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

Percentage Accurate: 80.0% → 88.3%

Time: 19.1s

Alternatives: 18

Speedup: 0.2×

• 36.8% 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: 80.0% 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: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-84}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c\_m}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, -4 \cdot \left(t \cdot a\right)\right), b\right)}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -1e-84)
      (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* z c_m))
      (if (<= t_1 0.0)
        (*
         (/ 1.0 z)
         (/ (fma z (fma 9.0 (* x (/ y z)) (* -4.0 (* t a))) b) c_m))
        (if (<= t_1 INFINITY)
          (/ (- (+ b (* 9.0 (* x y))) (* 4.0 (* z (* t a)))) (* z c_m))
          (* -4.0 (* a (/ t 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);
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -1e-84) {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (z * c_m);
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / z) * (fma(z, fma(9.0, (x * (y / z)), (-4.0 * (t * a))), b) / c_m);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	} else {
		tmp = -4.0 * (a * (t / 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])
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(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -1e-84)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c_m));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / z) * Float64(fma(z, fma(9.0, Float64(x * Float64(y / z)), Float64(-4.0 * Float64(t * a))), b) / c_m));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) - Float64(4.0 * Float64(z * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	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.
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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e-84], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(z * N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1e-84

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   if -1e-84 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 59.9%

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

      1. associate-+l- 59.9%

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

      2. *-commutative 59.9%

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

      3. associate-*r* 56.7%

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

      4. *-commutative 56.7%

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

      5. associate-+l- 56.7%

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

      6. associate-*l* 56.7%

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

      7. associate-*l* 59.9%

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

      8. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in z around inf 59.8%

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

      1. *-un-lft-identity 59.8%

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

      2. times-frac 95.9%

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

      3. fma-define 96.0%

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

      4. cancel-sign-sub-inv 96.0%

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

      5. fma-define 96.1%

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

      6. associate-/l* 93.0%

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

      7. metadata-eval 93.0%

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

   7. Applied egg-rr 93.0%

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

   if 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.3%

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

   3. Simplified 93.1%

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

      1. associate-*r* 92.1%

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

      2. metadata-eval 92.1%

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

      3. distribute-rgt-neg-in 92.1%

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

      4. distribute-rgt-neg-in 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-neg 92.1%

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

      7. +-commutative 92.1%

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

      8. associate-+r- 92.1%

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

      9. associate-*r* 92.2%

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

      10. *-commutative 92.2%

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

      11. associate-*l* 92.2%

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

      12. *-commutative 92.2%

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

      13. associate-*l* 92.2%

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

   6. Applied egg-rr 92.2%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 18.2%

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

      1. associate-*r* 18.2%

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

      2. metadata-eval 18.2%

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

      3. distribute-rgt-neg-in 18.2%

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

      4. distribute-rgt-neg-in 18.2%

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

      5. *-commutative 18.2%

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

      6. fma-neg 7.3%

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

      7. +-commutative 7.3%

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

      8. associate-+r- 7.3%

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

      9. associate-*r* 3.8%

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

      10. *-commutative 3.8%

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

      11. associate-*l* 7.3%

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

      12. *-commutative 7.3%

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

      13. associate-*l* 7.3%

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

   6. Applied egg-rr 7.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{-84}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, -4 \cdot \left(t \cdot a\right)\right), b\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+95}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c\_m}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -1e+95)
      (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* z c_m))
      (if (<= t_1 0.0)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)))
         z)
        (if (<= t_1 INFINITY)
          (/ (- (+ b (* 9.0 (* x y))) (* 4.0 (* z (* t a)))) (* z c_m))
          (* -4.0 (* a (/ t 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);
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -1e+95) {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (z * c_m);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	} else {
		tmp = -4.0 * (a * (t / 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])
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(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -1e+95)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c_m));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) - Float64(4.0 * Float64(z * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	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.
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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e+95], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000002e95

   1. Initial program 87.6%

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

   3. Simplified 88.8%

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

   if -1.00000000000000002e95 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 74.7%

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

      1. associate-+l- 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*r* 70.7%

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

      4. *-commutative 70.7%

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

      5. associate-+l- 70.7%

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

      6. associate-*l* 70.7%

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

      7. associate-*l* 74.6%

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

      8. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in z around 0 97.3%

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

   if 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.3%

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

   3. Simplified 93.1%

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

      1. associate-*r* 92.1%

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

      2. metadata-eval 92.1%

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

      3. distribute-rgt-neg-in 92.1%

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

      4. distribute-rgt-neg-in 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-neg 92.1%

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

      7. +-commutative 92.1%

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

      8. associate-+r- 92.1%

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

      9. associate-*r* 92.2%

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

      10. *-commutative 92.2%

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

      11. associate-*l* 92.2%

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

      12. *-commutative 92.2%

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

      13. associate-*l* 92.2%

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

   6. Applied egg-rr 92.2%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 18.2%

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

      1. associate-*r* 18.2%

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

      2. metadata-eval 18.2%

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

      3. distribute-rgt-neg-in 18.2%

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

      4. distribute-rgt-neg-in 18.2%

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

      5. *-commutative 18.2%

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

      6. fma-neg 7.3%

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

      7. +-commutative 7.3%

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

      8. associate-+r- 7.3%

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

      9. associate-*r* 3.8%

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

      10. *-commutative 3.8%

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

      11. associate-*l* 7.3%

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

      12. *-commutative 7.3%

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

      13. associate-*l* 7.3%

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

   6. Applied egg-rr 7.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{+95}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ t_2 := \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m)))
        (t_2 (/ (- (+ b (* 9.0 (* x y))) (* 4.0 (* z (* t a)))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -1e+95)
      t_2
      (if (<= t_1 0.0)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)))
         z)
        (if (<= t_1 INFINITY) t_2 (* -4.0 (* a (/ t 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);
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	double tmp;
	if (t_1 <= -1e+95) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / c_m));
	}
	return c_s * tmp;
}

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;
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	double tmp;
	if (t_1 <= -1e+95) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / 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])
[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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m)
	tmp = 0
	if t_1 <= -1e+95:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = -4.0 * (a * (t / 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])
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(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	t_2 = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) - Float64(4.0 * Float64(z * Float64(t * a)))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -1e+95)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m))) / z);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / 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])){:}
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -1e+95)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = -4.0 * (a * (t / 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.
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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e+95], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000002e95 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 88.5%

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

   3. Simplified 91.2%

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

      1. associate-*r* 90.6%

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

      2. metadata-eval 90.6%

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

      3. distribute-rgt-neg-in 90.6%

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

      4. distribute-rgt-neg-in 90.6%

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

      5. *-commutative 90.6%

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

      6. fma-neg 90.6%

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

      7. +-commutative 90.6%

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

      8. associate-+r- 90.6%

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

      9. associate-*r* 90.7%

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

      10. *-commutative 90.7%

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

      11. associate-*l* 90.7%

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

      12. *-commutative 90.7%

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

      13. associate-*l* 90.7%

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

   6. Applied egg-rr 90.7%

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

   if -1.00000000000000002e95 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 74.7%

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

      1. associate-+l- 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*r* 70.7%

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

      4. *-commutative 70.7%

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

      5. associate-+l- 70.7%

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

      6. associate-*l* 70.7%

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

      7. associate-*l* 74.6%

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

      8. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in z around 0 97.3%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 18.2%

