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

Percentage Accurate: 79.0% → 90.8%

Time: 18.3s

Alternatives: 21

Speedup: 0.8×

• 36.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\\ \mathbf{if}\;z \leq -3.65 \cdot 10^{+46}:\\ \;\;\;\;\frac{t_1 + {\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}{c}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-82}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma x (* 9.0 y) b) z)))
   (if (<= z -3.65e+46)
     (/ (+ t_1 (pow (cbrt (* (* t a) -4.0)) 3.0)) c)
     (if (<= z 4.7e-82)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ t_1 (* t (* a -4.0))) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (9.0 * y), b) / z;
	double tmp;
	if (z <= -3.65e+46) {
		tmp = (t_1 + pow(cbrt(((t * a) * -4.0)), 3.0)) / c;
	} else if (z <= 4.7e-82) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (t * (a * -4.0))) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(9.0 * y), b) / z)
	tmp = 0.0
	if (z <= -3.65e+46)
		tmp = Float64(Float64(t_1 + (cbrt(Float64(Float64(t * a) * -4.0)) ^ 3.0)) / c);
	elseif (z <= 4.7e-82)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(t * Float64(a * -4.0))) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -3.65e+46], N[(N[(t$95$1 + N[Power[N[Power[N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 4.7e-82], 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], N[(N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.65000000000000014e46

   1. Initial program 60.4%

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

      1. associate-/r* 75.4%

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

   3. Simplified 88.6%

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

      1. add-cube-cbrt 88.1%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 88.2%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 89.7%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 89.7%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   if -3.65000000000000014e46 < z < 4.7000000000000001e-82

   1. Initial program 95.7%

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

   if 4.7000000000000001e-82 < z

   1. Initial program 63.8%

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

      1. associate-/r* 70.4%

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

   3. Simplified 83.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}{c}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-82}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 2: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-131}:\\ \;\;\;\;\frac{t_2 + {\left(\frac{z}{t_1}\right)}^{-1}}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_1}{z} + t_2}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma x (* 9.0 y) b)) (t_2 (* t (* a -4.0))))
   (if (<= z -6e-131)
     (/ (+ t_2 (pow (/ z t_1) -1.0)) c)
     (if (<= z 5e-81)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ (/ t_1 z) t_2) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (9.0 * y), b);
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -6e-131) {
		tmp = (t_2 + pow((z / t_1), -1.0)) / c;
	} else if (z <= 5e-81) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((t_1 / z) + t_2) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(x, Float64(9.0 * y), b)
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -6e-131)
		tmp = Float64(Float64(t_2 + (Float64(z / t_1) ^ -1.0)) / c);
	elseif (z <= 5e-81)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t_1 / z) + t_2) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-131], N[(N[(t$95$2 + N[Power[N[(z / t$95$1), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 5e-81], 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], N[(N[(N[(t$95$1 / z), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999992e-131

   1. Initial program 73.5%

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

      1. associate-/r* 83.1%

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

   3. Simplified 91.5%

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

      1. clear-num 91.6%

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

      2. inv-pow 91.6%

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

   5. Applied egg-rr 91.6%

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

   if -5.99999999999999992e-131 < z < 4.99999999999999981e-81

   1. Initial program 95.3%

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

   if 4.99999999999999981e-81 < z

   1. Initial program 63.8%

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

      1. associate-/r* 70.4%

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

   3. Simplified 83.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-131}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + {\left(\frac{z}{\mathsf{fma}\left(x, 9 \cdot y, b\right)}\right)}^{-1}}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 3: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+50} \lor \neg \left(z \leq 2.2 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1e+50) (not (<= z 2.2e-81)))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e+50) || !(z <= 2.2e-81)) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1e+50) || !(z <= 2.2e-81))
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / 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

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1e+50], N[Not[LessEqual[z, 2.2e-81]], $MachinePrecision]], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $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 < -1.0000000000000001e50 or 2.1999999999999999e-81 < z

