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

Percentage Accurate: 79.2% → 91.6%

Time: 22.1s

Alternatives: 15

Speedup: 0.5×

• 37.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(y \cdot \frac{x}{z}, -9, a \cdot \left(t \cdot 4\right) - \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.2e+46)
   (/ (- (fma (* y (/ x z)) -9.0 (- (* a (* t 4.0)) (/ b z)))) c)
   (if (<= z 4.1e+54)
     (* (/ 1.0 z) (/ (+ b (fma x (* y 9.0) (* a (* z (* t -4.0))))) c))
     (fma -4.0 (/ a (/ c t)) (fma 9.0 (* (/ x c) (/ y z)) (/ b (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.2e+46) {
		tmp = -fma((y * (x / z)), -9.0, ((a * (t * 4.0)) - (b / z))) / c;
	} else if (z <= 4.1e+54) {
		tmp = (1.0 / z) * ((b + fma(x, (y * 9.0), (a * (z * (t * -4.0))))) / c);
	} else {
		tmp = fma(-4.0, (a / (c / t)), fma(9.0, ((x / c) * (y / z)), (b / (z * c))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.2e+46)
		tmp = Float64(Float64(-fma(Float64(y * Float64(x / z)), -9.0, Float64(Float64(a * Float64(t * 4.0)) - Float64(b / z)))) / c);
	elseif (z <= 4.1e+54)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(a * Float64(z * Float64(t * -4.0))))) / c));
	else
		tmp = fma(-4.0, Float64(a / Float64(c / t)), fma(9.0, Float64(Float64(x / c) * Float64(y / z)), Float64(b / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.2e+46], N[((-N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] * -9.0 + N[(N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] - N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) / c), $MachinePrecision], If[LessEqual[z, 4.1e+54], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + N[(a * N[(z * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1999999999999998e46

   1. Initial program 54.1%

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

      1. associate-+l- 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-*r* 43.9%

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

      4. *-commutative 43.9%

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

      5. associate-+l- 43.9%

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

      6. *-commutative 43.9%

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

      7. associate-*r* 54.1%

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

      8. *-commutative 54.1%

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

      9. associate-*l* 54.1%

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

      10. associate-*l* 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in x around 0 72.8%

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

      1. cancel-sign-sub-inv 72.8%

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

      2. metadata-eval 72.8%

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

      3. +-commutative 72.8%

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

      4. *-commutative 72.8%

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

      5. fma-def 72.8%

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

      6. associate-/l* 72.6%

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

      7. associate-/r/ 73.9%

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

      8. fma-def 73.8%

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

      9. *-commutative 73.8%

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

      10. *-commutative 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in c around -inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. mul-1-neg 82.9%

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

      3. *-commutative 82.9%

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

      4. fma-def 82.9%

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

      5. associate-*l/ 84.6%

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

      6. *-commutative 84.6%

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

      7. +-commutative 84.6%

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

      8. mul-1-neg 84.6%

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

      9. unsub-neg 84.6%

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

      10. *-commutative 84.6%

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

      11. associate-*l* 84.6%

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

   10. Simplified 84.6%

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

   if -3.1999999999999998e46 < z < 4.09999999999999967e54

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*r* 94.0%

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

      4. *-commutative 94.0%

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

      5. associate-+l- 94.0%

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

      6. *-commutative 94.0%

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

      7. associate-*r* 93.6%

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

      8. *-commutative 93.6%

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

      9. associate-*l* 93.7%

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

      10. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   6. Applied egg-rr 97.3%

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

   if 4.09999999999999967e54 < z

   1. Initial program 57.3%

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

      1. associate-+l- 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-*r* 55.1%

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

      4. *-commutative 55.1%

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

      5. associate-+l- 55.1%

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

      6. *-commutative 55.1%

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

      7. associate-*r* 57.3%

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

      8. *-commutative 57.3%

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

      9. associate-*l* 57.2%

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

      10. associate-*l* 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in x around 0 79.7%

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

      1. cancel-sign-sub-inv 79.7%

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

      2. metadata-eval 79.7%

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

      3. +-commutative 79.7%

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

      4. fma-def 79.7%

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

      5. associate-/l* 79.8%

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

      6. fma-def 79.8%

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

      7. times-frac 89.6%

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

      8. *-commutative 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(y \cdot \frac{x}{z}, -9, a \cdot \left(t \cdot 4\right) - \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+46} \lor \neg \left(z \leq 1.6 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{-\mathsf{fma}\left(y \cdot \frac{x}{z}, -9, a \cdot \left(t \cdot 4\right) - \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -8.8e+46) (not (<= z 1.6e-115)))
   (/ (- (fma (* y (/ x z)) -9.0 (- (* a (* t 4.0)) (/ b z)))) c)
   (* (/ 1.0 z) (/ (+ b (fma x (* y 9.0) (* a (* z (* t -4.0))))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -8.8e+46) || !(z <= 1.6e-115)) {
		tmp = -fma((y * (x / z)), -9.0, ((a * (t * 4.0)) - (b / z))) / c;
	} else {
		tmp = (1.0 / z) * ((b + fma(x, (y * 9.0), (a * (z * (t * -4.0))))) / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -8.8e+46) || !(z <= 1.6e-115))
		tmp = Float64(Float64(-fma(Float64(y * Float64(x / z)), -9.0, Float64(Float64(a * Float64(t * 4.0)) - Float64(b / z)))) / c);
	else
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(a * Float64(z * Float64(t * -4.0))))) / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -8.8e+46], N[Not[LessEqual[z, 1.6e-115]], $MachinePrecision]], N[((-N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] * -9.0 + N[(N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] - N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) / c), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + N[(a * N[(z * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000001e46 or 1.6e-115 < z

   1. Initial program 64.5%

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

      1. associate-+l- 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r* 59.4%

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

      4. *-commutative 59.4%

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

      5. associate-+l- 59.4%

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

      6. *-commutative 59.4%

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

      7. associate-*r* 64.5%

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

      8. *-commutative 64.5%

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

      9. associate-*l* 64.5%

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

      10. associate-*l* 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in x around 0 79.4%

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

      1. cancel-sign-sub-inv 79.4%

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

      2. metadata-eval 79.4%

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

      3. +-commutative 79.4%

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

      4. *-commutative 79.4%

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

      5. fma-def 79.4%

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

      6. associate-/l* 77.8%

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

      7. associate-/r/ 79.0%

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

      8. fma-def 79.0%

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

      9. *-commutative 79.0%

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

      10. *-commutative 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in c around -inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. mul-1-neg 87.1%

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

      3. *-commutative 87.1%

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

      4. fma-def 87.1%

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

      5. associate-*l/ 89.2%

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

      6. *-commutative 89.2%

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

      7. +-commutative 89.2%

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

      8. mul-1-neg 89.2%

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

      9. unsub-neg 89.2%

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

      10. *-commutative 89.2%

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

      11. associate-*l* 89.2%

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

   10. Simplified 89.2%

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

   if -8.8000000000000001e46 < z < 1.6e-115

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*r* 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-+l- 94.1%