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

      1. associate-*r* 18.2%

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

      2. metadata-eval 18.2%

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

      3. distribute-rgt-neg-in 18.2%

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

      4. distribute-rgt-neg-in 18.2%

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

      5. *-commutative 18.2%

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

      6. fma-neg 7.3%

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

      7. +-commutative 7.3%

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

      8. associate-+r- 7.3%

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

      9. associate-*r* 3.8%

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

      10. *-commutative 3.8%

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

      11. associate-*l* 7.3%

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

      12. *-commutative 7.3%

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

      13. associate-*l* 7.3%

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

   6. Applied egg-rr 7.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{+95}:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ t_3 := \frac{\left(b + t\_1\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-202}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(t\_1 + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)\right)}{c\_m}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 y)))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m)))
        (t_3 (/ (- (+ b t_1) (* 4.0 (* z (* t a)))) (* z c_m))))
   (*
    c_s
    (if (<= t_2 -5e-202)
      t_3
      (if (<= t_2 0.0)
        (* (/ 1.0 z) (/ (+ b (+ t_1 (* -4.0 (* a (* z t))))) c_m))
        (if (<= t_2 INFINITY) t_3 (* -4.0 (* a (/ t 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);
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 * y);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_3 = ((b + t_1) - (4.0 * (z * (t * a)))) / (z * c_m);
	double tmp;
	if (t_2 <= -5e-202) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (1.0 / z) * ((b + (t_1 + (-4.0 * (a * (z * t))))) / c_m);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = -4.0 * (a * (t / c_m));
	}
	return c_s * tmp;
}

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;
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 * y);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_3 = ((b + t_1) - (4.0 * (z * (t * a)))) / (z * c_m);
	double tmp;
	if (t_2 <= -5e-202) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (1.0 / z) * ((b + (t_1 + (-4.0 * (a * (z * t))))) / c_m);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = -4.0 * (a * (t / 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])
[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 * y)
	t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	t_3 = ((b + t_1) - (4.0 * (z * (t * a)))) / (z * c_m)
	tmp = 0
	if t_2 <= -5e-202:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = (1.0 / z) * ((b + (t_1 + (-4.0 * (a * (z * t))))) / c_m)
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = -4.0 * (a * (t / 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])
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(x * y))
	t_2 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	t_3 = Float64(Float64(Float64(b + t_1) - Float64(4.0 * Float64(z * Float64(t * a)))) / Float64(z * c_m))
	tmp = 0.0
	if (t_2 <= -5e-202)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(t_1 + Float64(-4.0 * Float64(a * Float64(z * t))))) / c_m));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / 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])){:}
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 * y);
	t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	t_3 = ((b + t_1) - (4.0 * (z * (t * a)))) / (z * c_m);
	tmp = 0.0;
	if (t_2 <= -5e-202)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = (1.0 / z) * ((b + (t_1 + (-4.0 * (a * (z * t))))) / c_m);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = -4.0 * (a * (t / 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.
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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b + t$95$1), $MachinePrecision] - N[(4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -5e-202], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(t$95$1 + N[(-4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.99999999999999973e-202 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.8%

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

   3. Simplified 91.6%

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

      1. associate-*r* 91.6%

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

      2. metadata-eval 91.6%

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

      3. distribute-rgt-neg-in 91.6%

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

      4. distribute-rgt-neg-in 91.6%

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

      5. *-commutative 91.6%

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

      6. fma-neg 91.6%

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

      7. +-commutative 91.6%

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

      8. associate-+r- 91.6%

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

      9. associate-*r* 91.7%

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

      10. *-commutative 91.7%

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

      11. associate-*l* 91.7%

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

      12. *-commutative 91.7%

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

      13. associate-*l* 91.7%

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

   6. Applied egg-rr 91.7%

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

   if -4.99999999999999973e-202 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 51.8%

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

      1. associate-+l- 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 48.1%

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

      4. *-commutative 48.1%

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

      5. associate-+l- 48.1%

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

      6. associate-*l* 48.1%

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

      7. associate-*l* 51.8%

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

      8. *-commutative 51.8%

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

   3. Simplified 51.8%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. *-un-lft-identity 51.8%

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

      2. times-frac 95.2%

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

      3. fma-define 95.3%

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

      4. cancel-sign-sub-inv 95.3%

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

      5. fma-define 95.3%

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

      6. associate-/l* 91.7%

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

      7. metadata-eval 91.7%

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

   7. Applied egg-rr 91.7%

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

   8. Taylor expanded in z around 0 95.3%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 18.2%

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

      1. associate-*r* 18.2%

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

      2. metadata-eval 18.2%

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

      3. distribute-rgt-neg-in 18.2%

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

      4. distribute-rgt-neg-in 18.2%

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

      5. *-commutative 18.2%

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

      6. fma-neg 7.3%

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

      7. +-commutative 7.3%

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

      8. associate-+r- 7.3%

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

      9. associate-*r* 3.8%

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

      10. *-commutative 3.8%

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

      11. associate-*l* 7.3%

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

      12. *-commutative 7.3%

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

      13. associate-*l* 7.3%

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

   6. Applied egg-rr 7.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-202}:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(9 \cdot \left(x \cdot y\right) + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ t_2 := \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m)))
        (t_2 (/ (- (+ b (* 9.0 (* x y))) (* 4.0 (* z (* t a)))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -5e-202)
      t_2
      (if (<= t_1 0.0)
        (/ (- (* 9.0 (/ (* x y) z)) (* 4.0 (* t a))) c_m)
        (if (<= t_1 INFINITY) t_2 (* -4.0 (* a (/ t 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);
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-202) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / c_m));
	}
	return c_s * tmp;
}

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;
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-202) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / 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])
[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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m)
	tmp = 0
	if t_1 <= -5e-202:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = -4.0 * (a * (t / 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])
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(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	t_2 = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) - Float64(4.0 * Float64(z * Float64(t * a)))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -5e-202)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(4.0 * Float64(t * a))) / c_m);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / 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])){:}
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	t_2 = ((b + (9.0 * (x * y))) - (4.0 * (z * (t * a)))) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -5e-202)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = -4.0 * (a * (t / 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.
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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-202], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.99999999999999973e-202 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.8%

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

   3. Simplified 91.6%

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

      1. associate-*r* 91.6%

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

      2. metadata-eval 91.6%

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

      3. distribute-rgt-neg-in 91.6%

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

      4. distribute-rgt-neg-in 91.6%

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

      5. *-commutative 91.6%

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

      6. fma-neg 91.6%

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

      7. +-commutative 91.6%

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

      8. associate-+r- 91.6%

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

      9. associate-*r* 91.7%

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

      10. *-commutative 91.7%

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

      11. associate-*l* 91.7%

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

      12. *-commutative 91.7%

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

      13. associate-*l* 91.7%

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

   6. Applied egg-rr 91.7%

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

   if -4.99999999999999973e-202 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 51.8%

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

      1. associate-+l- 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 48.1%

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

      4. *-commutative 48.1%

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

      5. associate-+l- 48.1%

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

      6. associate-*l* 48.1%

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

      7. associate-*l* 51.8%

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

      8. *-commutative 51.8%

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

   3. Simplified 51.8%

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

   5. Taylor expanded in z around inf 51.8%

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

   6. Taylor expanded in b around 0 84.1%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 18.2%

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

      1. associate-*r* 18.2%

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

      2. metadata-eval 18.2%

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

      3. distribute-rgt-neg-in 18.2%

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

      4. distribute-rgt-neg-in 18.2%

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

      5. *-commutative 18.2%

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

      6. fma-neg 7.3%

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

      7. +-commutative 7.3%

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

      8. associate-+r- 7.3%

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

      9. associate-*r* 3.8%

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

      10. *-commutative 3.8%

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

      11. associate-*l* 7.3%

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

      12. *-commutative 7.3%

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

      13. associate-*l* 7.3%

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

   6. Applied egg-rr 7.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-202}:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m)))
        (t_2 (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -5e-202)
      t_2
      (if (<= t_1 0.0)
        (/ (- (* 9.0 (/ (* x y) z)) (* 4.0 (* t a))) c_m)
        (if (<= t_1 INFINITY) t_2 (* -4.0 (* a (/ t 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);
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-202) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / c_m));
	}
	return c_s * tmp;
}