   1. Initial program 62.3%

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

      1. associate-/r* 72.5%

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

   3. Simplified 85.9%

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

   if -1.0000000000000001e50 < z < 2.1999999999999999e-81

   1. Initial program 95.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+50} \lor \neg \left(z \leq 2.2 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 4: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-319}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-249}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 10^{-128}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t_2 \leq 4:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* x 9.0) (* z (/ c y))))
        (t_2 (* y (* x 9.0)))
        (t_3 (* -4.0 (* t (/ a c)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-12)
       (* (/ 9.0 z) (/ (* x y) c))
       (if (<= t_2 -1e-319)
         t_3
         (if (<= t_2 2e-249)
           (* b (/ (/ 1.0 z) c))
           (if (<= t_2 1e-128)
             (* -4.0 (* a (/ t c)))
             (if (<= t_2 4.0)
               (/ (/ b c) z)
               (if (<= t_2 2e+110) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) / (z * (c / y));
	double t_2 = y * (x * 9.0);
	double t_3 = -4.0 * (t * (a / c));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-12) {
		tmp = (9.0 / z) * ((x * y) / c);
	} else if (t_2 <= -1e-319) {
		tmp = t_3;
	} else if (t_2 <= 2e-249) {
		tmp = b * ((1.0 / z) / c);
	} else if (t_2 <= 1e-128) {
		tmp = -4.0 * (a * (t / c));
	} else if (t_2 <= 4.0) {
		tmp = (b / c) / z;
	} else if (t_2 <= 2e+110) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) / (z * (c / y));
	double t_2 = y * (x * 9.0);
	double t_3 = -4.0 * (t * (a / c));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-12) {
		tmp = (9.0 / z) * ((x * y) / c);
	} else if (t_2 <= -1e-319) {
		tmp = t_3;
	} else if (t_2 <= 2e-249) {
		tmp = b * ((1.0 / z) / c);
	} else if (t_2 <= 1e-128) {
		tmp = -4.0 * (a * (t / c));
	} else if (t_2 <= 4.0) {
		tmp = (b / c) / z;
	} else if (t_2 <= 2e+110) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) / (z * (c / y))
	t_2 = y * (x * 9.0)
	t_3 = -4.0 * (t * (a / c))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-12:
		tmp = (9.0 / z) * ((x * y) / c)
	elif t_2 <= -1e-319:
		tmp = t_3
	elif t_2 <= 2e-249:
		tmp = b * ((1.0 / z) / c)
	elif t_2 <= 1e-128:
		tmp = -4.0 * (a * (t / c))
	elif t_2 <= 4.0:
		tmp = (b / c) / z
	elif t_2 <= 2e+110:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) / Float64(z * Float64(c / y)))
	t_2 = Float64(y * Float64(x * 9.0))
	t_3 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-12)
		tmp = Float64(Float64(9.0 / z) * Float64(Float64(x * y) / c));
	elseif (t_2 <= -1e-319)
		tmp = t_3;
	elseif (t_2 <= 2e-249)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (t_2 <= 1e-128)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (t_2 <= 4.0)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_2 <= 2e+110)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) / (z * (c / y));
	t_2 = y * (x * 9.0);
	t_3 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-12)
		tmp = (9.0 / z) * ((x * y) / c);
	elseif (t_2 <= -1e-319)
		tmp = t_3;
	elseif (t_2 <= 2e-249)
		tmp = b * ((1.0 / z) / c);
	elseif (t_2 <= 1e-128)
		tmp = -4.0 * (a * (t / c));
	elseif (t_2 <= 4.0)
		tmp = (b / c) / z;
	elseif (t_2 <= 2e+110)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-12], N[(N[(9.0 / z), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-319], t$95$3, If[LessEqual[t$95$2, 2e-249], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-128], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 2e+110], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 x 9) y) < -inf.0 or 2e110 < (*.f64 (*.f64 x 9) y)

   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-/r* 71.9%

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

   3. Simplified 70.3%

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

      1. add-cube-cbrt 70.3%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 70.2%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 70.2%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 70.2%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in x around inf 66.8%

