82.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.8%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.8%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 86.2%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 93.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around -inf 93.6%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 93.6%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 93.6%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 93.6%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 93.6%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. *-commutative 93.6%

          \[\leadsto \frac{a \cdot \color{blue}{\left(-4 \cdot t\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       6. mul-1-neg 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       7. sub-neg 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       8. *-commutative 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       9. *-commutative 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(y \cdot x\right)} \cdot -9 - b}{z}}{c} \]

       10. associate-*l* 93.5%

           \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{y \cdot \left(x \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 93.5%

       \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot t\right) - \frac{y \cdot \left(x \cdot -9\right) - b}{z}}}{c} \]

   if 1.0599999999999999e61 < c

   1. Initial program 63.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 67.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 67.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 79.4%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 79.4%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 79.4%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 86.7%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 86.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 79.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.06 \cdot 10^{+61}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ t_3 := \frac{\frac{b}{c\_m}}{z}\\ t_4 := \frac{b}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+206}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+173}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-98}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c\_m}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-276}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-281}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 0.12:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c_m))))
        (t_2 (* 9.0 (* x (/ y (* c_m z)))))
        (t_3 (/ (/ b c_m) z))
        (t_4 (/ b (* c_m z))))
   (*
    c_s
    (if (<= t -2.5e+206)
      (* -4.0 (* a (/ t c_m)))
      (if (<= t -1e+173)
        t_2
        (if (<= t -1.9e+89)
          t_1
          (if (<= t -4.5e+73)
            t_3
            (if (<= t -2.1e-98)
              (/ (* t (* a -4.0)) c_m)
              (if (<= t -2e-276)
                t_3
                (if (<= t 6.8e-281)
                  t_2
                  (if (<= t 1.9e-121)
                    t_4
                    (if (<= t 2.95e-77)
                      t_2
                      (if (<= t 0.12) t_4 t_1)))))))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double t_2 = 9.0 * (x * (y / (c_m * z)));
	double t_3 = (b / c_m) / z;
	double t_4 = b / (c_m * z);
	double tmp;
	if (t <= -2.5e+206) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -1e+173) {
		tmp = t_2;
	} else if (t <= -1.9e+89) {
		tmp = t_1;
	} else if (t <= -4.5e+73) {
		tmp = t_3;
	} else if (t <= -2.1e-98) {
		tmp = (t * (a * -4.0)) / c_m;
	} else if (t <= -2e-276) {
		tmp = t_3;
	} else if (t <= 6.8e-281) {
		tmp = t_2;
	} else if (t <= 1.9e-121) {
		tmp = t_4;
	} else if (t <= 2.95e-77) {
		tmp = t_2;
	} else if (t <= 0.12) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c_m))
    t_2 = 9.0d0 * (x * (y / (c_m * z)))
    t_3 = (b / c_m) / z
    t_4 = b / (c_m * z)
    if (t <= (-2.5d+206)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= (-1d+173)) then
        tmp = t_2
    else if (t <= (-1.9d+89)) then
        tmp = t_1
    else if (t <= (-4.5d+73)) then
        tmp = t_3
    else if (t <= (-2.1d-98)) then
        tmp = (t * (a * (-4.0d0))) / c_m
    else if (t <= (-2d-276)) then
        tmp = t_3
    else if (t <= 6.8d-281) then
        tmp = t_2
    else if (t <= 1.9d-121) then
        tmp = t_4
    else if (t <= 2.95d-77) then
        tmp = t_2
    else if (t <= 0.12d0) then
        tmp = t_4
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double t_2 = 9.0 * (x * (y / (c_m * z)));
	double t_3 = (b / c_m) / z;
	double t_4 = b / (c_m * z);
	double tmp;
	if (t <= -2.5e+206) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -1e+173) {
		tmp = t_2;
	} else if (t <= -1.9e+89) {
		tmp = t_1;
	} else if (t <= -4.5e+73) {
		tmp = t_3;
	} else if (t <= -2.1e-98) {
		tmp = (t * (a * -4.0)) / c_m;
	} else if (t <= -2e-276) {
		tmp = t_3;
	} else if (t <= 6.8e-281) {
		tmp = t_2;
	} else if (t <= 1.9e-121) {
		tmp = t_4;
	} else if (t <= 2.95e-77) {
		tmp = t_2;
	} else if (t <= 0.12) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * (t * (a / c_m))
	t_2 = 9.0 * (x * (y / (c_m * z)))
	t_3 = (b / c_m) / z
	t_4 = b / (c_m * z)
	tmp = 0
	if t <= -2.5e+206:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= -1e+173:
		tmp = t_2
	elif t <= -1.9e+89:
		tmp = t_1
	elif t <= -4.5e+73:
		tmp = t_3
	elif t <= -2.1e-98:
		tmp = (t * (a * -4.0)) / c_m
	elif t <= -2e-276:
		tmp = t_3
	elif t <= 6.8e-281:
		tmp = t_2
	elif t <= 1.9e-121:
		tmp = t_4
	elif t <= 2.95e-77:
		tmp = t_2
	elif t <= 0.12:
		tmp = t_4
	else:
		tmp = t_1
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c_m)))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))))
	t_3 = Float64(Float64(b / c_m) / z)
	t_4 = Float64(b / Float64(c_m * z))
	tmp = 0.0
	if (t <= -2.5e+206)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= -1e+173)
		tmp = t_2;
	elseif (t <= -1.9e+89)
		tmp = t_1;
	elseif (t <= -4.5e+73)
		tmp = t_3;
	elseif (t <= -2.1e-98)
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c_m);
	elseif (t <= -2e-276)
		tmp = t_3;
	elseif (t <= 6.8e-281)
		tmp = t_2;
	elseif (t <= 1.9e-121)
		tmp = t_4;
	elseif (t <= 2.95e-77)
		tmp = t_2;
	elseif (t <= 0.12)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * (t * (a / c_m));
	t_2 = 9.0 * (x * (y / (c_m * z)));
	t_3 = (b / c_m) / z;
	t_4 = b / (c_m * z);
	tmp = 0.0;
	if (t <= -2.5e+206)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= -1e+173)
		tmp = t_2;
	elseif (t <= -1.9e+89)
		tmp = t_1;
	elseif (t <= -4.5e+73)
		tmp = t_3;
	elseif (t <= -2.1e-98)
		tmp = (t * (a * -4.0)) / c_m;
	elseif (t <= -2e-276)
		tmp = t_3;
	elseif (t <= 6.8e-281)
		tmp = t_2;
	elseif (t <= 1.9e-121)
		tmp = t_4;
	elseif (t <= 2.95e-77)
		tmp = t_2;
	elseif (t <= 0.12)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$4 = N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t, -2.5e+206], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e+173], t$95$2, If[LessEqual[t, -1.9e+89], t$95$1, If[LessEqual[t, -4.5e+73], t$95$3, If[LessEqual[t, -2.1e-98], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t, -2e-276], t$95$3, If[LessEqual[t, 6.8e-281], t$95$2, If[LessEqual[t, 1.9e-121], t$95$4, If[LessEqual[t, 2.95e-77], t$95$2, If[LessEqual[t, 0.12], t$95$4, t$95$1]]]]]]]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.5000000000000001e206

   1. Initial program 56.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 61.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 61.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 61.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 61.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 61.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 61.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 74.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 78.8%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 78.8%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -2.5000000000000001e206 < t < -1e173 or -2e-276 < t < 6.8e-281 or 1.9e-121 < t < 2.94999999999999982e-77

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 73.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 83.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.9%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.6%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   7. Applied egg-rr 54.6%

      \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   if -1e173 < t < -1.90000000000000012e89 or 0.12 < t

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 80.6%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 80.6%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 80.6%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 80.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 75.8%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 75.8%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 68.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 65.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 65.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 76.2%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in a around inf 49.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 49.8%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 53.4%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   11. Simplified 53.4%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.90000000000000012e89 < t < -4.49999999999999985e73 or -2.09999999999999992e-98 < t < -2e-276

   1. Initial program 81.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 53.5%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 53.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -4.49999999999999985e73 < t < -2.09999999999999992e-98