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;
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-202) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / 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])
[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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m)
	tmp = 0
	if t_1 <= -5e-202:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = -4.0 * (a * (t / 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])
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(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	t_2 = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -5e-202)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(4.0 * Float64(t * a))) / c_m);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / 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])){:}
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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -5e-202)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = -4.0 * (a * (t / 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.
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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-202], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.99999999999999973e-202 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.8%

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

      1. associate-+l- 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

      6. associate-*l* 91.6%

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

      7. associate-*l* 91.6%

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

      8. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   if -4.99999999999999973e-202 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 51.8%

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

      1. associate-+l- 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 48.1%

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

      4. *-commutative 48.1%

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

      5. associate-+l- 48.1%

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

      6. associate-*l* 48.1%

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

      7. associate-*l* 51.8%

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

      8. *-commutative 51.8%

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

   3. Simplified 51.8%

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

   5. Taylor expanded in z around inf 51.8%

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

   6. Taylor expanded in b around 0 84.1%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 18.2%

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

      1. associate-*r* 18.2%

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

      2. metadata-eval 18.2%

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

      3. distribute-rgt-neg-in 18.2%

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

      4. distribute-rgt-neg-in 18.2%

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

      5. *-commutative 18.2%

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

      6. fma-neg 7.3%

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

      7. +-commutative 7.3%

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

      8. associate-+r- 7.3%

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

      9. associate-*r* 3.8%

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

      10. *-commutative 3.8%

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

      11. associate-*l* 7.3%

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

      12. *-commutative 7.3%

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

      13. associate-*l* 7.3%

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

   6. Applied egg-rr 7.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-202}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c\_m}\\ t_2 := t \cdot \left(-4 \cdot \frac{a}{c\_m} + \frac{b}{c\_m \cdot \left(z \cdot t\right)}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-60}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 y) z)) (* 4.0 (* t a))) c_m))
        (t_2 (* t (+ (* -4.0 (/ a c_m)) (/ b (* c_m (* z t)))))))
   (*
    c_s
    (if (<= t -2e+178)
      t_2
      (if (<= t -8.8e+47)
        t_1
        (if (<= t -7.2e-72)
          t_2
          (if (<= t 3.9e-60) (/ (+ b (* x (* 9.0 y))) (* z c_m)) 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);
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 * y) / z)) - (4.0 * (t * a))) / c_m;
	double t_2 = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))));
	double tmp;
	if (t <= -2e+178) {
		tmp = t_2;
	} else if (t <= -8.8e+47) {
		tmp = t_1;
	} else if (t <= -7.2e-72) {
		tmp = t_2;
	} else if (t <= 3.9e-60) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} 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.
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 = ((9.0d0 * ((x * y) / z)) - (4.0d0 * (t * a))) / c_m
    t_2 = t * (((-4.0d0) * (a / c_m)) + (b / (c_m * (z * t))))
    if (t <= (-2d+178)) then
        tmp = t_2
    else if (t <= (-8.8d+47)) then
        tmp = t_1
    else if (t <= (-7.2d-72)) then
        tmp = t_2
    else if (t <= 3.9d-60) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    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;
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 * y) / z)) - (4.0 * (t * a))) / c_m;
	double t_2 = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))));
	double tmp;
	if (t <= -2e+178) {
		tmp = t_2;
	} else if (t <= -8.8e+47) {
		tmp = t_1;
	} else if (t <= -7.2e-72) {
		tmp = t_2;
	} else if (t <= 3.9e-60) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} 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])
[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 * y) / z)) - (4.0 * (t * a))) / c_m
	t_2 = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))))
	tmp = 0
	if t <= -2e+178:
		tmp = t_2
	elif t <= -8.8e+47:
		tmp = t_1
	elif t <= -7.2e-72:
		tmp = t_2
	elif t <= 3.9e-60:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	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])
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(9.0 * Float64(Float64(x * y) / z)) - Float64(4.0 * Float64(t * a))) / c_m)
	t_2 = Float64(t * Float64(Float64(-4.0 * Float64(a / c_m)) + Float64(b / Float64(c_m * Float64(z * t)))))
	tmp = 0.0
	if (t <= -2e+178)
		tmp = t_2;
	elseif (t <= -8.8e+47)
		tmp = t_1;
	elseif (t <= -7.2e-72)
		tmp = t_2;
	elseif (t <= 3.9e-60)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	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])){:}
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 * y) / z)) - (4.0 * (t * a))) / c_m;
	t_2 = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))));
	tmp = 0.0;
	if (t <= -2e+178)
		tmp = t_2;
	elseif (t <= -8.8e+47)
		tmp = t_1;
	elseif (t <= -7.2e-72)
		tmp = t_2;
	elseif (t <= 3.9e-60)
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	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.
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[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t, -2e+178], t$95$2, If[LessEqual[t, -8.8e+47], t$95$1, If[LessEqual[t, -7.2e-72], t$95$2, If[LessEqual[t, 3.9e-60], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000001e178 or -8.7999999999999997e47 < t < -7.2e-72

   1. Initial program 63.2%

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

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. associate-*l* 68.1%

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

      7. associate-*l* 64.9%

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

      8. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in z around 0 70.0%

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

   6. Taylor expanded in x around 0 64.0%

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

   7. Taylor expanded in t around inf 79.7%

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

   if -2.0000000000000001e178 < t < -8.7999999999999997e47 or 3.9000000000000002e-60 < t

   1. Initial program 68.9%

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

      1. associate-+l- 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*r* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-+l- 74.3%