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

      1. times-frac 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*l* 81.2%

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

   8. Simplified 81.2%

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

      1. clear-num 81.1%

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

      2. associate-*l/ 81.1%

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

      3. frac-times 82.6%

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

      4. *-un-lft-identity 82.6%

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

   10. Applied egg-rr 82.6%

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

   if -inf.0 < (*.f64 (*.f64 x 9) y) < -4.9999999999999997e-12

   1. Initial program 79.3%

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

      1. associate-*l* 79.2%

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

      2. associate-*l* 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in x around inf 50.5%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. *-commutative 50.4%

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

   6. Applied egg-rr 50.4%

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

      1. times-frac 54.1%

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

   8. Applied egg-rr 54.1%

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

   if -4.9999999999999997e-12 < (*.f64 (*.f64 x 9) y) < -9.99989e-320 or 4 < (*.f64 (*.f64 x 9) y) < 2e110

   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%

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

      2. 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. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-/l* 58.4%

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

      3. associate-/r/ 64.3%

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

   6. Simplified 64.3%

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

   if -9.99989e-320 < (*.f64 (*.f64 x 9) y) < 2.00000000000000011e-249

   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%

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

      2. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in b around inf 60.5%

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

      1. *-commutative 60.5%

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

   6. Simplified 60.5%

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

      1. div-inv 60.4%

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

      2. associate-/r* 60.6%

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

   8. Applied egg-rr 60.6%

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

   if 2.00000000000000011e-249 < (*.f64 (*.f64 x 9) y) < 1.00000000000000005e-128

   1. Initial program 81.3%

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

      1. associate-*l* 81.3%

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

      2. associate-*l* 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in z around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-/l* 74.5%

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

      3. associate-/r/ 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in a around 0 73.4%

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

      1. expm1-log1p-u 18.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)\right)} \cdot -4 \]

      2. expm1-udef 10.0%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)} - 1\right)} \cdot -4 \]

      3. associate-/l* 10.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{c}{t}}}\right)} - 1\right) \cdot -4 \]

   9. Applied egg-rr 10.0%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)} - 1\right)} \cdot -4 \]
   10. Step-by-step derivation

       1. expm1-def 18.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)\right)} \cdot -4 \]

       2. expm1-log1p 74.5%

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

       3. associate-/l* 73.4%

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

       4. associate-*r/ 74.6%

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

   11. Simplified 74.6%

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

   if 1.00000000000000005e-128 < (*.f64 (*.f64 x 9) y) < 4

   1. Initial program 83.8%

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

      1. associate-/r* 78.7%

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

   3. Simplified 83.9%

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

      1. add-cube-cbrt 83.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 83.9%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 83.9%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 83.9%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in b around inf 61.5%