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

      6. *-commutative 94.1%

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

      7. associate-*r* 93.6%

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

      8. *-commutative 93.6%

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

      9. associate-*l* 93.7%

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

      10. associate-*l* 89.4%

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

   3. Simplified 89.4%

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

   6. Applied egg-rr 97.5%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+46} \lor \neg \left(z \leq 1.6 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{-\mathsf{fma}\left(y \cdot \frac{x}{z}, -9, a \cdot \left(t \cdot 4\right) - \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+46} \lor \neg \left(z \leq 6.2 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{-\mathsf{fma}\left(y \cdot \frac{x}{z}, -9, a \cdot \left(t \cdot 4\right) - \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5e+46) (not (<= z 6.2e-82)))
   (/ (- (fma (* y (/ x z)) -9.0 (- (* a (* t 4.0)) (/ b z)))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e+46) || !(z <= 6.2e-82)) {
		tmp = -fma((y * (x / z)), -9.0, ((a * (t * 4.0)) - (b / z))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e+46) || !(z <= 6.2e-82))
		tmp = Float64(Float64(-fma(Float64(y * Float64(x / z)), -9.0, Float64(Float64(a * Float64(t * 4.0)) - Float64(b / z)))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5e+46], N[Not[LessEqual[z, 6.2e-82]], $MachinePrecision]], N[((-N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] * -9.0 + N[(N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] - N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e46 or 6.19999999999999999e-82 < z

   1. Initial program 62.5%

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

      1. associate-+l- 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 57.2%

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

      4. *-commutative 57.2%

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

      5. associate-+l- 57.2%

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

      6. *-commutative 57.2%

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

      7. associate-*r* 62.5%

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

      8. *-commutative 62.5%

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

      9. associate-*l* 62.5%

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

      10. associate-*l* 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in x around 0 78.3%

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

      1. cancel-sign-sub-inv 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

      4. *-commutative 78.3%

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

      5. fma-def 78.3%

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

      6. associate-/l* 77.4%

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

      7. associate-/r/ 77.9%

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

      8. fma-def 77.9%

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

      9. *-commutative 77.9%

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

      10. *-commutative 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in c around -inf 86.4%

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

      1. associate-*r/ 86.4%

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

      2. mul-1-neg 86.4%

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

      3. *-commutative 86.4%

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

      4. fma-def 86.4%

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

      5. associate-*l/ 88.7%

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

      6. *-commutative 88.7%

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

      7. +-commutative 88.7%

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

      8. mul-1-neg 88.7%

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

      9. unsub-neg 88.7%

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

      10. *-commutative 88.7%

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

      11. associate-*l* 88.7%

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

   10. Simplified 88.7%

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

   if -5.0000000000000002e46 < z < 6.19999999999999999e-82

   1. Initial program 94.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+46} \lor \neg \left(z \leq 6.2 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{-\mathsf{fma}\left(y \cdot \frac{x}{z}, -9, a \cdot \left(t \cdot 4\right) - \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := 9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ t_3 := \frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{if}\;x \leq -3 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-241}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-295}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t))))
        (t_2 (* 9.0 (/ y (* z (/ c x)))))
        (t_3 (/ z (* z (/ (/ c (* a -4.0)) t)))))
   (if (<= x -3e+70)
     t_2
     (if (<= x -1.16e-37)
       t_1
       (if (<= x -8.2e-241)
         (/ b (* z c))
         (if (<= x -1.7e-277)
           t_1
           (if (<= x -7.5e-295)
             (* b (/ 1.0 (* z c)))
             (if (<= x 8.2e-262)
               t_3
               (if (<= x 1.15e-212)
                 (/ (/ b c) z)
                 (if (<= x 2.2e-32) t_3 t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * (y / (z * (c / x)));
	double t_3 = z / (z * ((c / (a * -4.0)) / t));
	double tmp;
	if (x <= -3e+70) {
		tmp = t_2;
	} else if (x <= -1.16e-37) {
		tmp = t_1;
	} else if (x <= -8.2e-241) {
		tmp = b / (z * c);
	} else if (x <= -1.7e-277) {
		tmp = t_1;
	} else if (x <= -7.5e-295) {
		tmp = b * (1.0 / (z * c));
	} else if (x <= 8.2e-262) {
		tmp = t_3;
	} else if (x <= 1.15e-212) {
		tmp = (b / c) / z;
	} else if (x <= 2.2e-32) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = 9.0d0 * (y / (z * (c / x)))
    t_3 = z / (z * ((c / (a * (-4.0d0))) / t))
    if (x <= (-3d+70)) then
        tmp = t_2
    else if (x <= (-1.16d-37)) then
        tmp = t_1
    else if (x <= (-8.2d-241)) then
        tmp = b / (z * c)
    else if (x <= (-1.7d-277)) then
        tmp = t_1
    else if (x <= (-7.5d-295)) then
        tmp = b * (1.0d0 / (z * c))
    else if (x <= 8.2d-262) then
        tmp = t_3
    else if (x <= 1.15d-212) then
        tmp = (b / c) / z
    else if (x <= 2.2d-32) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * (y / (z * (c / x)));
	double t_3 = z / (z * ((c / (a * -4.0)) / t));
	double tmp;
	if (x <= -3e+70) {
		tmp = t_2;
	} else if (x <= -1.16e-37) {
		tmp = t_1;
	} else if (x <= -8.2e-241) {
		tmp = b / (z * c);
	} else if (x <= -1.7e-277) {
		tmp = t_1;
	} else if (x <= -7.5e-295) {
		tmp = b * (1.0 / (z * c));
	} else if (x <= 8.2e-262) {
		tmp = t_3;
	} else if (x <= 1.15e-212) {
		tmp = (b / c) / z;
	} else if (x <= 2.2e-32) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	t_2 = 9.0 * (y / (z * (c / x)))
	t_3 = z / (z * ((c / (a * -4.0)) / t))
	tmp = 0
	if x <= -3e+70:
		tmp = t_2
	elif x <= -1.16e-37:
		tmp = t_1
	elif x <= -8.2e-241:
		tmp = b / (z * c)
	elif x <= -1.7e-277:
		tmp = t_1
	elif x <= -7.5e-295:
		tmp = b * (1.0 / (z * c))
	elif x <= 8.2e-262:
		tmp = t_3
	elif x <= 1.15e-212:
		tmp = (b / c) / z
	elif x <= 2.2e-32:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))))
	t_3 = Float64(z / Float64(z * Float64(Float64(c / Float64(a * -4.0)) / t)))
	tmp = 0.0
	if (x <= -3e+70)
		tmp = t_2;
	elseif (x <= -1.16e-37)
		tmp = t_1;
	elseif (x <= -8.2e-241)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= -1.7e-277)
		tmp = t_1;
	elseif (x <= -7.5e-295)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (x <= 8.2e-262)
		tmp = t_3;
	elseif (x <= 1.15e-212)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 2.2e-32)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	t_2 = 9.0 * (y / (z * (c / x)));
	t_3 = z / (z * ((c / (a * -4.0)) / t));
	tmp = 0.0;
	if (x <= -3e+70)
		tmp = t_2;
	elseif (x <= -1.16e-37)
		tmp = t_1;
	elseif (x <= -8.2e-241)
		tmp = b / (z * c);
	elseif (x <= -1.7e-277)
		tmp = t_1;
	elseif (x <= -7.5e-295)
		tmp = b * (1.0 / (z * c));
	elseif (x <= 8.2e-262)
		tmp = t_3;
	elseif (x <= 1.15e-212)
		tmp = (b / c) / z;
	elseif (x <= 2.2e-32)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(z * N[(N[(c / N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+70], t$95$2, If[LessEqual[x, -1.16e-37], t$95$1, If[LessEqual[x, -8.2e-241], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-277], t$95$1, If[LessEqual[x, -7.5e-295], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-262], t$95$3, If[LessEqual[x, 1.15e-212], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 2.2e-32], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.99999999999999976e70 or 2.2e-32 < x