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

      6. associate-*l* 74.3%

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

      7. associate-*l* 74.2%

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

      8. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in z around inf 73.0%

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

   6. Taylor expanded in b around 0 75.4%

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

   if -7.2e-72 < t < 3.9000000000000002e-60

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 87.3%

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

      4. *-commutative 87.3%

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

      5. associate-+l- 87.3%

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

      6. associate-*l* 87.3%

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

      7. associate-*l* 90.0%

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

      8. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in x around inf 81.1%

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

      1. associate-*r* 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*r* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+178}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-60}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := b \cdot \frac{\frac{1}{c\_m}}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} \cdot \frac{9}{c\_m}\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c\_m}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ (/ 1.0 c_m) z))))
   (*
    c_s
    (if (<= x -3.4e+187)
      (* x (* (/ y z) (/ 9.0 c_m)))
      (if (<= x -1.15e-5)
        (* -4.0 (/ (* t a) c_m))
        (if (<= x -1.05e-144)
          t_1
          (if (<= x -7.5e-248)
            (* t (/ (* a -4.0) c_m))
            (if (<= x 1.15e-124) t_1 (* 9.0 (* x (/ y (* 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);
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 * ((1.0 / c_m) / z);
	double tmp;
	if (x <= -3.4e+187) {
		tmp = x * ((y / z) * (9.0 / c_m));
	} else if (x <= -1.15e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -1.05e-144) {
		tmp = t_1;
	} else if (x <= -7.5e-248) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 1.15e-124) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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.
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 = b * ((1.0d0 / c_m) / z)
    if (x <= (-3.4d+187)) then
        tmp = x * ((y / z) * (9.0d0 / c_m))
    else if (x <= (-1.15d-5)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (x <= (-1.05d-144)) then
        tmp = t_1
    else if (x <= (-7.5d-248)) then
        tmp = t * ((a * (-4.0d0)) / c_m)
    else if (x <= 1.15d-124) then
        tmp = t_1
    else
        tmp = 9.0d0 * (x * (y / (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;
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 * ((1.0 / c_m) / z);
	double tmp;
	if (x <= -3.4e+187) {
		tmp = x * ((y / z) * (9.0 / c_m));
	} else if (x <= -1.15e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -1.05e-144) {
		tmp = t_1;
	} else if (x <= -7.5e-248) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 1.15e-124) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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])
[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 * ((1.0 / c_m) / z)
	tmp = 0
	if x <= -3.4e+187:
		tmp = x * ((y / z) * (9.0 / c_m))
	elif x <= -1.15e-5:
		tmp = -4.0 * ((t * a) / c_m)
	elif x <= -1.05e-144:
		tmp = t_1
	elif x <= -7.5e-248:
		tmp = t * ((a * -4.0) / c_m)
	elif x <= 1.15e-124:
		tmp = t_1
	else:
		tmp = 9.0 * (x * (y / (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])
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(b * Float64(Float64(1.0 / c_m) / z))
	tmp = 0.0
	if (x <= -3.4e+187)
		tmp = Float64(x * Float64(Float64(y / z) * Float64(9.0 / c_m)));
	elseif (x <= -1.15e-5)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (x <= -1.05e-144)
		tmp = t_1;
	elseif (x <= -7.5e-248)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c_m));
	elseif (x <= 1.15e-124)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(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])){:}
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 * ((1.0 / c_m) / z);
	tmp = 0.0;
	if (x <= -3.4e+187)
		tmp = x * ((y / z) * (9.0 / c_m));
	elseif (x <= -1.15e-5)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (x <= -1.05e-144)
		tmp = t_1;
	elseif (x <= -7.5e-248)
		tmp = t * ((a * -4.0) / c_m);
	elseif (x <= 1.15e-124)
		tmp = t_1;
	else
		tmp = 9.0 * (x * (y / (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.
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[(b * N[(N[(1.0 / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -3.4e+187], N[(x * N[(N[(y / z), $MachinePrecision] * N[(9.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-5], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e-144], t$95$1, If[LessEqual[x, -7.5e-248], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-124], t$95$1, N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if x < -3.4e187

   1. Initial program 61.3%

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

      1. associate-+l- 61.3%

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

      2. *-commutative 61.3%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.4%

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

      7. associate-*l* 64.4%

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

      8. *-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/l* 63.6%

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

      3. associate-*l* 63.6%

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

      4. *-commutative 63.6%

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

      5. associate-*r/ 63.7%

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

      6. *-commutative 63.7%

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

      7. *-commutative 63.7%

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

      8. times-frac 61.3%

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

   7. Simplified 61.3%

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

   if -3.4e187 < x < -1.15e-5

   1. Initial program 66.5%

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

      1. associate-+l- 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-+l- 69.2%

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

      6. associate-*l* 69.2%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -1.15e-5 < x < -1.0500000000000001e-144 or -7.4999999999999994e-248 < x < 1.15000000000000006e-124

   1. Initial program 85.9%

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

   3. Simplified 85.9%

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

      1. associate-*r* 86.0%

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

      2. metadata-eval 86.0%

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

      3. distribute-rgt-neg-in 86.0%

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

      4. distribute-rgt-neg-in 86.0%

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

      5. *-commutative 86.0%

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

      6. fma-neg 86.0%

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

      7. +-commutative 86.0%

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

      8. associate-+r- 86.0%

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

      9. associate-*r* 86.0%

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

      10. *-commutative 86.0%

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

      11. associate-*l* 86.0%

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

      12. *-commutative 86.0%

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

      13. associate-*l* 86.0%

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

   6. Applied egg-rr 86.0%

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

   7. Taylor expanded in b around inf 53.2%

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

      1. associate-/r* 47.7%

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

   9. Simplified 47.7%

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

       1. div-inv 47.7%

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

       2. *-un-lft-identity 47.7%

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

       3. times-frac 53.3%

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

   11. Applied egg-rr 53.3%

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

   if -1.0500000000000001e-144 < x < -7.4999999999999994e-248

   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* 69.3%

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

      4. *-commutative 69.3%

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

      5. associate-+l- 69.3%

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

      6. associate-*l* 69.0%

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

      7. associate-*l* 73.9%

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

      8. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 74.3%

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

      1. *-un-lft-identity 74.3%

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

      2. times-frac 73.9%

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

      3. fma-define 73.9%

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

      4. cancel-sign-sub-inv 73.9%

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

      5. fma-define 73.9%

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

      6. associate-/l* 73.9%

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

      7. metadata-eval 73.9%

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

   7. Applied egg-rr 73.9%

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

   8. Taylor expanded in z around inf 59.0%

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

      1. associate-*r/ 59.0%

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

      2. associate-*r* 59.0%

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

      3. *-commutative 59.0%

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

      4. associate-*r/ 63.9%

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

   10. Simplified 63.9%

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

   if 1.15000000000000006e-124 < x

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 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* 80.9%

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

      7. associate-*l* 82.0%

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

      8. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 39.0%

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

      1. associate-/l* 42.2%

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

      2. *-commutative 42.2%

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

   7. Simplified 42.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} \cdot \frac{9}{c\_m}\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c\_m}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (* z c_m))))
   (*
    c_s
    (if (<= x -9.5e+187)
      (* x (* (/ y z) (/ 9.0 c_m)))
      (if (<= x -8e-5)
        (* -4.0 (/ (* t a) c_m))
        (if (<= x -4.8e-147)
          t_1
          (if (<= x -9.5e-248)
            (* t (/ (* a -4.0) c_m))
            (if (<= x 4.2e-122) t_1 (* 9.0 (* x (/ y (* 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);
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 / (z * c_m);
	double tmp;
	if (x <= -9.5e+187) {
		tmp = x * ((y / z) * (9.0 / c_m));
	} else if (x <= -8e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -4.8e-147) {
		tmp = t_1;
	} else if (x <= -9.5e-248) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 4.2e-122) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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.
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 = b / (z * c_m)
    if (x <= (-9.5d+187)) then
        tmp = x * ((y / z) * (9.0d0 / c_m))
    else if (x <= (-8d-5)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (x <= (-4.8d-147)) then
        tmp = t_1
    else if (x <= (-9.5d-248)) then
        tmp = t * ((a * (-4.0d0)) / c_m)
    else if (x <= 4.2d-122) then
        tmp = t_1
    else
        tmp = 9.0d0 * (x * (y / (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;
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 / (z * c_m);
	double tmp;
	if (x <= -9.5e+187) {
		tmp = x * ((y / z) * (9.0 / c_m));
	} else if (x <= -8e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -4.8e-147) {
		tmp = t_1;
	} else if (x <= -9.5e-248) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 4.2e-122) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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])
[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 / (z * c_m)
	tmp = 0
	if x <= -9.5e+187:
		tmp = x * ((y / z) * (9.0 / c_m))
	elif x <= -8e-5:
		tmp = -4.0 * ((t * a) / c_m)
	elif x <= -4.8e-147:
		tmp = t_1
	elif x <= -9.5e-248:
		tmp = t * ((a * -4.0) / c_m)
	elif x <= 4.2e-122:
		tmp = t_1
	else:
		tmp = 9.0 * (x * (y / (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])
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(b / Float64(z * c_m))
	tmp = 0.0
	if (x <= -9.5e+187)
		tmp = Float64(x * Float64(Float64(y / z) * Float64(9.0 / c_m)));
	elseif (x <= -8e-5)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (x <= -4.8e-147)
		tmp = t_1;
	elseif (x <= -9.5e-248)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c_m));
	elseif (x <= 4.2e-122)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(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])){:}
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 / (z * c_m);
	tmp = 0.0;
	if (x <= -9.5e+187)
		tmp = x * ((y / z) * (9.0 / c_m));
	elseif (x <= -8e-5)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (x <= -4.8e-147)
		tmp = t_1;
	elseif (x <= -9.5e-248)
		tmp = t * ((a * -4.0) / c_m);
	elseif (x <= 4.2e-122)
		tmp = t_1;
	else
		tmp = 9.0 * (x * (y / (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.
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[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -9.5e+187], N[(x * N[(N[(y / z), $MachinePrecision] * N[(9.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-5], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-147], t$95$1, If[LessEqual[x, -9.5e-248], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-122], t$95$1, N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if x < -9.4999999999999996e187