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

      1. associate-/r* 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -\infty:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{-249}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-128}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+110}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 5: 79.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ t_3 := t \cdot \left(a \cdot -4\right)\\ t_4 := \frac{t_3 + \frac{9}{\frac{z}{x \cdot y}}}{c}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-12}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 10^{+54}:\\ \;\;\;\;\frac{t_3 + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+202}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* x 9.0) (* z (/ c y))))
        (t_2 (* y (* x 9.0)))
        (t_3 (* t (* a -4.0)))
        (t_4 (/ (+ t_3 (/ 9.0 (/ z (* x y)))) c)))
   (if (<= t_2 -1e+292)
     t_1
     (if (<= t_2 -5e-12)
       t_4
       (if (<= t_2 1e+54)
         (/ (+ t_3 (/ b z)) c)
         (if (<= t_2 1e+202) t_4 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) / (z * (c / y));
	double t_2 = y * (x * 9.0);
	double t_3 = t * (a * -4.0);
	double t_4 = (t_3 + (9.0 / (z / (x * y)))) / c;
	double tmp;
	if (t_2 <= -1e+292) {
		tmp = t_1;
	} else if (t_2 <= -5e-12) {
		tmp = t_4;
	} else if (t_2 <= 1e+54) {
		tmp = (t_3 + (b / z)) / c;
	} else if (t_2 <= 1e+202) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (x * 9.0d0) / (z * (c / y))
    t_2 = y * (x * 9.0d0)
    t_3 = t * (a * (-4.0d0))
    t_4 = (t_3 + (9.0d0 / (z / (x * y)))) / c
    if (t_2 <= (-1d+292)) then
        tmp = t_1
    else if (t_2 <= (-5d-12)) then
        tmp = t_4
    else if (t_2 <= 1d+54) then
        tmp = (t_3 + (b / z)) / c
    else if (t_2 <= 1d+202) then
        tmp = t_4
    else
        tmp = t_1
    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 = (x * 9.0) / (z * (c / y));
	double t_2 = y * (x * 9.0);
	double t_3 = t * (a * -4.0);
	double t_4 = (t_3 + (9.0 / (z / (x * y)))) / c;
	double tmp;
	if (t_2 <= -1e+292) {
		tmp = t_1;
	} else if (t_2 <= -5e-12) {
		tmp = t_4;
	} else if (t_2 <= 1e+54) {
		tmp = (t_3 + (b / z)) / c;
	} else if (t_2 <= 1e+202) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) / (z * (c / y))
	t_2 = y * (x * 9.0)
	t_3 = t * (a * -4.0)
	t_4 = (t_3 + (9.0 / (z / (x * y)))) / c
	tmp = 0
	if t_2 <= -1e+292:
		tmp = t_1
	elif t_2 <= -5e-12:
		tmp = t_4
	elif t_2 <= 1e+54:
		tmp = (t_3 + (b / z)) / c
	elif t_2 <= 1e+202:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) / Float64(z * Float64(c / y)))
	t_2 = Float64(y * Float64(x * 9.0))
	t_3 = Float64(t * Float64(a * -4.0))
	t_4 = Float64(Float64(t_3 + Float64(9.0 / Float64(z / Float64(x * y)))) / c)
	tmp = 0.0
	if (t_2 <= -1e+292)
		tmp = t_1;
	elseif (t_2 <= -5e-12)
		tmp = t_4;
	elseif (t_2 <= 1e+54)
		tmp = Float64(Float64(t_3 + Float64(b / z)) / c);
	elseif (t_2 <= 1e+202)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) / (z * (c / y));
	t_2 = y * (x * 9.0);
	t_3 = t * (a * -4.0);
	t_4 = (t_3 + (9.0 / (z / (x * y)))) / c;
	tmp = 0.0;
	if (t_2 <= -1e+292)
		tmp = t_1;
	elseif (t_2 <= -5e-12)
		tmp = t_4;
	elseif (t_2 <= 1e+54)
		tmp = (t_3 + (b / z)) / c;
	elseif (t_2 <= 1e+202)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(9.0 / N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+292], t$95$1, If[LessEqual[t$95$2, -5e-12], t$95$4, If[LessEqual[t$95$2, 1e+54], N[(N[(t$95$3 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 1e+202], t$95$4, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -1e292 or 9.999999999999999e201 < (*.f64 (*.f64 x 9) y)

   1. Initial program 72.2%

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

      1. associate-/r* 69.0%

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

   3. Simplified 65.3%

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

      1. add-cube-cbrt 65.3%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 65.3%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 65.3%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 65.3%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in x around inf 70.4%

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

      1. times-frac 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*l* 90.9%

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

   8. Simplified 90.9%

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

      1. clear-num 90.8%

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

      2. associate-*l/ 90.8%

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

      3. frac-times 90.7%

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

      4. *-un-lft-identity 90.7%

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

   10. Applied egg-rr 90.7%

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

   if -1e292 < (*.f64 (*.f64 x 9) y) < -4.9999999999999997e-12 or 1.0000000000000001e54 < (*.f64 (*.f64 x 9) y) < 9.999999999999999e201

   1. Initial program 77.7%

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

      1. associate-/r* 76.5%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 76.6%

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

      1. associate-*r/ 76.6%

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

      2. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   if -4.9999999999999997e-12 < (*.f64 (*.f64 x 9) y) < 1.0000000000000001e54

   1. Initial program 80.1%

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

      1. associate-/r* 81.9%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around 0 86.1%