   1. Initial program 78.6%

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

      1. associate-+l- 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-+l- 73.6%

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

      6. *-commutative 73.6%

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

      7. associate-*r* 78.6%

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

      8. *-commutative 78.6%

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

      9. associate-*l* 78.6%

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

      10. associate-*l* 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in x around 0 69.5%

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

      1. cancel-sign-sub-inv 69.5%

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

      2. metadata-eval 69.5%

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

      3. +-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. fma-def 69.5%

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

      6. associate-/l* 67.8%

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

      7. associate-/r/ 71.9%

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

      8. fma-def 71.9%

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

      9. *-commutative 71.9%

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

      10. *-commutative 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in c around -inf 76.3%

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

      1. associate-*r/ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. *-commutative 76.3%

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

      4. fma-def 76.3%

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

      5. associate-*l/ 78.8%

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

      6. *-commutative 78.8%

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

      7. +-commutative 78.8%

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

      8. mul-1-neg 78.8%

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

      9. unsub-neg 78.8%

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

      10. *-commutative 78.8%

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

      11. associate-*l* 78.8%

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

   10. Simplified 78.8%

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

   11. Taylor expanded in y around inf 55.2%

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

       1. associate-*r/ 55.1%

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

       2. times-frac 55.3%

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

       3. *-commutative 55.3%

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

       4. associate-/l* 60.8%

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

       5. times-frac 66.5%

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

       6. *-commutative 66.5%

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

       7. associate-/r/ 66.4%

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

       8. associate-*r/ 66.4%

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

       9. associate-/r/ 66.5%

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

       10. associate-*l/ 60.7%

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

       11. /-rgt-identity 60.7%

           \[\leadsto 9 \cdot \frac{y}{\frac{\color{blue}{\frac{z \cdot c}{1}}}{x}} \]

       12. associate-/r* 60.7%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z \cdot c}{1 \cdot x}}} \]

       13. times-frac 65.6%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z}{1} \cdot \frac{c}{x}}} \]

       14. /-rgt-identity 65.6%

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

   13. Simplified 65.6%

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

   if -2.99999999999999976e70 < x < -1.15999999999999998e-37 or -8.1999999999999997e-241 < x < -1.69999999999999991e-277

   1. Initial program 70.9%

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

      1. associate-+l- 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-+l- 79.0%

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

      6. *-commutative 79.0%

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

      7. associate-*r* 70.9%

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

      8. *-commutative 70.9%

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

      9. associate-*l* 70.9%

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

      10. associate-*l* 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in z around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-/l* 70.0%

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

   7. Simplified 70.0%

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

   if -1.15999999999999998e-37 < x < -8.1999999999999997e-241

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-+l- 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-*r* 85.3%

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

      8. *-commutative 85.3%

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

      9. associate-*l* 85.3%

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

      10. associate-*l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   7. Simplified 49.1%

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

   if -1.69999999999999991e-277 < x < -7.4999999999999997e-295

   1. Initial program 77.5%

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

      1. associate-+l- 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r* 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-+l- 77.5%

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

      6. *-commutative 77.5%

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

      7. associate-*r* 77.5%

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

      8. *-commutative 77.5%

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

      9. associate-*l* 77.5%

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

      10. associate-*l* 77.5%

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

   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 b around inf 28.3%

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

      1. *-commutative 28.3%

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

   7. Simplified 28.3%

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

      1. div-inv 27.9%

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

   9. Applied egg-rr 27.9%

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

   if -7.4999999999999997e-295 < x < 8.20000000000000052e-262 or 1.15e-212 < x < 2.2e-32

   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* 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-+l- 74.1%

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

      6. *-commutative 74.1%

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

      7. associate-*r* 74.7%

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

      8. *-commutative 74.7%

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

      9. associate-*l* 74.7%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

   6. Applied egg-rr 80.0%

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

   7. Taylor expanded in a around inf 29.8%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.8%

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

      2. associate-*r/ 29.8%

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

      3. metadata-eval 29.8%

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

      4. distribute-lft-neg-in 29.8%

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

      5. distribute-lft-neg-in 29.8%

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

      6. metadata-eval 29.8%

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

      7. associate-*r* 29.8%

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

      8. *-commutative 29.8%

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

      9. associate-/l* 31.5%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z \cdot t}{\frac{c}{-4 \cdot a}}} \]

   9. Simplified 31.5%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z \cdot t}{\frac{c}{-4 \cdot a}}} \]
   10. Step-by-step derivation

       1. associate-/l* 36.0%

          \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z}{\frac{\frac{c}{-4 \cdot a}}{t}}} \]

       2. frac-times 45.0%

          \[\leadsto \color{blue}{\frac{1 \cdot z}{z \cdot \frac{\frac{c}{-4 \cdot a}}{t}}} \]

       3. *-un-lft-identity 45.0%

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

       4. *-commutative 45.0%

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

   11. Applied egg-rr 45.0%

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

   if 8.20000000000000052e-262 < x < 1.15e-212

   1. Initial program 76.0%

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

      1. associate-+l- 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r* 67.9%

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

      4. *-commutative 67.9%

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

      5. associate-+l- 67.9%

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

      6. *-commutative 67.9%

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

      7. associate-*r* 76.0%

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

      8. *-commutative 76.0%

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

      9. associate-*l* 76.2%

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

      10. associate-*l* 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in b around inf 51.9%

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

      1. *-commutative 51.9%

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

   7. Simplified 51.9%

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

      1. div-inv 51.8%

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

   9. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   10. Step-by-step derivation

       1. *-commutative 51.8%

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

       2. div-inv 51.9%

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

       3. associate-/r* 59.9%

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

   11. Applied egg-rr 59.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+70}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-37}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-241}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-277}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-295}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-241}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-185}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))) (t_2 (* 9.0 (* (/ x z) (/ y c)))))
   (if (<= x -1.6e+72)
     t_2
     (if (<= x -4e-38)
       t_1
       (if (<= x -2.05e-241)
         (/ b (* z c))
         (if (<= x -1.85e-308)
           t_1
           (if (<= x 1e-185) (/ (/ b c) z) (if (<= x 2.1e-32) t_1 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -1.6e+72) {
		tmp = t_2;
	} else if (x <= -4e-38) {
		tmp = t_1;
	} else if (x <= -2.05e-241) {
		tmp = b / (z * c);
	} else if (x <= -1.85e-308) {
		tmp = t_1;
	} else if (x <= 1e-185) {
		tmp = (b / c) / z;
	} else if (x <= 2.1e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = 9.0d0 * ((x / z) * (y / c))
    if (x <= (-1.6d+72)) then
        tmp = t_2
    else if (x <= (-4d-38)) then
        tmp = t_1
    else if (x <= (-2.05d-241)) then
        tmp = b / (z * c)
    else if (x <= (-1.85d-308)) then
        tmp = t_1
    else if (x <= 1d-185) then
        tmp = (b / c) / z
    else if (x <= 2.1d-32) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -1.6e+72) {
		tmp = t_2;
	} else if (x <= -4e-38) {
		tmp = t_1;
	} else if (x <= -2.05e-241) {
		tmp = b / (z * c);
	} else if (x <= -1.85e-308) {
		tmp = t_1;
	} else if (x <= 1e-185) {
		tmp = (b / c) / z;
	} else if (x <= 2.1e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	t_2 = 9.0 * ((x / z) * (y / c))
	tmp = 0
	if x <= -1.6e+72:
		tmp = t_2
	elif x <= -4e-38:
		tmp = t_1
	elif x <= -2.05e-241:
		tmp = b / (z * c)
	elif x <= -1.85e-308:
		tmp = t_1
	elif x <= 1e-185:
		tmp = (b / c) / z
	elif x <= 2.1e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (x <= -1.6e+72)
		tmp = t_2;
	elseif (x <= -4e-38)
		tmp = t_1;
	elseif (x <= -2.05e-241)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= -1.85e-308)
		tmp = t_1;
	elseif (x <= 1e-185)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 2.1e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	t_2 = 9.0 * ((x / z) * (y / c));
	tmp = 0.0;
	if (x <= -1.6e+72)
		tmp = t_2;
	elseif (x <= -4e-38)
		tmp = t_1;
	elseif (x <= -2.05e-241)
		tmp = b / (z * c);
	elseif (x <= -1.85e-308)
		tmp = t_1;
	elseif (x <= 1e-185)
		tmp = (b / c) / z;
	elseif (x <= 2.1e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+72], t$95$2, If[LessEqual[x, -4e-38], t$95$1, If[LessEqual[x, -2.05e-241], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.85e-308], t$95$1, If[LessEqual[x, 1e-185], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 2.1e-32], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6000000000000001e72 or 2.0999999999999999e-32 < x