   1. Initial program 61.3%

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

      1. associate-+l- 61.3%

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

      2. *-commutative 61.3%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.4%

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

      7. associate-*l* 64.4%

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

      8. *-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/l* 63.6%

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

      3. associate-*l* 63.6%

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

      4. *-commutative 63.6%

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

      5. associate-*r/ 63.7%

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

      6. *-commutative 63.7%

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

      7. *-commutative 63.7%

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

      8. times-frac 61.3%

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

   7. Simplified 61.3%

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

   if -9.4999999999999996e187 < x < -8.00000000000000065e-5

   1. Initial program 66.5%

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

      1. associate-+l- 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-+l- 69.2%

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

      6. associate-*l* 69.2%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -8.00000000000000065e-5 < x < -4.79999999999999997e-147 or -9.49999999999999971e-248 < x < 4.19999999999999985e-122

   1. Initial program 86.1%

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

      1. associate-+l- 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in b around inf 52.6%

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

      1. *-commutative 52.6%

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

   7. Simplified 52.6%

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

   if -4.79999999999999997e-147 < x < -9.49999999999999971e-248

   1. Initial program 67.8%

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

      1. associate-+l- 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 67.7%

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

      4. *-commutative 67.7%

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

      5. associate-+l- 67.7%

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

      6. associate-*l* 67.3%

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

      7. associate-*l* 72.5%

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

      8. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in z around inf 73.0%

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

      1. *-un-lft-identity 73.0%

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

      2. times-frac 72.5%

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

      3. fma-define 72.5%

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

      4. cancel-sign-sub-inv 72.5%

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

      5. fma-define 72.5%

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

      6. associate-/l* 72.5%

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

      7. metadata-eval 72.5%

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

   7. Applied egg-rr 72.5%

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

   8. Taylor expanded in z around inf 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*r* 56.8%

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

      3. *-commutative 56.8%

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

      4. associate-*r/ 61.9%

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

   10. Simplified 61.9%

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

   if 4.19999999999999985e-122 < x

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 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* 80.9%

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

      7. associate-*l* 82.0%

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

      8. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 39.0%

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

      1. associate-/l* 42.2%

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

      2. *-commutative 42.2%

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

   7. Simplified 42.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-147}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c\_m}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (* z c_m))))
   (*
    c_s
    (if (<= x -2.7e+187)
      (* x (* (/ y c_m) (/ 9.0 z)))
      (if (<= x -6.5e-5)
        (* -4.0 (/ (* t a) c_m))
        (if (<= x -6.5e-151)
          t_1
          (if (<= x -1.4e-246)
            (* t (/ (* a -4.0) c_m))
            (if (<= x 2.3e-122) t_1 (* 9.0 (* x (/ y (* 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);
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 / (z * c_m);
	double tmp;
	if (x <= -2.7e+187) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (x <= -6.5e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -6.5e-151) {
		tmp = t_1;
	} else if (x <= -1.4e-246) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 2.3e-122) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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.
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 = b / (z * c_m)
    if (x <= (-2.7d+187)) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else if (x <= (-6.5d-5)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (x <= (-6.5d-151)) then
        tmp = t_1
    else if (x <= (-1.4d-246)) then
        tmp = t * ((a * (-4.0d0)) / c_m)
    else if (x <= 2.3d-122) then
        tmp = t_1
    else
        tmp = 9.0d0 * (x * (y / (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;
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 / (z * c_m);
	double tmp;
	if (x <= -2.7e+187) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (x <= -6.5e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -6.5e-151) {
		tmp = t_1;
	} else if (x <= -1.4e-246) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 2.3e-122) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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])
[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 / (z * c_m)
	tmp = 0
	if x <= -2.7e+187:
		tmp = x * ((y / c_m) * (9.0 / z))
	elif x <= -6.5e-5:
		tmp = -4.0 * ((t * a) / c_m)
	elif x <= -6.5e-151:
		tmp = t_1
	elif x <= -1.4e-246:
		tmp = t * ((a * -4.0) / c_m)
	elif x <= 2.3e-122:
		tmp = t_1
	else:
		tmp = 9.0 * (x * (y / (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])
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(b / Float64(z * c_m))
	tmp = 0.0
	if (x <= -2.7e+187)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	elseif (x <= -6.5e-5)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (x <= -6.5e-151)
		tmp = t_1;
	elseif (x <= -1.4e-246)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c_m));
	elseif (x <= 2.3e-122)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(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])){:}
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 / (z * c_m);
	tmp = 0.0;
	if (x <= -2.7e+187)
		tmp = x * ((y / c_m) * (9.0 / z));
	elseif (x <= -6.5e-5)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (x <= -6.5e-151)
		tmp = t_1;
	elseif (x <= -1.4e-246)
		tmp = t * ((a * -4.0) / c_m);
	elseif (x <= 2.3e-122)
		tmp = t_1;
	else
		tmp = 9.0 * (x * (y / (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.
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[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -2.7e+187], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-5], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-151], t$95$1, If[LessEqual[x, -1.4e-246], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-122], t$95$1, N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if x < -2.70000000000000008e187

   1. Initial program 61.3%

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

   3. Simplified 64.4%

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

      1. associate-*r* 64.4%

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

      2. metadata-eval 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

      4. distribute-rgt-neg-in 64.4%

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

      5. *-commutative 64.4%

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

      6. fma-neg 64.4%

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

      7. +-commutative 64.4%

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

      8. associate-+r- 64.4%

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

      9. associate-*r* 64.5%

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

      10. *-commutative 64.5%

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

      11. associate-*l* 64.4%

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

      12. *-commutative 64.4%

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

      13. associate-*l* 64.4%

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

   6. Applied egg-rr 64.4%

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

   7. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/l* 63.6%

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

      3. associate-*r* 63.6%

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

      4. *-commutative 63.6%

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

      5. associate-*r/ 63.7%

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

      6. *-commutative 63.7%

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

      7. times-frac 64.4%

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

   9. Simplified 64.4%

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

   if -2.70000000000000008e187 < x < -6.49999999999999943e-5

   1. Initial program 66.5%

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

      1. associate-+l- 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-+l- 69.2%

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

      6. associate-*l* 69.2%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -6.49999999999999943e-5 < x < -6.4999999999999994e-151 or -1.4e-246 < x < 2.30000000000000007e-122

   1. Initial program 86.2%

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

      1. associate-+l- 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*r* 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-+l- 86.3%

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

      6. associate-*l* 86.2%

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

      7. associate-*l* 86.3%

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

      8. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -6.4999999999999994e-151 < x < -1.4e-246

   1. Initial program 65.9%

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

      1. associate-+l- 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-*r* 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-+l- 65.8%

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

      6. associate-*l* 65.4%

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

      7. associate-*l* 71.0%

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

      8. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. *-un-lft-identity 71.5%

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

      2. times-frac 76.6%

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

      3. fma-define 76.6%

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

      4. cancel-sign-sub-inv 76.6%

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

      5. fma-define 76.6%

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

      6. associate-/l* 76.6%

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

      7. metadata-eval 76.6%

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

   7. Applied egg-rr 76.6%

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

   8. Taylor expanded in z around inf 54.3%

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

      1. associate-*r/ 54.3%

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

      2. associate-*r* 54.3%

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

      3. *-commutative 54.3%

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

      4. associate-*r/ 59.6%

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

   10. Simplified 59.6%

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

   if 2.30000000000000007e-122 < x

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 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* 80.9%