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

      1. associate-*r* 85.4%

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

      2. *-commutative 85.4%

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

      3. *-commutative 85.4%

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

   6. Simplified 85.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+292}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{9}{\frac{z}{x \cdot y}}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+54}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+202}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{9}{\frac{z}{x \cdot y}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 6: 47.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c))))
        (t_2 (/ (/ b c) z))
        (t_3 (* 9.0 (* (/ x z) (/ y c)))))
   (if (<= x -4.1e+114)
     (* (/ 9.0 z) (/ (* x y) c))
     (if (<= x -1.9e+71)
       t_2
       (if (<= x -4.3e+60)
         t_3
         (if (<= x -8.6e-26)
           t_1
           (if (<= x -4.5e-128)
             (* b (/ (/ 1.0 z) c))
             (if (<= x 8.5e-299)
               (* -4.0 (/ a (/ c t)))
               (if (<= x 2.05e-209) t_2 (if (<= x 8e-43) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double t_2 = (b / c) / z;
	double t_3 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -4.1e+114) {
		tmp = (9.0 / z) * ((x * y) / c);
	} else if (x <= -1.9e+71) {
		tmp = t_2;
	} else if (x <= -4.3e+60) {
		tmp = t_3;
	} else if (x <= -8.6e-26) {
		tmp = t_1;
	} else if (x <= -4.5e-128) {
		tmp = b * ((1.0 / z) / c);
	} else if (x <= 8.5e-299) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 2.05e-209) {
		tmp = t_2;
	} else if (x <= 8e-43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    t_2 = (b / c) / z
    t_3 = 9.0d0 * ((x / z) * (y / c))
    if (x <= (-4.1d+114)) then
        tmp = (9.0d0 / z) * ((x * y) / c)
    else if (x <= (-1.9d+71)) then
        tmp = t_2
    else if (x <= (-4.3d+60)) then
        tmp = t_3
    else if (x <= (-8.6d-26)) then
        tmp = t_1
    else if (x <= (-4.5d-128)) then
        tmp = b * ((1.0d0 / z) / c)
    else if (x <= 8.5d-299) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (x <= 2.05d-209) then
        tmp = t_2
    else if (x <= 8d-43) then
        tmp = t_1
    else
        tmp = t_3
    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 = -4.0 * (t * (a / c));
	double t_2 = (b / c) / z;
	double t_3 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -4.1e+114) {
		tmp = (9.0 / z) * ((x * y) / c);
	} else if (x <= -1.9e+71) {
		tmp = t_2;
	} else if (x <= -4.3e+60) {
		tmp = t_3;
	} else if (x <= -8.6e-26) {
		tmp = t_1;
	} else if (x <= -4.5e-128) {
		tmp = b * ((1.0 / z) / c);
	} else if (x <= 8.5e-299) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 2.05e-209) {
		tmp = t_2;
	} else if (x <= 8e-43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	t_2 = (b / c) / z
	t_3 = 9.0 * ((x / z) * (y / c))
	tmp = 0
	if x <= -4.1e+114:
		tmp = (9.0 / z) * ((x * y) / c)
	elif x <= -1.9e+71:
		tmp = t_2
	elif x <= -4.3e+60:
		tmp = t_3
	elif x <= -8.6e-26:
		tmp = t_1
	elif x <= -4.5e-128:
		tmp = b * ((1.0 / z) / c)
	elif x <= 8.5e-299:
		tmp = -4.0 * (a / (c / t))
	elif x <= 2.05e-209:
		tmp = t_2
	elif x <= 8e-43:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	t_2 = Float64(Float64(b / c) / z)
	t_3 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (x <= -4.1e+114)
		tmp = Float64(Float64(9.0 / z) * Float64(Float64(x * y) / c));
	elseif (x <= -1.9e+71)
		tmp = t_2;
	elseif (x <= -4.3e+60)
		tmp = t_3;
	elseif (x <= -8.6e-26)
		tmp = t_1;
	elseif (x <= -4.5e-128)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (x <= 8.5e-299)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (x <= 2.05e-209)
		tmp = t_2;
	elseif (x <= 8e-43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	t_2 = (b / c) / z;
	t_3 = 9.0 * ((x / z) * (y / c));
	tmp = 0.0;
	if (x <= -4.1e+114)
		tmp = (9.0 / z) * ((x * y) / c);
	elseif (x <= -1.9e+71)
		tmp = t_2;
	elseif (x <= -4.3e+60)
		tmp = t_3;
	elseif (x <= -8.6e-26)
		tmp = t_1;
	elseif (x <= -4.5e-128)
		tmp = b * ((1.0 / z) / c);
	elseif (x <= 8.5e-299)
		tmp = -4.0 * (a / (c / t));
	elseif (x <= 2.05e-209)
		tmp = t_2;
	elseif (x <= 8e-43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+114], N[(N[(9.0 / z), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e+71], t$95$2, If[LessEqual[x, -4.3e+60], t$95$3, If[LessEqual[x, -8.6e-26], t$95$1, If[LessEqual[x, -4.5e-128], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-299], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-209], t$95$2, If[LessEqual[x, 8e-43], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.1000000000000001e114