   1. Initial program 78.6%

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

      1. associate-+l- 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-+l- 73.6%

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

      6. *-commutative 73.6%

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

      7. associate-*r* 78.6%

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

      8. *-commutative 78.6%

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

      9. associate-*l* 78.6%

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

      10. associate-*l* 75.3%

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

   3. Simplified 75.3%

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

   6. Applied egg-rr 78.3%

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

   7. Taylor expanded in x around inf 55.2%

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

      1. *-commutative 55.2%

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

      2. times-frac 62.2%

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

   9. Simplified 62.2%

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

   if -1.6000000000000001e72 < x < -3.9999999999999998e-38 or -2.0499999999999999e-241 < x < -1.8499999999999998e-308 or 9.9999999999999999e-186 < x < 2.0999999999999999e-32

   1. Initial program 74.3%

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

      1. associate-+l- 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

      6. *-commutative 76.7%

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

      7. associate-*r* 74.3%

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

      8. *-commutative 74.3%

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

      9. associate-*l* 74.3%

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

      10. associate-*l* 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 60.6%

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

   7. Simplified 60.6%

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

   if -3.9999999999999998e-38 < x < -2.0499999999999999e-241

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-+l- 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-*r* 85.3%

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

      8. *-commutative 85.3%

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

      9. associate-*l* 85.3%

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

      10. associate-*l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   7. Simplified 49.1%

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

   if -1.8499999999999998e-308 < x < 9.9999999999999999e-186

   1. Initial program 73.7%

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

      1. associate-+l- 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*r* 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-+l- 70.8%

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

      6. *-commutative 70.8%

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

      7. associate-*r* 73.7%

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

      8. *-commutative 73.7%

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

      9. associate-*l* 73.8%

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

      10. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in b around inf 50.1%

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

      1. *-commutative 50.1%

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

   7. Simplified 50.1%

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

      1. div-inv 50.0%

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

   9. Applied egg-rr 50.0%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   10. Step-by-step derivation

       1. *-commutative 50.0%

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

       2. div-inv 50.1%

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

       3. associate-/r* 58.7%

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

   11. Applied egg-rr 58.7%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-241}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-308}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 10^{-185}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := 9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-242}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))) (t_2 (* 9.0 (/ y (* z (/ c x))))))
   (if (<= x -1.85e+72)
     t_2
     (if (<= x -5.8e-38)
       t_1
       (if (<= x -3e-242)
         (/ b (* z c))
         (if (<= x 1.95e-307)
           t_1
           (if (<= x 1.9e-185) (/ (/ b c) z) (if (<= x 3.8e-33) t_1 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * (y / (z * (c / x)));
	double tmp;
	if (x <= -1.85e+72) {
		tmp = t_2;
	} else if (x <= -5.8e-38) {
		tmp = t_1;
	} else if (x <= -3e-242) {
		tmp = b / (z * c);
	} else if (x <= 1.95e-307) {
		tmp = t_1;
	} else if (x <= 1.9e-185) {
		tmp = (b / c) / z;
	} else if (x <= 3.8e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = 9.0d0 * (y / (z * (c / x)))
    if (x <= (-1.85d+72)) then
        tmp = t_2
    else if (x <= (-5.8d-38)) then
        tmp = t_1
    else if (x <= (-3d-242)) then
        tmp = b / (z * c)
    else if (x <= 1.95d-307) then
        tmp = t_1
    else if (x <= 1.9d-185) then
        tmp = (b / c) / z
    else if (x <= 3.8d-33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * (y / (z * (c / x)));
	double tmp;
	if (x <= -1.85e+72) {
		tmp = t_2;
	} else if (x <= -5.8e-38) {
		tmp = t_1;
	} else if (x <= -3e-242) {
		tmp = b / (z * c);
	} else if (x <= 1.95e-307) {
		tmp = t_1;
	} else if (x <= 1.9e-185) {
		tmp = (b / c) / z;
	} else if (x <= 3.8e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	t_2 = 9.0 * (y / (z * (c / x)))
	tmp = 0
	if x <= -1.85e+72:
		tmp = t_2
	elif x <= -5.8e-38:
		tmp = t_1
	elif x <= -3e-242:
		tmp = b / (z * c)
	elif x <= 1.95e-307:
		tmp = t_1
	elif x <= 1.9e-185:
		tmp = (b / c) / z
	elif x <= 3.8e-33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))))
	tmp = 0.0
	if (x <= -1.85e+72)
		tmp = t_2;
	elseif (x <= -5.8e-38)
		tmp = t_1;
	elseif (x <= -3e-242)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 1.95e-307)
		tmp = t_1;
	elseif (x <= 1.9e-185)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 3.8e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	t_2 = 9.0 * (y / (z * (c / x)));
	tmp = 0.0;
	if (x <= -1.85e+72)
		tmp = t_2;
	elseif (x <= -5.8e-38)
		tmp = t_1;
	elseif (x <= -3e-242)
		tmp = b / (z * c);
	elseif (x <= 1.95e-307)
		tmp = t_1;
	elseif (x <= 1.9e-185)
		tmp = (b / c) / z;
	elseif (x <= 3.8e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e+72], t$95$2, If[LessEqual[x, -5.8e-38], t$95$1, If[LessEqual[x, -3e-242], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-307], t$95$1, If[LessEqual[x, 1.9e-185], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 3.8e-33], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8500000000000001e72 or 3.79999999999999994e-33 < x

   1. Initial program 78.6%

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

      1. associate-+l- 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-+l- 73.6%

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

      6. *-commutative 73.6%

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

      7. associate-*r* 78.6%

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

      8. *-commutative 78.6%

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

      9. associate-*l* 78.6%

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

      10. associate-*l* 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in x around 0 69.5%

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

      1. cancel-sign-sub-inv 69.5%

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

      2. metadata-eval 69.5%

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

      3. +-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. fma-def 69.5%

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

      6. associate-/l* 67.8%

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

      7. associate-/r/ 71.9%

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

      8. fma-def 71.9%

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

      9. *-commutative 71.9%

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

      10. *-commutative 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in c around -inf 76.3%

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

      1. associate-*r/ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. *-commutative 76.3%