   1. Initial program 78.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 78.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.5%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.5%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 81.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.3%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 81.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 80.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 83.1%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 84.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in a around inf 54.7%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]
   11. Step-by-step derivation

       1. associate-*r* 54.7%

          \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

   12. Simplified 54.7%

       \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

   if 6.8e-281 < t < 1.9e-121 or 2.94999999999999982e-77 < t < 0.12

   1. Initial program 87.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 85.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 85.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 85.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 85.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 87.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+206}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+173}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-98}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-276}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-281}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-77}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;t \leq 0.12:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-208}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c_m) (/ y z)))))
   (*
    c_s
    (if (<= a -1.5e-119)
      (* -4.0 (* a (/ t c_m)))
      (if (<= a -1.25e-208)
        (* 9.0 (* x (/ y (* c_m z))))
        (if (<= a -5.6e-307)
          (/ (/ b c_m) z)
          (if (<= a 2.15e-212)
            t_1
            (if (<= a 1.2e-46)
              (* b (/ 1.0 (* c_m z)))
              (if (<= a 2.25e-12) t_1 (* -4.0 (* t (/ a c_m))))))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x / c_m) * (y / z));
	double tmp;
	if (a <= -1.5e-119) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (a <= -1.25e-208) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (a <= -5.6e-307) {
		tmp = (b / c_m) / z;
	} else if (a <= 2.15e-212) {
		tmp = t_1;
	} else if (a <= 1.2e-46) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 2.25e-12) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / c_m) * (y / z))
    if (a <= (-1.5d-119)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (a <= (-1.25d-208)) then
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    else if (a <= (-5.6d-307)) then
        tmp = (b / c_m) / z
    else if (a <= 2.15d-212) then
        tmp = t_1
    else if (a <= 1.2d-46) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (a <= 2.25d-12) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x / c_m) * (y / z));
	double tmp;
	if (a <= -1.5e-119) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (a <= -1.25e-208) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (a <= -5.6e-307) {
		tmp = (b / c_m) / z;
	} else if (a <= 2.15e-212) {
		tmp = t_1;
	} else if (a <= 1.2e-46) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 2.25e-12) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((x / c_m) * (y / z))
	tmp = 0
	if a <= -1.5e-119:
		tmp = -4.0 * (a * (t / c_m))
	elif a <= -1.25e-208:
		tmp = 9.0 * (x * (y / (c_m * z)))
	elif a <= -5.6e-307:
		tmp = (b / c_m) / z
	elif a <= 2.15e-212:
		tmp = t_1
	elif a <= 1.2e-46:
		tmp = b * (1.0 / (c_m * z))
	elif a <= 2.25e-12:
		tmp = t_1
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)))
	tmp = 0.0
	if (a <= -1.5e-119)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (a <= -1.25e-208)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	elseif (a <= -5.6e-307)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (a <= 2.15e-212)
		tmp = t_1;
	elseif (a <= 1.2e-46)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (a <= 2.25e-12)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((x / c_m) * (y / z));
	tmp = 0.0;
	if (a <= -1.5e-119)
		tmp = -4.0 * (a * (t / c_m));
	elseif (a <= -1.25e-208)
		tmp = 9.0 * (x * (y / (c_m * z)));
	elseif (a <= -5.6e-307)
		tmp = (b / c_m) / z;
	elseif (a <= 2.15e-212)
		tmp = t_1;
	elseif (a <= 1.2e-46)
		tmp = b * (1.0 / (c_m * z));
	elseif (a <= 2.25e-12)
		tmp = t_1;
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1.5e-119], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-208], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.6e-307], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.15e-212], t$95$1, If[LessEqual[a, 1.2e-46], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-12], t$95$1, N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 6 regimes

2. if a < -1.5000000000000001e-119

   1. Initial program 78.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 54.7%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -1.5000000000000001e-119 < a < -1.24999999999999991e-208

   1. Initial program 88.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 93.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 93.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 93.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 48.2%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 42.8%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   7. Applied egg-rr 42.8%

      \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   if -1.24999999999999991e-208 < a < -5.6e-307

   1. Initial program 85.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 99.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 99.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 99.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 99.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 59.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 50.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -5.6e-307 < a < 2.14999999999999987e-212 or 1.20000000000000007e-46 < a < 2.2499999999999999e-12

   1. Initial program 69.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 79.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 46.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. times-frac 49.4%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   7. Simplified 49.4%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   if 2.14999999999999987e-212 < a < 1.20000000000000007e-46

   1. Initial program 82.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 82.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 54.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 58.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. associate-/l/ 54.9%

         \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

      2. div-inv 55.0%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      3. *-commutative 55.0%

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

   9. Applied egg-rr 55.0%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]

   if 2.2499999999999999e-12 < a

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 74.0%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 74.0%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 74.0%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 78.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 81.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 84.6%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in a around inf 43.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 43.5%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 56.0%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   11. Simplified 56.0%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-208}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-212}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{y \cdot x}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-303}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (/ (* y x) (* c_m z)))))
   (*
    c_s
    (if (<= a -5.5e-120)
      (* -4.0 (* a (/ t c_m)))
      (if (<= a -5.2e-206)
        t_1
        (if (<= a 1.3e-303)
          (/ (/ b c_m) z)
          (if (<= a 1.75e-177)
            t_1
            (if (<= a 3e-47)
              (* b (/ 1.0 (* c_m z)))
              (if (<= a 2.25e-12)
                (* 9.0 (* (/ x c_m) (/ y z)))
                (* -4.0 (* t (/ a c_m))))))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((y * x) / (c_m * z));
	double tmp;
	if (a <= -5.5e-120) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (a <= -5.2e-206) {
		tmp = t_1;
	} else if (a <= 1.3e-303) {
		tmp = (b / c_m) / z;
	} else if (a <= 1.75e-177) {
		tmp = t_1;
	} else if (a <= 3e-47) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 2.25e-12) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((y * x) / (c_m * z))
    if (a <= (-5.5d-120)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (a <= (-5.2d-206)) then
        tmp = t_1
    else if (a <= 1.3d-303) then
        tmp = (b / c_m) / z
    else if (a <= 1.75d-177) then
        tmp = t_1
    else if (a <= 3d-47) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (a <= 2.25d-12) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((y * x) / (c_m * z));
	double tmp;
	if (a <= -5.5e-120) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (a <= -5.2e-206) {
		tmp = t_1;
	} else if (a <= 1.3e-303) {
		tmp = (b / c_m) / z;
	} else if (a <= 1.75e-177) {
		tmp = t_1;
	} else if (a <= 3e-47) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 2.25e-12) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((y * x) / (c_m * z))
	tmp = 0
	if a <= -5.5e-120:
		tmp = -4.0 * (a * (t / c_m))
	elif a <= -5.2e-206:
		tmp = t_1
	elif a <= 1.3e-303:
		tmp = (b / c_m) / z
	elif a <= 1.75e-177:
		tmp = t_1
	elif a <= 3e-47:
		tmp = b * (1.0 / (c_m * z))
	elif a <= 2.25e-12:
		tmp = 9.0 * ((x / c_m) * (y / z))
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(y * x) / Float64(c_m * z)))
	tmp = 0.0
	if (a <= -5.5e-120)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (a <= -5.2e-206)
		tmp = t_1;
	elseif (a <= 1.3e-303)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (a <= 1.75e-177)
		tmp = t_1;
	elseif (a <= 3e-47)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (a <= 2.25e-12)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((y * x) / (c_m * z));
	tmp = 0.0;
	if (a <= -5.5e-120)
		tmp = -4.0 * (a * (t / c_m));
	elseif (a <= -5.2e-206)
		tmp = t_1;
	elseif (a <= 1.3e-303)
		tmp = (b / c_m) / z;
	elseif (a <= 1.75e-177)
		tmp = t_1;
	elseif (a <= 3e-47)
		tmp = b * (1.0 / (c_m * z));
	elseif (a <= 2.25e-12)
		tmp = 9.0 * ((x / c_m) * (y / z));
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -5.5e-120], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e-206], t$95$1, If[LessEqual[a, 1.3e-303], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.75e-177], t$95$1, If[LessEqual[a, 3e-47], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-12], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 6 regimes