   1. Initial program 74.2%

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

      1. associate-*l* 74.1%

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

      2. associate-*l* 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. associate-*r/ 61.4%

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

      2. *-commutative 61.4%

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

      3. *-commutative 61.4%

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

   6. Applied egg-rr 61.4%

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

      1. times-frac 65.7%

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

   8. Applied egg-rr 65.7%

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

   if -4.1000000000000001e114 < x < -1.9e71 or 8.5e-299 < x < 2.04999999999999989e-209

   1. Initial program 80.0%

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

      1. associate-/r* 76.4%

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

   3. Simplified 72.3%

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

      1. add-cube-cbrt 72.1%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 72.1%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 72.1%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 72.1%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in b around inf 55.1%

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

      1. associate-/r* 59.3%

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

   8. Simplified 59.3%

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

   if -1.9e71 < x < -4.29999999999999971e60 or 8.00000000000000062e-43 < x

   1. Initial program 77.4%

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

      1. associate-/r* 77.6%

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

   3. Simplified 82.9%

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

      1. add-cube-cbrt 82.7%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 82.7%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 84.0%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 84.0%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in x around inf 46.0%

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

      1. times-frac 48.6%

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

   8. Simplified 48.6%

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

   if -4.29999999999999971e60 < x < -8.59999999999999976e-26 or 2.04999999999999989e-209 < x < 8.00000000000000062e-43

   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%

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

      2. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 54.9%

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

      3. associate-/r/ 60.6%

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

   6. Simplified 60.6%

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

   if -8.59999999999999976e-26 < x < -4.4999999999999999e-128

   1. Initial program 82.1%

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

      1. associate-*l* 81.8%

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

      2. associate-*l* 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

      1. div-inv 45.2%

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

      2. associate-/r* 45.3%

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

   8. Applied egg-rr 45.3%

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

   if -4.4999999999999999e-128 < x < 8.5e-299

   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%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-26}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 7: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + \frac{b}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+151}:\\ \;\;\;\;\frac{1}{c} \cdot t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* t (* a -4.0)) (/ b z))))
   (if (<= z -2.2e+151)
     (* (/ 1.0 c) t_1)
     (if (<= z 2.8e+114)
       (/ (+ b (- (* x (* 9.0 y)) (* (* t a) (* z 4.0)))) (* z c))
       (/ t_1 c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -2.2e+151) {
		tmp = (1.0 / c) * t_1;
	} else if (z <= 2.8e+114) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (z * c);
	} else {
		tmp = t_1 / c;
	}
	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) :: tmp
    t_1 = (t * (a * (-4.0d0))) + (b / z)
    if (z <= (-2.2d+151)) then
        tmp = (1.0d0 / c) * t_1
    else if (z <= 2.8d+114) then
        tmp = (b + ((x * (9.0d0 * y)) - ((t * a) * (z * 4.0d0)))) / (z * c)
    else
        tmp = t_1 / c
    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 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -2.2e+151) {
		tmp = (1.0 / c) * t_1;
	} else if (z <= 2.8e+114) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (z * c);
	} else {
		tmp = t_1 / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * (a * -4.0)) + (b / z)
	tmp = 0
	if z <= -2.2e+151:
		tmp = (1.0 / c) * t_1
	elif z <= 2.8e+114:
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (z * c)
	else:
		tmp = t_1 / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z))
	tmp = 0.0
	if (z <= -2.2e+151)
		tmp = Float64(Float64(1.0 / c) * t_1);
	elseif (z <= 2.8e+114)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(t * a) * Float64(z * 4.0)))) / Float64(z * c));
	else
		tmp = Float64(t_1 / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * (a * -4.0)) + (b / z);
	tmp = 0.0;
	if (z <= -2.2e+151)
		tmp = (1.0 / c) * t_1;
	elseif (z <= 2.8e+114)
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (z * c);
	else
		tmp = t_1 / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+151], N[(N[(1.0 / c), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[z, 2.8e+114], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000007e151