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

      4. fma-def 76.3%

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

      5. associate-*l/ 78.8%

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

      6. *-commutative 78.8%

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

      7. +-commutative 78.8%

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

      8. mul-1-neg 78.8%

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

      9. unsub-neg 78.8%

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

      10. *-commutative 78.8%

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

      11. associate-*l* 78.8%

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

   10. Simplified 78.8%

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

   11. Taylor expanded in y around inf 55.2%

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

       1. associate-*r/ 55.1%

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

       2. times-frac 55.3%

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

       3. *-commutative 55.3%

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

       4. associate-/l* 60.8%

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

       5. times-frac 66.5%

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

       6. *-commutative 66.5%

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

       7. associate-/r/ 66.4%

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

       8. associate-*r/ 66.4%

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

       9. associate-/r/ 66.5%

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

       10. associate-*l/ 60.7%

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

       11. /-rgt-identity 60.7%

           \[\leadsto 9 \cdot \frac{y}{\frac{\color{blue}{\frac{z \cdot c}{1}}}{x}} \]

       12. associate-/r* 60.7%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z \cdot c}{1 \cdot x}}} \]

       13. times-frac 65.6%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z}{1} \cdot \frac{c}{x}}} \]

       14. /-rgt-identity 65.6%

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

   13. Simplified 65.6%

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

   if -1.8500000000000001e72 < x < -5.79999999999999988e-38 or -3e-242 < x < 1.95e-307 or 1.9e-185 < x < 3.79999999999999994e-33

   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* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

      6. *-commutative 77.1%

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

      7. associate-*r* 74.7%

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

      8. *-commutative 74.7%

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

      9. associate-*l* 74.7%

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

      10. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in z around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. associate-/l* 61.3%

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

   7. Simplified 61.3%

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

   if -5.79999999999999988e-38 < x < -3e-242

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-+l- 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-*r* 85.3%

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

      8. *-commutative 85.3%

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

      9. associate-*l* 85.3%

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

      10. associate-*l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   7. Simplified 49.1%

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

   if 1.95e-307 < x < 1.9e-185

   1. Initial program 72.9%

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

      1. associate-+l- 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*r* 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. *-commutative 69.9%

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

      7. associate-*r* 72.9%

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

      8. *-commutative 72.9%

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

      9. associate-*l* 72.9%

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

      10. associate-*l* 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in b around inf 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

      1. div-inv 51.5%

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

   9. Applied egg-rr 51.5%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   10. Step-by-step derivation

       1. *-commutative 51.5%

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

       2. div-inv 51.6%

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

       3. associate-/r* 60.5%

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

   11. Applied egg-rr 60.5%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+72}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-242}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-307}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-33}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+257}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+248}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot 9\right) \cdot \frac{x}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -1e+257)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= t_1 1e+248)
       (/ (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* y x) z)))) c)
       (/ (* (* y 9.0) (/ x c)) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+257) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t_1 <= 1e+248) {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z)))) / c;
	} else {
		tmp = ((y * 9.0) * (x / c)) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-1d+257)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (t_1 <= 1d+248) then
        tmp = (((-4.0d0) * (a * t)) + ((b / z) + (9.0d0 * ((y * x) / z)))) / c
    else
        tmp = ((y * 9.0d0) * (x / c)) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+257) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t_1 <= 1e+248) {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z)))) / c;
	} else {
		tmp = ((y * 9.0) * (x / c)) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -1e+257:
		tmp = 9.0 * ((x / z) * (y / c))
	elif t_1 <= 1e+248:
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z)))) / c
	else:
		tmp = ((y * 9.0) * (x / c)) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+257)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (t_1 <= 1e+248)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(y * x) / z)))) / c);
	else
		tmp = Float64(Float64(Float64(y * 9.0) * Float64(x / c)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -1e+257)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (t_1 <= 1e+248)
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z)))) / c;
	else
		tmp = ((y * 9.0) * (x / c)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+257], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+248], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y * 9.0), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -1.00000000000000003e257

   1. Initial program 63.5%

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

      1. associate-+l- 63.5%

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

      2. *-commutative 63.5%

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

      3. associate-*r* 63.5%

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

      4. *-commutative 63.5%

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

      5. associate-+l- 63.5%

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

      6. *-commutative 63.5%

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

      7. associate-*r* 63.5%

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

      8. *-commutative 63.5%

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

      9. associate-*l* 63.5%

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

      10. associate-*l* 59.3%

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

   3. Simplified 59.3%

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

   6. Applied egg-rr 67.8%

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

   7. Taylor expanded in x around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. times-frac 94.8%

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

   9. Simplified 94.8%

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

   if -1.00000000000000003e257 < (*.f64 (*.f64 x 9) y) < 1.00000000000000005e248

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 75.7%

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

      4. *-commutative 75.7%

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

      5. associate-+l- 75.7%

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

      6. *-commutative 75.7%

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

      7. associate-*r* 78.8%

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

      8. *-commutative 78.8%

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

      9. associate-*l* 78.8%

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

      10. associate-*l* 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in x around 0 80.2%

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

      1. cancel-sign-sub-inv 80.2%

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

      2. metadata-eval 80.2%

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

      3. +-commutative 80.2%

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

      4. *-commutative 80.2%

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

      5. fma-def 80.2%

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

      6. associate-/l* 81.5%

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

      7. associate-/r/ 80.8%

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

      8. fma-def 80.8%

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

      9. *-commutative 80.8%

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

      10. *-commutative 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in c around 0 89.8%

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

   if 1.00000000000000005e248 < (*.f64 (*.f64 x 9) y)

   1. Initial program 86.4%

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

      1. associate-+l- 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*r* 86.4%

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

      4. *-commutative 86.4%

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

      5. associate-+l- 86.4%

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

      6. *-commutative 86.4%

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

      7. associate-*r* 86.4%

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

      8. *-commutative 86.4%

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

      9. associate-*l* 86.3%

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

      10. associate-*l* 77.5%

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

   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 86.5%

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

      1. associate-*r/ 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*r* 86.3%

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

      4. *-commutative 86.3%

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

      5. times-frac 90.9%

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

   7. Simplified 90.9%

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

      1. associate-*l/ 95.3%

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

   9. Applied egg-rr 95.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+257}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+248}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot 9\right) \cdot \frac{x}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{b}{z} - t \cdot \left(a \cdot 4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -5.8e+266)
   (* 9.0 (/ y (* z (/ c x))))
   (if (<= x -9.2e+70)
     (/ (/ (+ b (* y (* x 9.0))) c) z)
     (if (<= x 5.2e-84)
       (/ (- (/ b z) (* t (* a 4.0))) c)
       (+ (* -4.0 (/ (* a t) c)) (* 9.0 (/ (* y x) (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -5.8e+266) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (x <= -9.2e+70) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else if (x <= 5.2e-84) {
		tmp = ((b / z) - (t * (a * 4.0))) / c;
	} else {
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((y * x) / (z * c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if (x <= (-5.8d+266)) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else if (x <= (-9.2d+70)) then
        tmp = ((b + (y * (x * 9.0d0))) / c) / z
    else if (x <= 5.2d-84) then
        tmp = ((b / z) - (t * (a * 4.0d0))) / c
    else
        tmp = ((-4.0d0) * ((a * t) / c)) + (9.0d0 * ((y * x) / (z * c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -5.8e+266) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (x <= -9.2e+70) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else if (x <= 5.2e-84) {
		tmp = ((b / z) - (t * (a * 4.0))) / c;
	} else {
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((y * x) / (z * c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -5.8e+266:
		tmp = 9.0 * (y / (z * (c / x)))
	elif x <= -9.2e+70:
		tmp = ((b + (y * (x * 9.0))) / c) / z
	elif x <= 5.2e-84:
		tmp = ((b / z) - (t * (a * 4.0))) / c
	else:
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((y * x) / (z * c)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -5.8e+266)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	elseif (x <= -9.2e+70)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c) / z);
	elseif (x <= 5.2e-84)
		tmp = Float64(Float64(Float64(b / z) - Float64(t * Float64(a * 4.0))) / c);
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c)) + Float64(9.0 * Float64(Float64(y * x) / Float64(z * c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -5.8e+266)
		tmp = 9.0 * (y / (z * (c / x)));
	elseif (x <= -9.2e+70)
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	elseif (x <= 5.2e-84)
		tmp = ((b / z) - (t * (a * 4.0))) / c;
	else
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((y * x) / (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -5.8e+266], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e+70], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 5.2e-84], N[(N[(N[(b / z), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.80000000000000035e266