2. if a < -5.5000000000000001e-120

   1. Initial program 78.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 54.7%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -5.5000000000000001e-120 < a < -5.2000000000000001e-206 or 1.30000000000000002e-303 < a < 1.7500000000000001e-177

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 92.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 92.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 92.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 92.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 92.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 92.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.9%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -5.2000000000000001e-206 < a < 1.30000000000000002e-303

   1. Initial program 85.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 99.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 99.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 99.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 99.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 99.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 99.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 61.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 52.5%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if 1.7500000000000001e-177 < a < 3.00000000000000017e-47

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 79.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 56.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. associate-/l/ 51.6%

         \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

      2. div-inv 51.8%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      3. *-commutative 51.8%

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

   9. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]

   if 3.00000000000000017e-47 < a < 2.2499999999999999e-12

   1. Initial program 56.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 56.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 56.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 56.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 23.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. times-frac 32.1%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   if 2.2499999999999999e-12 < a

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 74.0%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 74.0%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 74.0%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 78.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 81.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 84.6%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in a around inf 43.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 43.5%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 56.0%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   11. Simplified 56.0%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-206}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-303}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-177}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{-220}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{c\_m \cdot z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-182}:\\ \;\;\;\;\frac{y}{c\_m} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= a -9.2e-120)
    (* -4.0 (* a (/ t c_m)))
    (if (<= a -6.3e-220)
      (* 9.0 (/ (* y x) (* c_m z)))
      (if (<= a -6e-307)
        (/ (/ b c_m) z)
        (if (<= a 5.4e-182)
          (* (/ y c_m) (/ (* x 9.0) z))
          (if (<= a 1.5e-47)
            (* b (/ 1.0 (* c_m z)))
            (if (<= a 2.4e-12)
              (* 9.0 (* (/ x c_m) (/ y z)))
              (* -4.0 (* t (/ a c_m)))))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -9.2e-120) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (a <= -6.3e-220) {
		tmp = 9.0 * ((y * x) / (c_m * z));
	} else if (a <= -6e-307) {
		tmp = (b / c_m) / z;
	} else if (a <= 5.4e-182) {
		tmp = (y / c_m) * ((x * 9.0) / z);
	} else if (a <= 1.5e-47) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 2.4e-12) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (a <= (-9.2d-120)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (a <= (-6.3d-220)) then
        tmp = 9.0d0 * ((y * x) / (c_m * z))
    else if (a <= (-6d-307)) then
        tmp = (b / c_m) / z
    else if (a <= 5.4d-182) then
        tmp = (y / c_m) * ((x * 9.0d0) / z)
    else if (a <= 1.5d-47) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (a <= 2.4d-12) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -9.2e-120) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (a <= -6.3e-220) {
		tmp = 9.0 * ((y * x) / (c_m * z));
	} else if (a <= -6e-307) {
		tmp = (b / c_m) / z;
	} else if (a <= 5.4e-182) {
		tmp = (y / c_m) * ((x * 9.0) / z);
	} else if (a <= 1.5e-47) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 2.4e-12) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if a <= -9.2e-120:
		tmp = -4.0 * (a * (t / c_m))
	elif a <= -6.3e-220:
		tmp = 9.0 * ((y * x) / (c_m * z))
	elif a <= -6e-307:
		tmp = (b / c_m) / z
	elif a <= 5.4e-182:
		tmp = (y / c_m) * ((x * 9.0) / z)
	elif a <= 1.5e-47:
		tmp = b * (1.0 / (c_m * z))
	elif a <= 2.4e-12:
		tmp = 9.0 * ((x / c_m) * (y / z))
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (a <= -9.2e-120)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (a <= -6.3e-220)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(c_m * z)));
	elseif (a <= -6e-307)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (a <= 5.4e-182)
		tmp = Float64(Float64(y / c_m) * Float64(Float64(x * 9.0) / z));
	elseif (a <= 1.5e-47)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (a <= 2.4e-12)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (a <= -9.2e-120)
		tmp = -4.0 * (a * (t / c_m));
	elseif (a <= -6.3e-220)
		tmp = 9.0 * ((y * x) / (c_m * z));
	elseif (a <= -6e-307)
		tmp = (b / c_m) / z;
	elseif (a <= 5.4e-182)
		tmp = (y / c_m) * ((x * 9.0) / z);
	elseif (a <= 1.5e-47)
		tmp = b * (1.0 / (c_m * z));
	elseif (a <= 2.4e-12)
		tmp = 9.0 * ((x / c_m) * (y / z));
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[a, -9.2e-120], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.3e-220], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-307], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 5.4e-182], N[(N[(y / c$95$m), $MachinePrecision] * N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-47], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-12], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]), $MachinePrecision]

Derivation

1. Split input into 7 regimes

2. if a < -9.19999999999999946e-120

   1. Initial program 78.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 54.7%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -9.19999999999999946e-120 < a < -6.30000000000000017e-220

   1. Initial program 89.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 89.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 89.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 94.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 94.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 94.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 94.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 94.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 48.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -6.30000000000000017e-220 < a < -5.9999999999999999e-307

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 99.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 99.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 99.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 99.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 60.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 55.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 55.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -5.9999999999999999e-307 < a < 5.39999999999999999e-182

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 92.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 92.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 92.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 57.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 57.3%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. associate-*r* 57.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

      3. *-commutative 57.1%

         \[\leadsto \frac{\left(9 \cdot x\right) \cdot y}{\color{blue}{z \cdot c}} \]

   7. Simplified 57.1%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot x\right) \cdot y}{z \cdot c}} \]
   8. Step-by-step derivation

      1. times-frac 53.5%

         \[\leadsto \color{blue}{\frac{9 \cdot x}{z} \cdot \frac{y}{c}} \]

      2. *-commutative 53.5%

         \[\leadsto \frac{\color{blue}{x \cdot 9}}{z} \cdot \frac{y}{c} \]

   9. Applied egg-rr 53.5%

      \[\leadsto \color{blue}{\frac{x \cdot 9}{z} \cdot \frac{y}{c}} \]

   if 5.39999999999999999e-182 < a < 1.50000000000000008e-47

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 79.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 56.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. associate-/l/ 51.6%

         \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

      2. div-inv 51.8%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      3. *-commutative 51.8%

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

   9. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]

   if 1.50000000000000008e-47 < a < 2.39999999999999987e-12

   1. Initial program 56.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 56.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 56.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 56.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 23.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. times-frac 32.1%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   if 2.39999999999999987e-12 < a

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 74.0%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 74.0%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 74.0%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 78.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 81.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 84.6%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in a around inf 43.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 43.5%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 56.0%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   11. Simplified 56.0%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{-220}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-182}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141} \lor \neg \left(x \cdot 9 \leq -1 \cdot 10^{+59}\right) \land \left(x \cdot 9 \leq -1 \cdot 10^{+25} \lor \neg \left(x \cdot 9 \leq 5000000000000\right)\right):\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= (* x 9.0) -1e+141)
          (and (not (<= (* x 9.0) -1e+59))
               (or (<= (* x 9.0) -1e+25)
                   (not (<= (* x 9.0) 5000000000000.0)))))
    (/ (+ b (* y (* x 9.0))) (* c_m z))
    (/ (+ (* -4.0 (* a t)) (/ b z)) c_m))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (((x * 9.0) <= -1e+141) || (!((x * 9.0) <= -1e+59) && (((x * 9.0) <= -1e+25) || !((x * 9.0) <= 5000000000000.0)))) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (((x * 9.0d0) <= (-1d+141)) .or. (.not. ((x * 9.0d0) <= (-1d+59))) .and. ((x * 9.0d0) <= (-1d+25)) .or. (.not. ((x * 9.0d0) <= 5000000000000.0d0))) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (((x * 9.0) <= -1e+141) || (!((x * 9.0) <= -1e+59) && (((x * 9.0) <= -1e+25) || !((x * 9.0) <= 5000000000000.0)))) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if ((x * 9.0) <= -1e+141) or (not ((x * 9.0) <= -1e+59) and (((x * 9.0) <= -1e+25) or not ((x * 9.0) <= 5000000000000.0))):
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	else:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((Float64(x * 9.0) <= -1e+141) || (!(Float64(x * 9.0) <= -1e+59) && ((Float64(x * 9.0) <= -1e+25) || !(Float64(x * 9.0) <= 5000000000000.0))))
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (((x * 9.0) <= -1e+141) || (~(((x * 9.0) <= -1e+59)) && (((x * 9.0) <= -1e+25) || ~(((x * 9.0) <= 5000000000000.0)))))
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	else
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+141], And[N[Not[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+59]], $MachinePrecision], Or[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+25], N[Not[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0]], $MachinePrecision]]]], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 9) < -1.00000000000000002e141 or -9.99999999999999972e58 < (*.f64 x 9) < -1.00000000000000009e25 or 5e12 < (*.f64 x 9)