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

      7. associate-*l* 82.0%

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

      8. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 39.0%

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

      1. associate-/l* 42.2%

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

      2. *-commutative 42.2%

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

   7. Simplified 42.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+187}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \mathbf{elif}\;x \leq -2.62 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c\_m}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (* z c_m))))
   (*
    c_s
    (if (<= x -2.5e+187)
      (* 9.0 (* x (/ (/ y c_m) z)))
      (if (<= x -2.62e-5)
        (* -4.0 (/ (* t a) c_m))
        (if (<= x -5.8e-150)
          t_1
          (if (<= x -2.1e-245)
            (* t (/ (* a -4.0) c_m))
            (if (<= x 4.2e-122) t_1 (* 9.0 (* x (/ y (* 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);
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 / (z * c_m);
	double tmp;
	if (x <= -2.5e+187) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else if (x <= -2.62e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -5.8e-150) {
		tmp = t_1;
	} else if (x <= -2.1e-245) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 4.2e-122) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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.
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 = b / (z * c_m)
    if (x <= (-2.5d+187)) then
        tmp = 9.0d0 * (x * ((y / c_m) / z))
    else if (x <= (-2.62d-5)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (x <= (-5.8d-150)) then
        tmp = t_1
    else if (x <= (-2.1d-245)) then
        tmp = t * ((a * (-4.0d0)) / c_m)
    else if (x <= 4.2d-122) then
        tmp = t_1
    else
        tmp = 9.0d0 * (x * (y / (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;
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 / (z * c_m);
	double tmp;
	if (x <= -2.5e+187) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else if (x <= -2.62e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -5.8e-150) {
		tmp = t_1;
	} else if (x <= -2.1e-245) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 4.2e-122) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (x * (y / (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])
[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 / (z * c_m)
	tmp = 0
	if x <= -2.5e+187:
		tmp = 9.0 * (x * ((y / c_m) / z))
	elif x <= -2.62e-5:
		tmp = -4.0 * ((t * a) / c_m)
	elif x <= -5.8e-150:
		tmp = t_1
	elif x <= -2.1e-245:
		tmp = t * ((a * -4.0) / c_m)
	elif x <= 4.2e-122:
		tmp = t_1
	else:
		tmp = 9.0 * (x * (y / (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])
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(b / Float64(z * c_m))
	tmp = 0.0
	if (x <= -2.5e+187)
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c_m) / z)));
	elseif (x <= -2.62e-5)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (x <= -5.8e-150)
		tmp = t_1;
	elseif (x <= -2.1e-245)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c_m));
	elseif (x <= 4.2e-122)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(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])){:}
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 / (z * c_m);
	tmp = 0.0;
	if (x <= -2.5e+187)
		tmp = 9.0 * (x * ((y / c_m) / z));
	elseif (x <= -2.62e-5)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (x <= -5.8e-150)
		tmp = t_1;
	elseif (x <= -2.1e-245)
		tmp = t * ((a * -4.0) / c_m);
	elseif (x <= 4.2e-122)
		tmp = t_1;
	else
		tmp = 9.0 * (x * (y / (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.
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[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -2.5e+187], N[(9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.62e-5], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-150], t$95$1, If[LessEqual[x, -2.1e-245], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-122], t$95$1, N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if x < -2.5000000000000001e187

   1. Initial program 61.3%

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

   3. Simplified 64.4%

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

      1. associate-*r* 64.4%

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

      2. metadata-eval 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

      4. distribute-rgt-neg-in 64.4%

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

      5. *-commutative 64.4%

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

      6. fma-neg 64.4%

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

      7. +-commutative 64.4%

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

      8. associate-+r- 64.4%

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

      9. associate-*r* 64.5%

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

      10. *-commutative 64.5%

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

      11. associate-*l* 64.4%

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

      12. *-commutative 64.4%

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

      13. associate-*l* 64.4%

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

   6. Applied egg-rr 64.4%

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

   7. Taylor expanded in x around inf 57.7%

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

      1. associate-/l* 63.6%

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

      2. associate-/r* 64.4%

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

   9. Simplified 64.4%

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

   if -2.5000000000000001e187 < x < -2.62e-5

   1. Initial program 66.5%

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

      1. associate-+l- 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-+l- 69.2%

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

      6. associate-*l* 69.2%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -2.62e-5 < x < -5.7999999999999996e-150 or -2.1000000000000001e-245 < x < 4.19999999999999985e-122

   1. Initial program 86.2%

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

      1. associate-+l- 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*r* 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-+l- 86.3%

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

      6. associate-*l* 86.2%

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

      7. associate-*l* 86.3%

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

      8. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -5.7999999999999996e-150 < x < -2.1000000000000001e-245

   1. Initial program 65.9%

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

      1. associate-+l- 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-*r* 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-+l- 65.8%

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

      6. associate-*l* 65.4%

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

      7. associate-*l* 71.0%

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

      8. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. *-un-lft-identity 71.5%

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

      2. times-frac 76.6%

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

      3. fma-define 76.6%

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

      4. cancel-sign-sub-inv 76.6%

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

      5. fma-define 76.6%

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

      6. associate-/l* 76.6%

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

      7. metadata-eval 76.6%

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

   7. Applied egg-rr 76.6%

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

   8. Taylor expanded in z around inf 54.3%

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

      1. associate-*r/ 54.3%

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

      2. associate-*r* 54.3%

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

      3. *-commutative 54.3%

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

      4. associate-*r/ 59.6%

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

   10. Simplified 59.6%

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

   if 4.19999999999999985e-122 < x

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 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* 80.9%

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

      7. associate-*l* 82.0%

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

      8. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 39.0%

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

      1. associate-/l* 42.2%

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

      2. *-commutative 42.2%

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

   7. Simplified 42.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+187}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -2.62 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c\_m}\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c\_m}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (* z c_m))) (t_2 (* 9.0 (* x (/ y (* z c_m))))))
   (*
    c_s
    (if (<= x -9.5e+187)
      t_2
      (if (<= x -1.8e-5)
        (* -4.0 (/ (* t a) c_m))
        (if (<= x -5.6e-147)
          t_1
          (if (<= x -6.5e-248)
            (* t (/ (* a -4.0) c_m))
            (if (<= x 4.2e-122) t_1 t_2))))))))