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

      5. associate-+l- 76.6%

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

      6. *-commutative 76.6%

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

      7. associate-*r* 76.6%

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

      8. *-commutative 76.6%

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

      9. associate-*l* 76.6%

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

      10. associate-*l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. cancel-sign-sub-inv 76.6%

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

      2. metadata-eval 76.6%

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

      3. +-commutative 76.6%

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

      4. *-commutative 76.6%

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

      5. fma-def 76.6%

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

      6. associate-/l* 51.6%

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

      7. associate-/r/ 76.6%

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

      8. fma-def 76.6%

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

      9. *-commutative 76.6%

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

      10. *-commutative 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in c around -inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. mul-1-neg 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. associate-*l/ 99.6%

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

      6. *-commutative 99.6%

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

      7. +-commutative 99.6%

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

      8. mul-1-neg 99.6%

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

      9. unsub-neg 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-*l* 99.6%

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

   10. Simplified 99.6%

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

   11. Taylor expanded in y around inf 76.6%

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

       1. associate-*r/ 76.6%

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

       2. times-frac 99.6%

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

       3. *-commutative 99.6%

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

       4. associate-/l* 99.2%

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

       5. times-frac 100.0%

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

       6. *-commutative 100.0%

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

       7. associate-/r/ 99.6%

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

       8. associate-*r/ 99.6%

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

       9. associate-/r/ 100.0%

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

       10. associate-*l/ 76.6%

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

       11. /-rgt-identity 76.6%

           \[\leadsto 9 \cdot \frac{y}{\frac{\color{blue}{\frac{z \cdot c}{1}}}{x}} \]

       12. associate-/r* 76.6%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z \cdot c}{1 \cdot x}}} \]

       13. times-frac 99.6%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z}{1} \cdot \frac{c}{x}}} \]

       14. /-rgt-identity 99.6%

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

   13. Simplified 99.6%

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

   if -5.80000000000000035e266 < x < -9.19999999999999975e70

   1. Initial program 69.8%

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

      1. associate-+l- 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 60.1%

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

      4. *-commutative 60.1%

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

      5. associate-+l- 60.1%

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

      6. *-commutative 60.1%

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

      7. associate-*r* 69.8%

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

      8. *-commutative 69.8%

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

      9. associate-*l* 69.8%

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

      10. associate-*l* 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. cancel-sign-sub-inv 56.0%

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

      2. metadata-eval 56.0%

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

      3. +-commutative 56.0%

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

      4. *-commutative 56.0%

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

      5. fma-def 56.0%

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

      6. associate-/l* 53.5%

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

      7. associate-/r/ 62.7%

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

      8. fma-def 62.7%

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

      9. *-commutative 62.7%

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

      10. *-commutative 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in z around 0 56.0%

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

   9. Taylor expanded in c around 0 65.6%

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

       1. associate-*r* 65.6%

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

   11. Simplified 65.6%

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

   if -9.19999999999999975e70 < x < 5.2e-84

   1. Initial program 76.7%

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

      1. associate-+l- 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*r* 77.2%

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

      4. *-commutative 77.2%

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

      5. associate-+l- 77.2%

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

      6. *-commutative 77.2%

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

      7. associate-*r* 76.7%

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

      8. *-commutative 76.7%

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

      9. associate-*l* 76.8%

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

      10. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x around 0 79.0%

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

      1. cancel-sign-sub-inv 79.0%

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

      2. metadata-eval 79.0%

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

      3. +-commutative 79.0%

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

      4. *-commutative 79.0%

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

      5. fma-def 79.0%

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

      6. associate-/l* 82.5%

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

      7. associate-/r/ 79.3%

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

      8. fma-def 79.3%

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

      9. *-commutative 79.3%

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

      10. *-commutative 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in c around -inf 91.6%

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

      1. associate-*r/ 91.6%

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

      2. mul-1-neg 91.6%

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

      3. *-commutative 91.6%

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

      4. fma-def 91.6%

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

      5. associate-*l/ 90.1%

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

      6. *-commutative 90.1%

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

      7. +-commutative 90.1%

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

      8. mul-1-neg 90.1%

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

      9. unsub-neg 90.1%

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

      10. *-commutative 90.1%

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

      11. associate-*l* 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in y around 0 78.0%

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

       1. associate-*r/ 78.0%

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

       2. *-commutative 78.0%

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

       3. associate-*r* 78.0%

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

       4. mul-1-neg 78.0%

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

       5. *-commutative 78.0%

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

       6. associate-*l* 78.0%

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

   13. Simplified 78.0%

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

   if 5.2e-84 < x

   1. Initial program 84.3%

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

      1. associate-+l- 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*r* 80.8%

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

      4. *-commutative 80.8%

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

      5. associate-+l- 80.8%

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

      6. *-commutative 80.8%

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

      7. associate-*r* 84.3%

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

      8. *-commutative 84.3%

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

      9. associate-*l* 84.3%

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

      10. associate-*l* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around 0 69.1%

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

   6. Taylor expanded in x around 0 69.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{x \cdot y}{c \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{b}{z} - t \cdot \left(a \cdot 4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+267}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+73} \lor \neg \left(x \leq 6.5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - t \cdot \left(a \cdot 4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.7e+267)
   (* 9.0 (/ y (* z (/ c x))))
   (if (or (<= x -1.8e+73) (not (<= x 6.5e-97)))
     (/ (/ (+ b (* y (* x 9.0))) c) z)
     (/ (- (/ b z) (* t (* a 4.0))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.7e+267) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if ((x <= -1.8e+73) || !(x <= 6.5e-97)) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else {
		tmp = ((b / z) - (t * (a * 4.0))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if (x <= (-1.7d+267)) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else if ((x <= (-1.8d+73)) .or. (.not. (x <= 6.5d-97))) then
        tmp = ((b + (y * (x * 9.0d0))) / c) / z
    else
        tmp = ((b / z) - (t * (a * 4.0d0))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.7e+267) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if ((x <= -1.8e+73) || !(x <= 6.5e-97)) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else {
		tmp = ((b / z) - (t * (a * 4.0))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.7e+267:
		tmp = 9.0 * (y / (z * (c / x)))
	elif (x <= -1.8e+73) or not (x <= 6.5e-97):
		tmp = ((b + (y * (x * 9.0))) / c) / z
	else:
		tmp = ((b / z) - (t * (a * 4.0))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.7e+267)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	elseif ((x <= -1.8e+73) || !(x <= 6.5e-97))
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c) / z);
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(t * Float64(a * 4.0))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.7e+267)
		tmp = 9.0 * (y / (z * (c / x)));
	elseif ((x <= -1.8e+73) || ~((x <= 6.5e-97)))
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	else
		tmp = ((b / z) - (t * (a * 4.0))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.7e+267], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.8e+73], N[Not[LessEqual[x, 6.5e-97]], $MachinePrecision]], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999991e267