   1. Initial program 71.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 74.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.2%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 62.1%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if -1.00000000000000002e141 < (*.f64 x 9) < -9.99999999999999972e58 or -1.00000000000000009e25 < (*.f64 x 9) < 5e12

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 83.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 83.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.1%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.0%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 91.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 78.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141} \lor \neg \left(x \cdot 9 \leq -1 \cdot 10^{+59}\right) \land \left(x \cdot 9 \leq -1 \cdot 10^{+25} \lor \neg \left(x \cdot 9 \leq 5000000000000\right)\right):\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ t_2 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (* y (* x 9.0))) (* c_m z)))
        (t_2 (/ (+ (* -4.0 (* a t)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= (* x 9.0) -1e+141)
      t_1
      (if (<= (* x 9.0) -1e+59)
        t_2
        (if (<= (* x 9.0) -1e+25)
          t_1
          (if (<= (* x 9.0) 5000000000000.0)
            t_2
            (/ (/ (+ b (* 9.0 (* y x))) z) c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + (y * (x * 9.0))) / (c_m * z);
	double t_2 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_2;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = t_1;
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_2;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b + (y * (x * 9.0d0))) / (c_m * z)
    t_2 = (((-4.0d0) * (a * t)) + (b / z)) / c_m
    if ((x * 9.0d0) <= (-1d+141)) then
        tmp = t_1
    else if ((x * 9.0d0) <= (-1d+59)) then
        tmp = t_2
    else if ((x * 9.0d0) <= (-1d+25)) then
        tmp = t_1
    else if ((x * 9.0d0) <= 5000000000000.0d0) then
        tmp = t_2
    else
        tmp = ((b + (9.0d0 * (y * x))) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + (y * (x * 9.0))) / (c_m * z);
	double t_2 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_2;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = t_1;
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_2;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + (y * (x * 9.0))) / (c_m * z)
	t_2 = ((-4.0 * (a * t)) + (b / z)) / c_m
	tmp = 0
	if (x * 9.0) <= -1e+141:
		tmp = t_1
	elif (x * 9.0) <= -1e+59:
		tmp = t_2
	elif (x * 9.0) <= -1e+25:
		tmp = t_1
	elif (x * 9.0) <= 5000000000000.0:
		tmp = t_2
	else:
		tmp = ((b + (9.0 * (y * x))) / z) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z))
	t_2 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (Float64(x * 9.0) <= -1e+141)
		tmp = t_1;
	elseif (Float64(x * 9.0) <= -1e+59)
		tmp = t_2;
	elseif (Float64(x * 9.0) <= -1e+25)
		tmp = t_1;
	elseif (Float64(x * 9.0) <= 5000000000000.0)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + (y * (x * 9.0))) / (c_m * z);
	t_2 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	tmp = 0.0;
	if ((x * 9.0) <= -1e+141)
		tmp = t_1;
	elseif ((x * 9.0) <= -1e+59)
		tmp = t_2;
	elseif ((x * 9.0) <= -1e+25)
		tmp = t_1;
	elseif ((x * 9.0) <= 5000000000000.0)
		tmp = t_2;
	else
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+141], t$95$1, If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+59], t$95$2, If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+25], t$95$1, If[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0], t$95$2, N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 9) < -1.00000000000000002e141 or -9.99999999999999972e58 < (*.f64 x 9) < -1.00000000000000009e25

   1. Initial program 67.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 67.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 67.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 69.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 66.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 66.0%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if -1.00000000000000002e141 < (*.f64 x 9) < -9.99999999999999972e58 or -1.00000000000000009e25 < (*.f64 x 9) < 5e12

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 83.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 83.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.1%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.0%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 91.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 78.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 79.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 79.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 83.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 83.7%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 88.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around 0 60.6%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{b}{c\_m} + 9 \cdot \frac{y \cdot x}{c\_m}}{z}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* a t)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= (* x 9.0) -1e+141)
      (/ (+ (/ b c_m) (* 9.0 (/ (* y x) c_m))) z)
      (if (<= (* x 9.0) -1e+59)
        t_1
        (if (<= (* x 9.0) -1e+25)
          (/ (+ b (* y (* x 9.0))) (* c_m z))
          (if (<= (* x 9.0) 5000000000000.0)
            t_1
            (/ (/ (+ b (* 9.0 (* y x))) z) c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = ((b / c_m) + (9.0 * ((y * x) / c_m))) / z;
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_1;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (a * t)) + (b / z)) / c_m
    if ((x * 9.0d0) <= (-1d+141)) then
        tmp = ((b / c_m) + (9.0d0 * ((y * x) / c_m))) / z
    else if ((x * 9.0d0) <= (-1d+59)) then
        tmp = t_1
    else if ((x * 9.0d0) <= (-1d+25)) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else if ((x * 9.0d0) <= 5000000000000.0d0) then
        tmp = t_1
    else
        tmp = ((b + (9.0d0 * (y * x))) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = ((b / c_m) + (9.0 * ((y * x) / c_m))) / z;
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_1;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m
	tmp = 0
	if (x * 9.0) <= -1e+141:
		tmp = ((b / c_m) + (9.0 * ((y * x) / c_m))) / z
	elif (x * 9.0) <= -1e+59:
		tmp = t_1
	elif (x * 9.0) <= -1e+25:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	elif (x * 9.0) <= 5000000000000.0:
		tmp = t_1
	else:
		tmp = ((b + (9.0 * (y * x))) / z) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (Float64(x * 9.0) <= -1e+141)
		tmp = Float64(Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(y * x) / c_m))) / z);
	elseif (Float64(x * 9.0) <= -1e+59)
		tmp = t_1;
	elseif (Float64(x * 9.0) <= -1e+25)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	elseif (Float64(x * 9.0) <= 5000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	tmp = 0.0;
	if ((x * 9.0) <= -1e+141)
		tmp = ((b / c_m) + (9.0 * ((y * x) / c_m))) / z;
	elseif ((x * 9.0) <= -1e+59)
		tmp = t_1;
	elseif ((x * 9.0) <= -1e+25)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	elseif ((x * 9.0) <= 5000000000000.0)
		tmp = t_1;
	else
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+141], N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+59], t$95$1, If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+25], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0], t$95$1, N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x 9) < -1.00000000000000002e141

   1. Initial program 69.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 75.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 75.4%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 75.4%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 75.4%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 75.5%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 75.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 75.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 78.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 84.6%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in z around 0 70.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]

   if -1.00000000000000002e141 < (*.f64 x 9) < -9.99999999999999972e58 or -1.00000000000000009e25 < (*.f64 x 9) < 5e12

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 83.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 83.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.1%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.0%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 91.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 78.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -9.99999999999999972e58 < (*.f64 x 9) < -1.00000000000000009e25