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);
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 / (z * c_m);
	double t_2 = 9.0 * (x * (y / (z * c_m)));
	double tmp;
	if (x <= -9.5e+187) {
		tmp = t_2;
	} else if (x <= -1.8e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -5.6e-147) {
		tmp = t_1;
	} else if (x <= -6.5e-248) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 4.2e-122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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.
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 / (z * c_m)
    t_2 = 9.0d0 * (x * (y / (z * c_m)))
    if (x <= (-9.5d+187)) then
        tmp = t_2
    else if (x <= (-1.8d-5)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (x <= (-5.6d-147)) then
        tmp = t_1
    else if (x <= (-6.5d-248)) then
        tmp = t * ((a * (-4.0d0)) / c_m)
    else if (x <= 4.2d-122) then
        tmp = t_1
    else
        tmp = t_2
    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;
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 / (z * c_m);
	double t_2 = 9.0 * (x * (y / (z * c_m)));
	double tmp;
	if (x <= -9.5e+187) {
		tmp = t_2;
	} else if (x <= -1.8e-5) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= -5.6e-147) {
		tmp = t_1;
	} else if (x <= -6.5e-248) {
		tmp = t * ((a * -4.0) / c_m);
	} else if (x <= 4.2e-122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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])
[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 / (z * c_m)
	t_2 = 9.0 * (x * (y / (z * c_m)))
	tmp = 0
	if x <= -9.5e+187:
		tmp = t_2
	elif x <= -1.8e-5:
		tmp = -4.0 * ((t * a) / c_m)
	elif x <= -5.6e-147:
		tmp = t_1
	elif x <= -6.5e-248:
		tmp = t * ((a * -4.0) / c_m)
	elif x <= 4.2e-122:
		tmp = t_1
	else:
		tmp = t_2
	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])
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(b / Float64(z * c_m))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c_m))))
	tmp = 0.0
	if (x <= -9.5e+187)
		tmp = t_2;
	elseif (x <= -1.8e-5)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (x <= -5.6e-147)
		tmp = t_1;
	elseif (x <= -6.5e-248)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c_m));
	elseif (x <= 4.2e-122)
		tmp = t_1;
	else
		tmp = t_2;
	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])){:}
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 / (z * c_m);
	t_2 = 9.0 * (x * (y / (z * c_m)));
	tmp = 0.0;
	if (x <= -9.5e+187)
		tmp = t_2;
	elseif (x <= -1.8e-5)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (x <= -5.6e-147)
		tmp = t_1;
	elseif (x <= -6.5e-248)
		tmp = t * ((a * -4.0) / c_m);
	elseif (x <= 4.2e-122)
		tmp = t_1;
	else
		tmp = t_2;
	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.
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[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -9.5e+187], t$95$2, If[LessEqual[x, -1.8e-5], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e-147], t$95$1, If[LessEqual[x, -6.5e-248], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-122], t$95$1, t$95$2]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.4999999999999996e187 or 4.19999999999999985e-122 < x

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-+l- 75.8%

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

      6. associate-*l* 76.7%

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

      7. associate-*l* 77.5%

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

      8. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x around inf 43.8%

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

      1. associate-/l* 47.7%

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

      2. *-commutative 47.7%

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

   7. Simplified 47.7%

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

   if -9.4999999999999996e187 < x < -1.80000000000000005e-5

   1. Initial program 66.5%

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

      1. associate-+l- 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-+l- 69.2%

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

      6. associate-*l* 69.2%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -1.80000000000000005e-5 < x < -5.6000000000000001e-147 or -6.5e-248 < x < 4.19999999999999985e-122

   1. Initial program 86.1%

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

      1. associate-+l- 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in b around inf 52.6%

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

      1. *-commutative 52.6%

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

   7. Simplified 52.6%

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

   if -5.6000000000000001e-147 < x < -6.5e-248

   1. Initial program 67.8%

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

      1. associate-+l- 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 67.7%

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

      4. *-commutative 67.7%

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

      5. associate-+l- 67.7%

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

      6. associate-*l* 67.3%

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

      7. associate-*l* 72.5%

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

      8. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in z around inf 73.0%

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

      1. *-un-lft-identity 73.0%

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

      2. times-frac 72.5%

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

      3. fma-define 72.5%

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

      4. cancel-sign-sub-inv 72.5%

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

      5. fma-define 72.5%

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

      6. associate-/l* 72.5%

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

      7. metadata-eval 72.5%

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

   7. Applied egg-rr 72.5%

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

   8. Taylor expanded in z around inf 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*r* 56.8%

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

      3. *-commutative 56.8%

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

      4. associate-*r/ 61.9%

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

   10. Simplified 61.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-69}:\\ \;\;\;\;\frac{b - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)}{z \cdot c\_m}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (* a (/ (* t -4.0) c_m))))
   (*
    c_s
    (if (<= t -1.3e+235)
      t_1
      (if (<= t -5.5e-69)
        (/ (- b (* z (* a (* 4.0 t)))) (* z c_m))
        (if (<= t 4.2e-15) (/ (+ b (* x (* 9.0 y))) (* z c_m)) 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);
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 = a * ((t * -4.0) / c_m);
	double tmp;
	if (t <= -1.3e+235) {
		tmp = t_1;
	} else if (t <= -5.5e-69) {
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c_m);
	} else if (t <= 4.2e-15) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} 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.
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 = a * ((t * (-4.0d0)) / c_m)
    if (t <= (-1.3d+235)) then
        tmp = t_1
    else if (t <= (-5.5d-69)) then
        tmp = (b - (z * (a * (4.0d0 * t)))) / (z * c_m)
    else if (t <= 4.2d-15) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    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;
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 = a * ((t * -4.0) / c_m);
	double tmp;
	if (t <= -1.3e+235) {
		tmp = t_1;
	} else if (t <= -5.5e-69) {
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c_m);
	} else if (t <= 4.2e-15) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} 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])
[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 = a * ((t * -4.0) / c_m)
	tmp = 0
	if t <= -1.3e+235:
		tmp = t_1
	elif t <= -5.5e-69:
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c_m)
	elif t <= 4.2e-15:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	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])
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(a * Float64(Float64(t * -4.0) / c_m))
	tmp = 0.0
	if (t <= -1.3e+235)
		tmp = t_1;
	elseif (t <= -5.5e-69)
		tmp = Float64(Float64(b - Float64(z * Float64(a * Float64(4.0 * t)))) / Float64(z * c_m));
	elseif (t <= 4.2e-15)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	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])){:}
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 = a * ((t * -4.0) / c_m);
	tmp = 0.0;
	if (t <= -1.3e+235)
		tmp = t_1;
	elseif (t <= -5.5e-69)
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c_m);
	elseif (t <= 4.2e-15)
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	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.
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[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t, -1.3e+235], t$95$1, If[LessEqual[t, -5.5e-69], N[(N[(b - N[(z * N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-15], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2999999999999999e235 or 4.19999999999999962e-15 < t

   1. Initial program 60.0%

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

      1. associate-+l- 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*r* 64.2%

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

      4. *-commutative 64.2%

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

      5. associate-+l- 64.2%

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

      6. associate-*l* 64.1%

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

      7. associate-*l* 64.1%

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

      8. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in z around inf 62.1%

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

      1. associate-/l* 71.3%

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

      2. associate-*r* 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-*r* 71.3%

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

      5. *-commutative 71.3%

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

      6. associate-*l/ 71.3%

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

   7. Simplified 71.3%

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

   if -1.2999999999999999e235 < t < -5.50000000000000006e-69

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-+l- 78.6%

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

      6. associate-*l* 80.1%

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

      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 x around 0 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-*r* 59.1%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-*r* 63.1%