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

      5. associate-+l- 76.6%

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

      6. *-commutative 76.6%

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

      7. associate-*r* 76.6%

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

      8. *-commutative 76.6%

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

      9. associate-*l* 76.6%

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

      10. associate-*l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. cancel-sign-sub-inv 76.6%

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

      2. metadata-eval 76.6%

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

      3. +-commutative 76.6%

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

      4. *-commutative 76.6%

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

      5. fma-def 76.6%

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

      6. associate-/l* 51.6%

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

      7. associate-/r/ 76.6%

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

      8. fma-def 76.6%

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

      9. *-commutative 76.6%

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

      10. *-commutative 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in c around -inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. mul-1-neg 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. associate-*l/ 99.6%

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

      6. *-commutative 99.6%

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

      7. +-commutative 99.6%

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

      8. mul-1-neg 99.6%

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

      9. unsub-neg 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-*l* 99.6%

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

   10. Simplified 99.6%

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

   11. Taylor expanded in y around inf 76.6%

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

       1. associate-*r/ 76.6%

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

       2. times-frac 99.6%

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

       3. *-commutative 99.6%

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

       4. associate-/l* 99.2%

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

       5. times-frac 100.0%

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

       6. *-commutative 100.0%

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

       7. associate-/r/ 99.6%

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

       8. associate-*r/ 99.6%

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

       9. associate-/r/ 100.0%

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

       10. associate-*l/ 76.6%

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

       11. /-rgt-identity 76.6%

           \[\leadsto 9 \cdot \frac{y}{\frac{\color{blue}{\frac{z \cdot c}{1}}}{x}} \]

       12. associate-/r* 76.6%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z \cdot c}{1 \cdot x}}} \]

       13. times-frac 99.6%

           \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z}{1} \cdot \frac{c}{x}}} \]

       14. /-rgt-identity 99.6%

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

   13. Simplified 99.6%

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

   if -1.69999999999999991e267 < x < -1.7999999999999999e73 or 6.5000000000000004e-97 < x

   1. Initial program 78.5%

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

      1. associate-+l- 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 73.1%

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

      4. *-commutative 73.1%

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

      5. associate-+l- 73.1%

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

      6. *-commutative 73.1%

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

      7. associate-*r* 78.5%

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

      8. *-commutative 78.5%

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

      9. associate-*l* 78.6%

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

      10. associate-*l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in x around 0 70.1%

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

      1. cancel-sign-sub-inv 70.1%

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

      2. metadata-eval 70.1%

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

      3. +-commutative 70.1%

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

      4. *-commutative 70.1%

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

      5. fma-def 70.1%

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

      6. associate-/l* 69.3%

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

      7. associate-/r/ 72.3%

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

      8. fma-def 72.3%

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

      9. *-commutative 72.3%

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

      10. *-commutative 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in z around 0 61.9%

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

   9. Taylor expanded in c around 0 66.7%

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

       1. associate-*r* 66.7%

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

   11. Simplified 66.7%

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

   if -1.7999999999999999e73 < x < 6.5000000000000004e-97

   1. Initial program 77.5%

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

      1. associate-+l- 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r* 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-+l- 78.0%

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

      6. *-commutative 78.0%

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

      7. associate-*r* 77.5%

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

      8. *-commutative 77.5%

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

      9. associate-*l* 77.6%

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

      10. associate-*l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around 0 79.9%

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

      1. cancel-sign-sub-inv 79.9%

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

      2. metadata-eval 79.9%

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

      3. +-commutative 79.9%

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

      4. *-commutative 79.9%

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

      5. fma-def 79.9%

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

      6. associate-/l* 83.5%

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

      7. associate-/r/ 80.1%

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

      8. fma-def 80.1%

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

      9. *-commutative 80.1%

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

      10. *-commutative 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in c around -inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. mul-1-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. fma-def 91.3%

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

      5. associate-*l/ 89.8%

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

      6. *-commutative 89.8%

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

      7. +-commutative 89.8%

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

      8. mul-1-neg 89.8%

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

      9. unsub-neg 89.8%

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

      10. *-commutative 89.8%

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

      11. associate-*l* 89.8%

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

   10. Simplified 89.8%

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

   11. Taylor expanded in y around 0 77.3%

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

       1. associate-*r/ 77.3%

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

       2. *-commutative 77.3%

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

       3. associate-*r* 77.3%

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

       4. mul-1-neg 77.3%

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

       5. *-commutative 77.3%

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

       6. associate-*l* 77.3%

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

   13. Simplified 77.3%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+267}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+73} \lor \neg \left(x \leq 6.5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - t \cdot \left(a \cdot 4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -2.2e+158)
   (/ z (* z (/ (/ c (* a -4.0)) t)))
   (if (<= t 1.2e+42)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (* -4.0 (/ a (/ c t))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2.2e+158) {
		tmp = z / (z * ((c / (a * -4.0)) / t));
	} else if (t <= 1.2e+42) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if (t <= (-2.2d+158)) then
        tmp = z / (z * ((c / (a * (-4.0d0))) / t))
    else if (t <= 1.2d+42) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2.2e+158) {
		tmp = z / (z * ((c / (a * -4.0)) / t));
	} else if (t <= 1.2e+42) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -2.2e+158:
		tmp = z / (z * ((c / (a * -4.0)) / t))
	elif t <= 1.2e+42:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -2.2e+158)
		tmp = Float64(z / Float64(z * Float64(Float64(c / Float64(a * -4.0)) / t)));
	elseif (t <= 1.2e+42)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -2.2e+158)
		tmp = z / (z * ((c / (a * -4.0)) / t));
	elseif (t <= 1.2e+42)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -2.2e+158], N[(z / N[(z * N[(N[(c / N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+42], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2000000000000001e158

   1. Initial program 68.6%

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

      1. associate-+l- 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*r* 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 72.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 68.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 64.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   6. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   7. Taylor expanded in a around inf 57.7%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto \frac{1}{z} \cdot \left(-4 \cdot \frac{a \cdot \color{blue}{\left(z \cdot t\right)}}{c}\right) \]

      2. associate-*r/ 57.7%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{-4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c}} \]

      3. metadata-eval 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(-4\right)} \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c} \]

      4. distribute-lft-neg-in 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{-4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}}{c} \]

      5. distribute-lft-neg-in 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(-4\right) \cdot \left(a \cdot \left(z \cdot t\right)\right)}}{c} \]

      6. metadata-eval 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{-4} \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c} \]

      7. associate-*r* 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(-4 \cdot a\right) \cdot \left(z \cdot t\right)}}{c} \]

      8. *-commutative 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(z \cdot t\right) \cdot \left(-4 \cdot a\right)}}{c} \]

      9. associate-/l* 61.5%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z \cdot t}{\frac{c}{-4 \cdot a}}} \]

   9. Simplified 61.5%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z \cdot t}{\frac{c}{-4 \cdot a}}} \]
   10. Step-by-step derivation

       1. associate-/l* 69.3%

          \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z}{\frac{\frac{c}{-4 \cdot a}}{t}}} \]

       2. frac-times 87.8%

          \[\leadsto \color{blue}{\frac{1 \cdot z}{z \cdot \frac{\frac{c}{-4 \cdot a}}{t}}} \]

       3. *-un-lft-identity 87.8%

          \[\leadsto \frac{\color{blue}{z}}{z \cdot \frac{\frac{c}{-4 \cdot a}}{t}} \]

       4. *-commutative 87.8%

          \[\leadsto \frac{z}{z \cdot \frac{\frac{c}{\color{blue}{a \cdot -4}}}{t}} \]