   1. Initial program 60.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 60.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 60.6%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 79.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 79.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 83.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 83.7%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 88.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around 0 60.6%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{b}{c} + 9 \cdot \frac{y \cdot x}{c}}{z}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := \frac{t\_1 + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{t\_1 + 9 \cdot \frac{y \cdot x}{z}}{c\_m}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))) (t_2 (/ (+ t_1 (/ b z)) c_m)))
   (*
    c_s
    (if (<= (* x 9.0) -1e+141)
      (/ (+ t_1 (* 9.0 (/ (* y x) z))) c_m)
      (if (<= (* x 9.0) -1e+59)
        t_2
        (if (<= (* x 9.0) -1e+25)
          (/ (+ b (* y (* x 9.0))) (* c_m z))
          (if (<= (* x 9.0) 5000000000000.0)
            t_2
            (/ (/ (+ b (* 9.0 (* y x))) z) c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (a * t);
	double t_2 = (t_1 + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c_m;
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_2;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_2;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    t_2 = (t_1 + (b / z)) / c_m
    if ((x * 9.0d0) <= (-1d+141)) then
        tmp = (t_1 + (9.0d0 * ((y * x) / z))) / c_m
    else if ((x * 9.0d0) <= (-1d+59)) then
        tmp = t_2
    else if ((x * 9.0d0) <= (-1d+25)) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else if ((x * 9.0d0) <= 5000000000000.0d0) then
        tmp = t_2
    else
        tmp = ((b + (9.0d0 * (y * x))) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (a * t);
	double t_2 = (t_1 + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c_m;
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_2;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_2;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * (a * t)
	t_2 = (t_1 + (b / z)) / c_m
	tmp = 0
	if (x * 9.0) <= -1e+141:
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c_m
	elif (x * 9.0) <= -1e+59:
		tmp = t_2
	elif (x * 9.0) <= -1e+25:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	elif (x * 9.0) <= 5000000000000.0:
		tmp = t_2
	else:
		tmp = ((b + (9.0 * (y * x))) / z) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(a * t))
	t_2 = Float64(Float64(t_1 + Float64(b / z)) / c_m)
	tmp = 0.0
	if (Float64(x * 9.0) <= -1e+141)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(y * x) / z))) / c_m);
	elseif (Float64(x * 9.0) <= -1e+59)
		tmp = t_2;
	elseif (Float64(x * 9.0) <= -1e+25)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	elseif (Float64(x * 9.0) <= 5000000000000.0)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * (a * t);
	t_2 = (t_1 + (b / z)) / c_m;
	tmp = 0.0;
	if ((x * 9.0) <= -1e+141)
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c_m;
	elseif ((x * 9.0) <= -1e+59)
		tmp = t_2;
	elseif ((x * 9.0) <= -1e+25)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	elseif ((x * 9.0) <= 5000000000000.0)
		tmp = t_2;
	else
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+141], N[(N[(t$95$1 + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+59], t$95$2, If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+25], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0], t$95$2, N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x 9) < -1.00000000000000002e141

   1. Initial program 69.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 75.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 75.4%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 75.4%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 75.4%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 75.5%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 75.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 75.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 78.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 84.6%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 87.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in b around 0 82.1%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}} \]

   if -1.00000000000000002e141 < (*.f64 x 9) < -9.99999999999999972e58 or -1.00000000000000009e25 < (*.f64 x 9) < 5e12

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 83.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 83.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.1%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.0%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 91.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 78.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -9.99999999999999972e58 < (*.f64 x 9) < -1.00000000000000009e25

   1. Initial program 60.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 60.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 60.6%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 79.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 79.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 83.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 83.7%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 88.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around 0 60.6%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + 9 \cdot \frac{y \cdot x}{c\_m \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* a t)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= (* x 9.0) -1e+141)
      (+ (* -4.0 (/ (* a t) c_m)) (* 9.0 (/ (* y x) (* c_m z))))
      (if (<= (* x 9.0) -1e+59)
        t_1
        (if (<= (* x 9.0) -1e+25)
          (/ (+ b (* y (* x 9.0))) (* c_m z))
          (if (<= (* x 9.0) 5000000000000.0)
            t_1
            (/ (/ (+ b (* 9.0 (* y x))) z) c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = (-4.0 * ((a * t) / c_m)) + (9.0 * ((y * x) / (c_m * z)));
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_1;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (a * t)) + (b / z)) / c_m
    if ((x * 9.0d0) <= (-1d+141)) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + (9.0d0 * ((y * x) / (c_m * z)))
    else if ((x * 9.0d0) <= (-1d+59)) then
        tmp = t_1
    else if ((x * 9.0d0) <= (-1d+25)) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else if ((x * 9.0d0) <= 5000000000000.0d0) then
        tmp = t_1
    else
        tmp = ((b + (9.0d0 * (y * x))) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = (-4.0 * ((a * t) / c_m)) + (9.0 * ((y * x) / (c_m * z)));
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_1;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m
	tmp = 0
	if (x * 9.0) <= -1e+141:
		tmp = (-4.0 * ((a * t) / c_m)) + (9.0 * ((y * x) / (c_m * z)))
	elif (x * 9.0) <= -1e+59:
		tmp = t_1
	elif (x * 9.0) <= -1e+25:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	elif (x * 9.0) <= 5000000000000.0:
		tmp = t_1
	else:
		tmp = ((b + (9.0 * (y * x))) / z) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (Float64(x * 9.0) <= -1e+141)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(9.0 * Float64(Float64(y * x) / Float64(c_m * z))));
	elseif (Float64(x * 9.0) <= -1e+59)
		tmp = t_1;
	elseif (Float64(x * 9.0) <= -1e+25)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	elseif (Float64(x * 9.0) <= 5000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	tmp = 0.0;
	if ((x * 9.0) <= -1e+141)
		tmp = (-4.0 * ((a * t) / c_m)) + (9.0 * ((y * x) / (c_m * z)));
	elseif ((x * 9.0) <= -1e+59)
		tmp = t_1;
	elseif ((x * 9.0) <= -1e+25)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	elseif ((x * 9.0) <= 5000000000000.0)
		tmp = t_1;
	else
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+141], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+59], t$95$1, If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+25], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0], t$95$1, N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x 9) < -1.00000000000000002e141

   1. Initial program 69.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 75.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 66.5%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   6. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -1.00000000000000002e141 < (*.f64 x 9) < -9.99999999999999972e58 or -1.00000000000000009e25 < (*.f64 x 9) < 5e12

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 83.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 83.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.1%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.0%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 91.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 78.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -9.99999999999999972e58 < (*.f64 x 9) < -1.00000000000000009e25

   1. Initial program 60.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 60.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 60.6%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 79.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 79.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 83.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 83.7%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 88.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around 0 60.6%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y \cdot 9\right)}{c\_m}}{z} - \left(a \cdot \frac{t}{c\_m}\right) \cdot 4\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* a t)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= (* x 9.0) -1e+141)
      (- (/ (/ (* x (* y 9.0)) c_m) z) (* (* a (/ t c_m)) 4.0))
      (if (<= (* x 9.0) -1e+59)
        t_1
        (if (<= (* x 9.0) -1e+25)
          (/ (+ b (* y (* x 9.0))) (* c_m z))
          (if (<= (* x 9.0) 5000000000000.0)
            t_1
            (/ (/ (+ b (* 9.0 (* y x))) z) c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0);
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_1;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (a * t)) + (b / z)) / c_m
    if ((x * 9.0d0) <= (-1d+141)) then
        tmp = (((x * (y * 9.0d0)) / c_m) / z) - ((a * (t / c_m)) * 4.0d0)
    else if ((x * 9.0d0) <= (-1d+59)) then
        tmp = t_1
    else if ((x * 9.0d0) <= (-1d+25)) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else if ((x * 9.0d0) <= 5000000000000.0d0) then
        tmp = t_1
    else
        tmp = ((b + (9.0d0 * (y * x))) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	double tmp;
	if ((x * 9.0) <= -1e+141) {
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0);
	} else if ((x * 9.0) <= -1e+59) {
		tmp = t_1;
	} else if ((x * 9.0) <= -1e+25) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = t_1;
	} else {
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m
	tmp = 0
	if (x * 9.0) <= -1e+141:
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0)
	elif (x * 9.0) <= -1e+59:
		tmp = t_1
	elif (x * 9.0) <= -1e+25:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	elif (x * 9.0) <= 5000000000000.0:
		tmp = t_1
	else:
		tmp = ((b + (9.0 * (y * x))) / z) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (Float64(x * 9.0) <= -1e+141)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y * 9.0)) / c_m) / z) - Float64(Float64(a * Float64(t / c_m)) * 4.0));
	elseif (Float64(x * 9.0) <= -1e+59)
		tmp = t_1;
	elseif (Float64(x * 9.0) <= -1e+25)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	elseif (Float64(x * 9.0) <= 5000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((-4.0 * (a * t)) + (b / z)) / c_m;
	tmp = 0.0;
	if ((x * 9.0) <= -1e+141)
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0);
	elseif ((x * 9.0) <= -1e+59)
		tmp = t_1;
	elseif ((x * 9.0) <= -1e+25)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	elseif ((x * 9.0) <= 5000000000000.0)
		tmp = t_1;
	else
		tmp = ((b + (9.0 * (y * x))) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+141], N[(N[(N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision] - N[(N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+59], t$95$1, If[LessEqual[N[(x * 9.0), $MachinePrecision], -1e+25], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0], t$95$1, N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x 9) < -1.00000000000000002e141