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

      6. *-commutative 63.1%

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

   7. Simplified 63.1%

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

   if -5.50000000000000006e-69 < t < 4.19999999999999962e-15

   1. Initial program 88.1%

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

      1. associate-+l- 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*r* 85.7%

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

      4. *-commutative 85.7%

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

      5. associate-+l- 85.7%

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

      6. associate-*l* 85.7%

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

      7. associate-*l* 88.1%

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

      8. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around inf 77.9%

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

      1. associate-*r* 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+235}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-69}:\\ \;\;\;\;\frac{b - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-71} \lor \neg \left(t \leq 3.7 \cdot 10^{-56}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c\_m} + \frac{b}{c\_m \cdot \left(z \cdot t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= t -1.8e-71) (not (<= t 3.7e-56)))
    (* t (+ (* -4.0 (/ a c_m)) (/ b (* c_m (* z t)))))
    (/ (+ b (* x (* 9.0 y))) (* 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);
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 <= -1.8e-71) || !(t <= 3.7e-56)) {
		tmp = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))));
	} else {
		tmp = (b + (x * (9.0 * y))) / (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.
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 <= (-1.8d-71)) .or. (.not. (t <= 3.7d-56))) then
        tmp = t * (((-4.0d0) * (a / c_m)) + (b / (c_m * (z * t))))
    else
        tmp = (b + (x * (9.0d0 * y))) / (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;
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 <= -1.8e-71) || !(t <= 3.7e-56)) {
		tmp = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))));
	} else {
		tmp = (b + (x * (9.0 * y))) / (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])
[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 <= -1.8e-71) or not (t <= 3.7e-56):
		tmp = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))))
	else:
		tmp = (b + (x * (9.0 * y))) / (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])
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 <= -1.8e-71) || !(t <= 3.7e-56))
		tmp = Float64(t * Float64(Float64(-4.0 * Float64(a / c_m)) + Float64(b / Float64(c_m * Float64(z * t)))));
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(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])){:}
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 <= -1.8e-71) || ~((t <= 3.7e-56)))
		tmp = t * ((-4.0 * (a / c_m)) + (b / (c_m * (z * t))));
	else
		tmp = (b + (x * (9.0 * y))) / (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.
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[t, -1.8e-71], N[Not[LessEqual[t, 3.7e-56]], $MachinePrecision]], N[(t * N[(N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e-71 or 3.7000000000000002e-56 < t

   1. Initial program 66.2%

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

      1. associate-+l- 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-*r* 70.9%

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

      4. *-commutative 70.9%

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

      5. associate-+l- 70.9%

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

      6. associate-*l* 71.5%

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

      7. associate-*l* 70.2%

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

      8. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in z around 0 68.5%

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

   6. Taylor expanded in x around 0 57.9%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \frac{b}{c}}{z}} \]

   7. Taylor expanded in t around inf 75.9%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]

   if -1.8e-71 < t < 3.7000000000000002e-56

   1. Initial program 90.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 87.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 90.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 90.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 90.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.8%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 80.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 80.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 80.8%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 80.8%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-71} \lor \neg \left(t \leq 3.7 \cdot 10^{-56}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+68} \lor \neg \left(t \leq 5.9 \cdot 10^{-15}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= t -2.7e+68) (not (<= t 5.9e-15)))
    (* a (/ (* t -4.0) c_m))
    (/ (+ b (* x (* 9.0 y))) (* 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);
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 <= -2.7e+68) || !(t <= 5.9e-15)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = (b + (x * (9.0 * y))) / (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.
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 <= (-2.7d+68)) .or. (.not. (t <= 5.9d-15))) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else
        tmp = (b + (x * (9.0d0 * y))) / (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;
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 <= -2.7e+68) || !(t <= 5.9e-15)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = (b + (x * (9.0 * y))) / (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])
[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 <= -2.7e+68) or not (t <= 5.9e-15):
		tmp = a * ((t * -4.0) / c_m)
	else:
		tmp = (b + (x * (9.0 * y))) / (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])
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 <= -2.7e+68) || !(t <= 5.9e-15))
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(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])){:}
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 <= -2.7e+68) || ~((t <= 5.9e-15)))
		tmp = a * ((t * -4.0) / c_m);
	else
		tmp = (b + (x * (9.0 * y))) / (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.
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[t, -2.7e+68], N[Not[LessEqual[t, 5.9e-15]], $MachinePrecision]], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999991e68 or 5.89999999999999963e-15 < t

   1. Initial program 61.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 61.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 61.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 68.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 66.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.0%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. associate-*r* 67.0%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot \frac{t}{c}} \]

      3. *-commutative 67.0%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot \frac{t}{c} \]

      4. associate-*r* 67.0%

         \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 67.0%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 67.0%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 67.0%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -2.69999999999999991e68 < t < 5.89999999999999963e-15

   1. Initial program 85.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 84.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 84.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 84.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 84.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 72.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 72.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 72.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 72.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 72.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+68} \lor \neg \left(t \leq 5.9 \cdot 10^{-15}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-55} \lor \neg \left(z \leq 9 \cdot 10^{-106}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= z -1.85e-55) (not (<= z 9e-106)))
    (* a (/ (* t -4.0) c_m))
    (/ 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);
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 <= -1.85e-55) || !(z <= 9e-106)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = 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.
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 <= (-1.85d-55)) .or. (.not. (z <= 9d-106))) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else
        tmp = 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;
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 <= -1.85e-55) || !(z <= 9e-106)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = 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])
[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 <= -1.85e-55) or not (z <= 9e-106):
		tmp = a * ((t * -4.0) / c_m)
	else:
		tmp = 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])
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 <= -1.85e-55) || !(z <= 9e-106))
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	else
		tmp = Float64(b / Float64(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])){:}
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 <= -1.85e-55) || ~((z <= 9e-106)))
		tmp = a * ((t * -4.0) / c_m);
	else
		tmp = 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.
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[z, -1.85e-55], N[Not[LessEqual[z, 9e-106]], $MachinePrecision]], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999993e-55 or 8.99999999999999911e-106 < z

   1. Initial program 66.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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* 69.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 70.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 70.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 55.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.2%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. associate-*r* 54.2%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot \frac{t}{c}} \]

      3. *-commutative 54.2%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot \frac{t}{c} \]

      4. associate-*r* 54.2%

         \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 54.2%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 54.3%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 54.3%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -1.84999999999999993e-55 < z < 8.99999999999999911e-106

   1. Initial program 96.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 96.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 96.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 96.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      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 b around inf 68.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-55} \lor \neg \left(z \leq 9 \cdot 10^{-106}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-51}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-104}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 -9.5e-51)
    (* -4.0 (/ (* t a) c_m))
    (if (<= z 2.55e-104) (/ b (* z c_m)) (* a (/ (* t -4.0) 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);
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 <= -9.5e-51) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (z <= 2.55e-104) {
		tmp = b / (z * c_m);
	} else {
		tmp = a * ((t * -4.0) / 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.
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 <= (-9.5d-51)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (z <= 2.55d-104) then
        tmp = b / (z * c_m)
    else
        tmp = a * ((t * (-4.0d0)) / 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;
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 <= -9.5e-51) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (z <= 2.55e-104) {
		tmp = b / (z * c_m);
	} else {
		tmp = a * ((t * -4.0) / 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])
[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 <= -9.5e-51:
		tmp = -4.0 * ((t * a) / c_m)
	elif z <= 2.55e-104:
		tmp = b / (z * c_m)
	else:
		tmp = a * ((t * -4.0) / 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])
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 <= -9.5e-51)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (z <= 2.55e-104)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / 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])){:}
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 <= -9.5e-51)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (z <= 2.55e-104)
		tmp = b / (z * c_m);
	else
		tmp = a * ((t * -4.0) / 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.
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, -9.5e-51], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-104], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999998e-51

   1. Initial program 61.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 61.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 61.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 68.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 69.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

   if -9.4999999999999998e-51 < z < 2.54999999999999996e-104

   1. Initial program 96.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 96.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 96.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 96.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 92.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 92.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 68.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 68.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 2.54999999999999996e-104 < z

   1. Initial program 71.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 69.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 69.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 69.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 69.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 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 z around inf 52.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-/l* 52.2%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. associate-*r* 52.2%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot \frac{t}{c}} \]

      3. *-commutative 52.2%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot \frac{t}{c} \]

      4. associate-*r* 52.2%

         \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 52.2%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 52.3%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-51}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-104}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{z \cdot c\_m} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (* 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);
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 / (z * c_m));
}

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.
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 / (z * c_m))
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;
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 / (z * c_m));
}

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])
[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 / (z * c_m))

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])
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(z * c_m)))
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])){:}
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 / (z * c_m));
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.
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[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 76.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 76.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 77.8%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 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* 78.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 78.5%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 37.7%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 37.7%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 37.7%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer target: 80.5% 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 2024110 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (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)))