   11. Applied egg-rr 87.8%

       \[\leadsto \color{blue}{\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}} \]

   if -2.2000000000000001e158 < t < 1.1999999999999999e42

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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. *-commutative 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 69.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 1.1999999999999999e42 < t

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 75.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 43.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 57.7%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+156}:\\ \;\;\;\;\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.9e+156)
   (/ z (* z (/ (/ c (* a -4.0)) t)))
   (if (<= t 7.6e+53)
     (/ (/ (+ b (* y (* x 9.0))) c) z)
     (* -4.0 (/ a (/ c t))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.9e+156) {
		tmp = z / (z * ((c / (a * -4.0)) / t));
	} else if (t <= 7.6e+53) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if (t <= (-1.9d+156)) then
        tmp = z / (z * ((c / (a * (-4.0d0))) / t))
    else if (t <= 7.6d+53) then
        tmp = ((b + (y * (x * 9.0d0))) / c) / z
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.9e+156) {
		tmp = z / (z * ((c / (a * -4.0)) / t));
	} else if (t <= 7.6e+53) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.9e+156:
		tmp = z / (z * ((c / (a * -4.0)) / t))
	elif t <= 7.6e+53:
		tmp = ((b + (y * (x * 9.0))) / c) / z
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.9e+156)
		tmp = Float64(z / Float64(z * Float64(Float64(c / Float64(a * -4.0)) / t)));
	elseif (t <= 7.6e+53)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c) / z);
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.9e+156)
		tmp = z / (z * ((c / (a * -4.0)) / t));
	elseif (t <= 7.6e+53)
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.9e+156], N[(z / N[(z * N[(N[(c / N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+53], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000012e156

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 72.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 68.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 64.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   6. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   7. Taylor expanded in a around inf 57.7%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto \frac{1}{z} \cdot \left(-4 \cdot \frac{a \cdot \color{blue}{\left(z \cdot t\right)}}{c}\right) \]

      2. associate-*r/ 57.7%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{-4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c}} \]

      3. metadata-eval 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(-4\right)} \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c} \]

      4. distribute-lft-neg-in 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{-4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}}{c} \]

      5. distribute-lft-neg-in 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(-4\right) \cdot \left(a \cdot \left(z \cdot t\right)\right)}}{c} \]

      6. metadata-eval 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{-4} \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c} \]

      7. associate-*r* 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(-4 \cdot a\right) \cdot \left(z \cdot t\right)}}{c} \]

      8. *-commutative 57.7%

         \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{\left(z \cdot t\right) \cdot \left(-4 \cdot a\right)}}{c} \]

      9. associate-/l* 61.5%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z \cdot t}{\frac{c}{-4 \cdot a}}} \]

   9. Simplified 61.5%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z \cdot t}{\frac{c}{-4 \cdot a}}} \]
   10. Step-by-step derivation

       1. associate-/l* 69.3%

          \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{z}{\frac{\frac{c}{-4 \cdot a}}{t}}} \]

       2. frac-times 87.8%

          \[\leadsto \color{blue}{\frac{1 \cdot z}{z \cdot \frac{\frac{c}{-4 \cdot a}}{t}}} \]

       3. *-un-lft-identity 87.8%

          \[\leadsto \frac{\color{blue}{z}}{z \cdot \frac{\frac{c}{-4 \cdot a}}{t}} \]

       4. *-commutative 87.8%

          \[\leadsto \frac{z}{z \cdot \frac{\frac{c}{\color{blue}{a \cdot -4}}}{t}} \]

   11. Applied egg-rr 87.8%

       \[\leadsto \color{blue}{\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}} \]

   if -1.90000000000000012e156 < t < 7.59999999999999995e53

   1. Initial program 80.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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. *-commutative 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 76.3%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 76.3%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 76.3%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 76.3%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 73.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 71.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 71.5%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 71.5%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 71.5%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in z around 0 71.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]

   9. Taylor expanded in c around 0 75.6%

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]
   10. Step-by-step derivation

       1. associate-*r* 75.6%

          \[\leadsto \frac{\frac{b + \color{blue}{\left(9 \cdot x\right) \cdot y}}{c}}{z} \]

   11. Simplified 75.6%

       \[\leadsto \frac{\color{blue}{\frac{b + \left(9 \cdot x\right) \cdot y}{c}}}{z} \]

   if 7.59999999999999995e53 < t

   1. Initial program 75.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 75.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 45.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 59.6%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+156}:\\ \;\;\;\;\frac{z}{z \cdot \frac{\frac{c}{a \cdot -4}}{t}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+26} \lor \neg \left(b \leq 1.2 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.45e+26) (not (<= b 1.2e-18)))
   (/ (/ b c) z)
   (* -4.0 (/ (* a t) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.45e+26) || !(b <= 1.2e-18)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if ((b <= (-1.45d+26)) .or. (.not. (b <= 1.2d-18))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.45e+26) || !(b <= 1.2e-18)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.45e+26) or not (b <= 1.2e-18):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.45e+26) || !(b <= 1.2e-18))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.45e+26) || ~((b <= 1.2e-18)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.45e+26], N[Not[LessEqual[b, 1.2e-18]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.45e26 or 1.19999999999999997e-18 < b

   1. Initial program 77.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 72.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 77.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 51.2%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 51.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   10. Step-by-step derivation

       1. *-commutative 51.2%

          \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

       2. div-inv 51.2%

          \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

       3. associate-/r* 53.6%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   11. Applied egg-rr 53.6%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -1.45e26 < b < 1.19999999999999997e-18

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      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. *-commutative 78.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 46.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+26} \lor \neg \left(b \leq 1.2 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-80} \lor \neg \left(t \leq 3.6 \cdot 10^{-73}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.4e-80) (not (<= t 3.6e-73)))
   (* -4.0 (/ a (/ c t)))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.4e-80) || !(t <= 3.6e-73)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if ((t <= (-3.4d-80)) .or. (.not. (t <= 3.6d-73))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.4e-80) || !(t <= 3.6e-73)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.4e-80) or not (t <= 3.6e-73):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.4e-80) || !(t <= 3.6e-73))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3.4e-80) || ~((t <= 3.6e-73)))
		tmp = -4.0 * (a / (c / t));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.4e-80], N[Not[LessEqual[t, 3.6e-73]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e-80 or 3.5999999999999999e-73 < t

   1. Initial program 75.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 75.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 43.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 50.9%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 50.9%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -3.4000000000000001e-80 < t < 3.5999999999999999e-73

   1. Initial program 81.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 72.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 82.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 48.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-80} \lor \neg \left(t \leq 3.6 \cdot 10^{-73}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 2e-121) (/ (/ b c) z) (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 2e-121) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    if (a <= 2d-121) then
        tmp = (b / c) / z
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 2e-121) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 2e-121:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 2e-121)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 2e-121)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 2e-121], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2e-121

   1. Initial program 76.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 75.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 76.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 34.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 34.1%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 34.1%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   10. Step-by-step derivation

       1. *-commutative 34.1%

          \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

       2. div-inv 34.2%

          \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

       3. associate-/r* 35.3%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   11. Applied egg-rr 35.3%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if 2e-121 < a

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 75.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 31.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 31.7%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.0%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.0%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 75.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 75.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 75.5%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 75.5%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 78.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 78.0%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 77.9%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 77.9%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 33.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 33.3%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 33.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 33.3%

   \[\leadsto \frac{b}{z \cdot c} \]
9. Add Preprocessing

Developer target: 80.6% 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 2024019 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))