   1. Initial program 69.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 75.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 66.5%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. div-sub 60.2%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

      2. associate-*r/ 60.3%

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      3. frac-times 57.4%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      4. *-commutative 57.4%

         \[\leadsto \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right) \cdot 9} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      5. frac-times 60.3%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z}} \cdot 9 - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      6. associate-/l* 55.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      7. *-commutative 55.3%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{4 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)}}{c \cdot z} \]

      8. *-commutative 55.3%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{4 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot a\right)}{c \cdot z} \]

      9. associate-*r* 58.7%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{4 \cdot \color{blue}{\left(z \cdot \left(t \cdot a\right)\right)}}{c \cdot z} \]

      10. associate-*r* 58.7%

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{\color{blue}{\left(4 \cdot z\right) \cdot \left(t \cdot a\right)}}{c \cdot z} \]

      11. *-commutative 58.7%

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{\left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}}{c \cdot z} \]

   7. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}{c \cdot z}} \]
   8. Step-by-step derivation

      1. associate-/l* 61.6%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \color{blue}{\left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z}} \]

      2. *-commutative 61.6%

         \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      3. associate-*r/ 66.7%

         \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot y}{c \cdot z}} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      4. associate-*r/ 66.6%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      5. associate-/r* 69.6%

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right)}{c}}{z}} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      6. *-commutative 69.6%

         \[\leadsto \frac{\frac{\color{blue}{\left(x \cdot y\right) \cdot 9}}{c}}{z} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      7. associate-*r* 69.7%

         \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(y \cdot 9\right)}}{c}}{z} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      8. *-commutative 69.7%

         \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \color{blue}{\left(z \cdot 4\right)} \cdot \frac{a \cdot t}{c \cdot z} \]

   9. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \left(z \cdot 4\right) \cdot \frac{a \cdot t}{c \cdot z}} \]

   10. Taylor expanded in z around 0 82.1%

       \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \color{blue}{4 \cdot \frac{a \cdot t}{c}} \]
   11. Step-by-step derivation

       1. associate-*r/ 82.2%

          \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - 4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

   12. Simplified 82.2%

       \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \color{blue}{4 \cdot \left(a \cdot \frac{t}{c}\right)} \]

   if -1.00000000000000002e141 < (*.f64 x 9) < -9.99999999999999972e58 or -1.00000000000000009e25 < (*.f64 x 9) < 5e12

   1. Initial program 83.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 83.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 83.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 81.1%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 81.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.0%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 91.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 78.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -9.99999999999999972e58 < (*.f64 x 9) < -1.00000000000000009e25

   1. Initial program 60.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 60.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 50.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 60.6%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 79.6%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 79.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 83.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 83.7%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 88.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around 0 60.6%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \left(a \cdot \frac{t}{c}\right) \cdot 4\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right)}{c\_m}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-153}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -1.95e+48)
    (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* y x) z)) (/ b z))) c_m)
    (if (<= z 2e-153)
      (/ (+ b (- (* x (* y 9.0)) (* (* z 4.0) (* a t)))) (* c_m z))
      (/ (+ (* a (* -4.0 t)) (/ (- b (* y (* x -9.0))) z)) c_m)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.95e+48) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m;
	} else if (z <= 2e-153) {
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (c_m * z);
	} else {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-1.95d+48)) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((y * x) / z)) + (b / z))) / c_m
    else if (z <= 2d-153) then
        tmp = (b + ((x * (y * 9.0d0)) - ((z * 4.0d0) * (a * t)))) / (c_m * z)
    else
        tmp = ((a * ((-4.0d0) * t)) + ((b - (y * (x * (-9.0d0)))) / z)) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.95e+48) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m;
	} else if (z <= 2e-153) {
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (c_m * z);
	} else {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -1.95e+48:
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m
	elif z <= 2e-153:
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (c_m * z)
	else:
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -1.95e+48)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(y * x) / z)) + Float64(b / z))) / c_m);
	elseif (z <= 2e-153)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * t)) + Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z)) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -1.95e+48)
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m;
	elseif (z <= 2e-153)
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (c_m * z);
	else
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -1.95e+48], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[z, 2e-153], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e48

   1. Initial program 61.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 61.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 62.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 62.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 68.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.9%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 76.9%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 76.9%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 76.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.7%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 83.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 81.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.2%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 87.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   if -1.95e48 < z < 2.00000000000000008e-153

   1. Initial program 94.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 94.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 94.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 93.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 93.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   if 2.00000000000000008e-153 < z

   1. Initial program 71.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 74.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.9%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.9%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.9%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 80.7%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 80.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 82.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 86.9%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 94.1%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around -inf 94.2%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 94.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 94.2%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 94.2%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 94.2%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. *-commutative 94.2%

          \[\leadsto \frac{a \cdot \color{blue}{\left(-4 \cdot t\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       6. mul-1-neg 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       7. sub-neg 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       8. *-commutative 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       9. *-commutative 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(y \cdot x\right)} \cdot -9 - b}{z}}{c} \]

       10. associate-*l* 94.2%

           \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{y \cdot \left(x \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 94.2%

       \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot t\right) - \frac{y \cdot \left(x \cdot -9\right) - b}{z}}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-153}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right)}{c\_m}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -1.95e+48)
    (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* y x) z)) (/ b z))) c_m)
    (if (<= z 1.9e-149)
      (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))
      (/ (+ (* a (* -4.0 t)) (/ (- b (* y (* x -9.0))) z)) c_m)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.95e+48) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m;
	} else if (z <= 1.9e-149) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-1.95d+48)) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((y * x) / z)) + (b / z))) / c_m
    else if (z <= 1.9d-149) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c_m * z)
    else
        tmp = ((a * ((-4.0d0) * t)) + ((b - (y * (x * (-9.0d0)))) / z)) / c_m
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.95e+48) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m;
	} else if (z <= 1.9e-149) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -1.95e+48:
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m
	elif z <= 1.9e-149:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	else:
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -1.95e+48)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(y * x) / z)) + Float64(b / z))) / c_m);
	elseif (z <= 1.9e-149)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * t)) + Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z)) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -1.95e+48)
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((y * x) / z)) + (b / z))) / c_m;
	elseif (z <= 1.9e-149)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	else
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -1.95e+48], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[z, 1.9e-149], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e48

   1. Initial program 61.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 61.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 62.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 62.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 68.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.9%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 76.9%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 76.9%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 76.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.7%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 83.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 81.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 87.2%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 87.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   if -1.95e48 < z < 1.90000000000000003e-149

   1. Initial program 94.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   if 1.90000000000000003e-149 < z

   1. Initial program 71.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 74.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.9%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 82.9%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 82.9%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 82.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 80.7%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 80.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 82.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 82.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 86.9%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 94.1%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around -inf 94.2%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 94.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 94.2%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 94.2%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 94.2%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. *-commutative 94.2%

          \[\leadsto \frac{a \cdot \color{blue}{\left(-4 \cdot t\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       6. mul-1-neg 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       7. sub-neg 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       8. *-commutative 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       9. *-commutative 94.2%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(y \cdot x\right)} \cdot -9 - b}{z}}{c} \]

       10. associate-*l* 94.2%

           \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{y \cdot \left(x \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 94.2%

       \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot t\right) - \frac{y \cdot \left(x \cdot -9\right) - b}{z}}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-5} \lor \neg \left(t \leq 0.215\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c_m)))))
   (*
    c_s
    (if (<= t -1.95e+89)
      t_1
      (if (<= t -1.3e+74)
        (/ (/ b c_m) z)
        (if (or (<= t -4.8e-5) (not (<= t 0.215))) t_1 (/ b (* c_m z))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double tmp;
	if (t <= -1.95e+89) {
		tmp = t_1;
	} else if (t <= -1.3e+74) {
		tmp = (b / c_m) / z;
	} else if ((t <= -4.8e-5) || !(t <= 0.215)) {
		tmp = t_1;
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c_m))
    if (t <= (-1.95d+89)) then
        tmp = t_1
    else if (t <= (-1.3d+74)) then
        tmp = (b / c_m) / z
    else if ((t <= (-4.8d-5)) .or. (.not. (t <= 0.215d0))) then
        tmp = t_1
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double tmp;
	if (t <= -1.95e+89) {
		tmp = t_1;
	} else if (t <= -1.3e+74) {
		tmp = (b / c_m) / z;
	} else if ((t <= -4.8e-5) || !(t <= 0.215)) {
		tmp = t_1;
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * (t * (a / c_m))
	tmp = 0
	if t <= -1.95e+89:
		tmp = t_1
	elif t <= -1.3e+74:
		tmp = (b / c_m) / z
	elif (t <= -4.8e-5) or not (t <= 0.215):
		tmp = t_1
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c_m)))
	tmp = 0.0
	if (t <= -1.95e+89)
		tmp = t_1;
	elseif (t <= -1.3e+74)
		tmp = Float64(Float64(b / c_m) / z);
	elseif ((t <= -4.8e-5) || !(t <= 0.215))
		tmp = t_1;
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * (t * (a / c_m));
	tmp = 0.0;
	if (t <= -1.95e+89)
		tmp = t_1;
	elseif (t <= -1.3e+74)
		tmp = (b / c_m) / z;
	elseif ((t <= -4.8e-5) || ~((t <= 0.215)))
		tmp = t_1;
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t, -1.95e+89], t$95$1, If[LessEqual[t, -1.3e+74], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, -4.8e-5], N[Not[LessEqual[t, 0.215]], $MachinePrecision]], t$95$1, N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if t < -1.95000000000000005e89 or -1.3e74 < t < -4.8000000000000001e-5 or 0.214999999999999997 < t

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 76.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 78.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 78.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 78.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 78.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.4%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 74.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 72.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 77.4%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in a around inf 55.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 55.8%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 58.1%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   11. Simplified 58.1%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.95000000000000005e89 < t < -1.3e74

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 100.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 100.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 35.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 35.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -4.8000000000000001e-5 < t < 0.214999999999999997

   1. Initial program 84.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 80.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-5} \lor \neg \left(t \leq 0.215\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -0.00032 \lor \neg \left(t \leq 4.7\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -1.9e+89)
    (* -4.0 (* a (/ t c_m)))
    (if (<= t -2.15e+74)
      (/ (/ b c_m) z)
      (if (or (<= t -0.00032) (not (<= t 4.7)))
        (* -4.0 (* t (/ a c_m)))
        (/ b (* c_m z)))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -1.9e+89) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -2.15e+74) {
		tmp = (b / c_m) / z;
	} else if ((t <= -0.00032) || !(t <= 4.7)) {
		tmp = -4.0 * (t * (a / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (t <= (-1.9d+89)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= (-2.15d+74)) then
        tmp = (b / c_m) / z
    else if ((t <= (-0.00032d0)) .or. (.not. (t <= 4.7d0))) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -1.9e+89) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -2.15e+74) {
		tmp = (b / c_m) / z;
	} else if ((t <= -0.00032) || !(t <= 4.7)) {
		tmp = -4.0 * (t * (a / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -1.9e+89:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= -2.15e+74:
		tmp = (b / c_m) / z
	elif (t <= -0.00032) or not (t <= 4.7):
		tmp = -4.0 * (t * (a / c_m))
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -1.9e+89)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= -2.15e+74)
		tmp = Float64(Float64(b / c_m) / z);
	elseif ((t <= -0.00032) || !(t <= 4.7))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -1.9e+89)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= -2.15e+74)
		tmp = (b / c_m) / z;
	elseif ((t <= -0.00032) || ~((t <= 4.7)))
		tmp = -4.0 * (t * (a / c_m));
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -1.9e+89], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e+74], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, -0.00032], N[Not[LessEqual[t, 4.7]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.90000000000000012e89

   1. Initial program 62.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 62.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 62.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 68.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 68.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 68.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 68.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 68.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 65.6%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 65.6%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -1.90000000000000012e89 < t < -2.15e74

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 100.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 100.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 35.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 35.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -2.15e74 < t < -3.20000000000000026e-4 or 4.70000000000000018 < t

   1. Initial program 77.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 82.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 78.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 78.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 78.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 78.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.0%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 72.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 70.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 78.8%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in a around inf 52.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 52.9%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 55.4%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   11. Simplified 55.4%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -3.20000000000000026e-4 < t < 4.70000000000000018

   1. Initial program 84.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 80.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -0.00032 \lor \neg \left(t \leq 4.7\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.06 \cdot 10^{+61}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) + \frac{\frac{b}{c\_m} - \left(x \cdot \frac{y}{c\_m}\right) \cdot -9}{z}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.06e+61)
    (/ (+ (* a (* -4.0 t)) (/ (- b (* y (* x -9.0))) z)) c_m)
    (+
     (* -4.0 (* t (/ a c_m)))
     (/ (- (/ b c_m) (* (* x (/ y c_m)) -9.0)) z)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.06e+61) {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / z);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (c_m <= 1.06d+61) then
        tmp = ((a * ((-4.0d0) * t)) + ((b - (y * (x * (-9.0d0)))) / z)) / c_m
    else
        tmp = ((-4.0d0) * (t * (a / c_m))) + (((b / c_m) - ((x * (y / c_m)) * (-9.0d0))) / z)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.06e+61) {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / z);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 1.06e+61:
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m
	else:
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / z)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.06e+61)
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * t)) + Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z)) / c_m);
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) + Float64(Float64(Float64(b / c_m) - Float64(Float64(x * Float64(y / c_m)) * -9.0)) / z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 1.06e+61)
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	else
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.06e+61], N[(N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c$95$m), $MachinePrecision] - N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.0599999999999999e61

   1. Initial program 82.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 82.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.8%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.8%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 86.2%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 93.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around -inf 93.6%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 93.6%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 93.6%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 93.6%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 93.6%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. *-commutative 93.6%

          \[\leadsto \frac{a \cdot \color{blue}{\left(-4 \cdot t\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       6. mul-1-neg 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       7. sub-neg 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       8. *-commutative 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       9. *-commutative 93.6%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(y \cdot x\right)} \cdot -9 - b}{z}}{c} \]

       10. associate-*l* 93.5%

           \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{y \cdot \left(x \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 93.5%

       \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot t\right) - \frac{y \cdot \left(x \cdot -9\right) - b}{z}}}{c} \]

   if 1.0599999999999999e61 < c

   1. Initial program 63.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 67.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 67.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 79.4%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 79.4%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 79.4%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 86.7%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 86.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 79.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 75.5%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in z around -inf 84.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 84.8%

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}\right)} \]

       2. unsub-neg 84.8%

          \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]

       3. *-commutative 84.8%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

       4. associate-/l* 90.4%

          \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

       5. mul-1-neg 90.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{-9 \cdot \frac{x \cdot y}{c} + \color{blue}{\left(-\frac{b}{c}\right)}}{z} \]

       6. unsub-neg 90.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{-9 \cdot \frac{x \cdot y}{c} - \frac{b}{c}}}{z} \]

       7. associate-/l* 88.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{-9 \cdot \color{blue}{\left(x \cdot \frac{y}{c}\right)} - \frac{b}{c}}{z} \]

   11. Simplified 88.6%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{-9 \cdot \left(x \cdot \frac{y}{c}\right) - \frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.06 \cdot 10^{+61}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c} - \left(x \cdot \frac{y}{c}\right) \cdot -9}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -5 \cdot 10^{+175}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= (* x 9.0) -5e+175)
    (* 9.0 (* (/ x c_m) (/ y z)))
    (if (<= (* x 9.0) 5000000000000.0)
      (/ (+ (* -4.0 (* a t)) (/ b z)) c_m)
      (* 9.0 (* x (/ y (* c_m z))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((x * 9.0) <= -5e+175) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m;
	} else {
		tmp = 9.0 * (x * (y / (c_m * z)));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((x * 9.0d0) <= (-5d+175)) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else if ((x * 9.0d0) <= 5000000000000.0d0) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c_m
    else
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((x * 9.0) <= -5e+175) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if ((x * 9.0) <= 5000000000000.0) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m;
	} else {
		tmp = 9.0 * (x * (y / (c_m * z)));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (x * 9.0) <= -5e+175:
		tmp = 9.0 * ((x / c_m) * (y / z))
	elif (x * 9.0) <= 5000000000000.0:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m
	else:
		tmp = 9.0 * (x * (y / (c_m * z)))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (Float64(x * 9.0) <= -5e+175)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	elseif (Float64(x * 9.0) <= 5000000000000.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c_m);
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((x * 9.0) <= -5e+175)
		tmp = 9.0 * ((x / c_m) * (y / z));
	elseif ((x * 9.0) <= 5000000000000.0)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c_m;
	else
		tmp = 9.0 * (x * (y / (c_m * z)));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[N[(x * 9.0), $MachinePrecision], -5e+175], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 9.0), $MachinePrecision], 5000000000000.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 9) < -5e175

   1. Initial program 69.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 72.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 73.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.7%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. times-frac 60.5%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   7. Simplified 60.5%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

   if -5e175 < (*.f64 x 9) < 5e12

   1. Initial program 81.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 82.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 83.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.4%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.4%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.4%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 81.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 79.5%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 79.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 77.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 77.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 84.4%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 88.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in x around 0 75.3%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 43.2%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 44.8%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   7. Applied egg-rr 44.8%

      \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -5 \cdot 10^{+175}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \cdot 9 \leq 5000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.6 \cdot 10^{+272}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y \cdot 9\right)}{c\_m}}{z} - \left(a \cdot \frac{t}{c\_m}\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.6e+272)
    (/ (+ (* a (* -4.0 t)) (/ (- b (* y (* x -9.0))) z)) c_m)
    (- (/ (/ (* x (* y 9.0)) c_m) z) (* (* a (/ t c_m)) 4.0)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.6e+272) {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	} else {
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (c_m <= 1.6d+272) then
        tmp = ((a * ((-4.0d0) * t)) + ((b - (y * (x * (-9.0d0)))) / z)) / c_m
    else
        tmp = (((x * (y * 9.0d0)) / c_m) / z) - ((a * (t / c_m)) * 4.0d0)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.6e+272) {
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	} else {
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 1.6e+272:
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m
	else:
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.6e+272)
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * t)) + Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z)) / c_m);
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(y * 9.0)) / c_m) / z) - Float64(Float64(a * Float64(t / c_m)) * 4.0));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 1.6e+272)
		tmp = ((a * (-4.0 * t)) + ((b - (y * (x * -9.0))) / z)) / c_m;
	else
		tmp = (((x * (y * 9.0)) / c_m) / z) - ((a * (t / c_m)) * 4.0);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.6e+272], N[(N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision] - N[(N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.59999999999999992e272

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.2%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.2%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.2%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 81.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 78.4%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 78.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 79.1%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 85.1%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 90.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in z around -inf 90.8%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 90.8%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 90.8%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 90.8%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 90.8%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. *-commutative 90.8%

          \[\leadsto \frac{a \cdot \color{blue}{\left(-4 \cdot t\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       6. mul-1-neg 90.8%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       7. sub-neg 90.8%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       8. *-commutative 90.8%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       9. *-commutative 90.8%

          \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{\left(y \cdot x\right)} \cdot -9 - b}{z}}{c} \]

       10. associate-*l* 90.8%

           \[\leadsto \frac{a \cdot \left(-4 \cdot t\right) - \frac{\color{blue}{y \cdot \left(x \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 90.8%

       \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot t\right) - \frac{y \cdot \left(x \cdot -9\right) - b}{z}}}{c} \]

   if 1.59999999999999992e272 < c

   1. Initial program 56.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 56.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 56.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 56.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 56.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 56.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 56.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 45.2%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. div-sub 45.2%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

      2. associate-*r/ 45.4%

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      3. frac-times 34.3%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      4. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right) \cdot 9} - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      5. frac-times 45.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z}} \cdot 9 - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      6. associate-/l* 45.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 - \frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z} \]

      7. *-commutative 45.2%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{4 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)}}{c \cdot z} \]

      8. *-commutative 45.2%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{4 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot a\right)}{c \cdot z} \]

      9. associate-*r* 45.2%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{4 \cdot \color{blue}{\left(z \cdot \left(t \cdot a\right)\right)}}{c \cdot z} \]

      10. associate-*r* 45.2%

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{\color{blue}{\left(4 \cdot z\right) \cdot \left(t \cdot a\right)}}{c \cdot z} \]

      11. *-commutative 45.2%

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{\left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}}{c \cdot z} \]

   7. Applied egg-rr 45.2%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \frac{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}{c \cdot z}} \]
   8. Step-by-step derivation

      1. associate-/l* 45.6%

         \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 - \color{blue}{\left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z}} \]

      2. *-commutative 45.6%

         \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      3. associate-*r/ 45.8%

         \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot y}{c \cdot z}} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      4. associate-*r/ 45.6%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      5. associate-/r* 56.4%

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right)}{c}}{z}} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      6. *-commutative 56.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(x \cdot y\right) \cdot 9}}{c}}{z} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      7. associate-*r* 56.4%

         \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(y \cdot 9\right)}}{c}}{z} - \left(4 \cdot z\right) \cdot \frac{a \cdot t}{c \cdot z} \]

      8. *-commutative 56.4%

         \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \color{blue}{\left(z \cdot 4\right)} \cdot \frac{a \cdot t}{c \cdot z} \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \left(z \cdot 4\right) \cdot \frac{a \cdot t}{c \cdot z}} \]

   10. Taylor expanded in z around 0 67.7%

       \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \color{blue}{4 \cdot \frac{a \cdot t}{c}} \]
   11. Step-by-step derivation

       1. associate-*r/ 88.3%

          \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - 4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

   12. Simplified 88.3%

       \[\leadsto \frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \color{blue}{4 \cdot \left(a \cdot \frac{t}{c}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.6 \cdot 10^{+272}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y \cdot 9\right)}{c}}{z} - \left(a \cdot \frac{t}{c}\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 5 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (* c_s (if (<= c_m 5e+60) (/ (/ b z) c_m) (/ (/ b c_m) z))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 5e+60) {
		tmp = (b / z) / c_m;
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (c_m <= 5d+60) then
        tmp = (b / z) / c_m
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 5e+60) {
		tmp = (b / z) / c_m;
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 5e+60:
		tmp = (b / z) / c_m
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 5e+60)
		tmp = Float64(Float64(b / z) / c_m);
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 5e+60)
		tmp = (b / z) / c_m;
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 5e+60], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 4.99999999999999975e60

   1. Initial program 82.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 82.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. fma-define 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      5. associate-/l* 76.8%

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. fma-define 76.8%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      7. times-frac 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \color{blue}{\frac{x}{c} \cdot \frac{y}{z}}, \frac{b}{c \cdot z}\right)\right) \]

      8. associate-/r* 78.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   7. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   8. Taylor expanded in c around 0 86.2%

      \[\leadsto \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}}\right) \]

   9. Taylor expanded in c around 0 93.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}} \]

   10. Taylor expanded in b around inf 37.2%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

   if 4.99999999999999975e60 < c

   1. Initial program 63.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 67.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 67.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 28.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 29.8%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 29.8%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    code = c_s * (b / (c_m * z))
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 79.0%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 81.0%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 81.0%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 34.1%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 34.1%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Alternative 21: 35.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{\frac{b}{c\_m}}{z} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ (/ b c_m) z)))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * ((b / c_m) / z);
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    code = c_s * ((b / c_m) / z)
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * ((b / c_m) / z);
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * ((b / c_m) / z)

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(Float64(b / c_m) / z))
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * ((b / c_m) / z);
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 79.0%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 81.0%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 81.0%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. associate-/r* 34.8%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

7. Simplified 34.8%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

8. Final simplification 34.8%

   \[\leadsto \frac{\frac{b}{c}}{z} \]
9. Add Preprocessing

Developer target: 80.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))