   1. Initial program 46.1%

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

      1. associate-/r* 66.7%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in x around 0 83.3%

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

      1. associate-*r* 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

   6. Simplified 80.0%

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

      1. div-inv 80.0%

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

      2. associate-*r* 83.3%

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

      3. add-cube-cbrt 82.9%

         \[\leadsto \left(\frac{b}{z} + \color{blue}{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4} \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}\right) \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}}\right) \cdot \frac{1}{c} \]

      4. unpow3 82.8%

         \[\leadsto \left(\frac{b}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}\right) \cdot \frac{1}{c} \]

      5. +-commutative 82.8%

         \[\leadsto \color{blue}{\left({\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      6. unpow3 82.9%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4} \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}\right) \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}} + \frac{b}{z}\right) \cdot \frac{1}{c} \]

      7. add-cube-cbrt 83.3%

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

      8. associate-*r* 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -2.20000000000000007e151 < z < 2.8e114

   1. Initial program 89.4%

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

      1. associate-*l* 89.4%

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

      2. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   if 2.8e114 < z

   1. Initial program 48.0%

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

      1. associate-/r* 60.3%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 80.9%

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

      1. associate-*r* 80.9%

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

      2. *-commutative 80.9%

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

      3. *-commutative 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+151}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b}{z}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 8: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + \frac{b}{z}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+151}:\\ \;\;\;\;\frac{1}{c} \cdot t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* t (* a -4.0)) (/ b z))))
   (if (<= z -2.15e+151)
     (* (/ 1.0 c) t_1)
     (if (<= z 1.4e+114)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       (/ t_1 c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -2.15e+151) {
		tmp = (1.0 / c) * t_1;
	} else if (z <= 1.4e+114) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1 / c;
	}
	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) :: tmp
    t_1 = (t * (a * (-4.0d0))) + (b / z)
    if (z <= (-2.15d+151)) then
        tmp = (1.0d0 / c) * t_1
    else if (z <= 1.4d+114) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = t_1 / c
    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 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -2.15e+151) {
		tmp = (1.0 / c) * t_1;
	} else if (z <= 1.4e+114) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1 / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * (a * -4.0)) + (b / z)
	tmp = 0
	if z <= -2.15e+151:
		tmp = (1.0 / c) * t_1
	elif z <= 1.4e+114:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = t_1 / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z))
	tmp = 0.0
	if (z <= -2.15e+151)
		tmp = Float64(Float64(1.0 / c) * t_1);
	elseif (z <= 1.4e+114)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(t_1 / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * (a * -4.0)) + (b / z);
	tmp = 0.0;
	if (z <= -2.15e+151)
		tmp = (1.0 / c) * t_1;
	elseif (z <= 1.4e+114)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = t_1 / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+151], N[(N[(1.0 / c), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[z, 1.4e+114], 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], N[(t$95$1 / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.14999999999999991e151

   1. Initial program 46.1%

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

      1. associate-/r* 66.7%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in x around 0 83.3%

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

      1. associate-*r* 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

   6. Simplified 80.0%

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

      1. div-inv 80.0%

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

      2. associate-*r* 83.3%

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

      3. add-cube-cbrt 82.9%

         \[\leadsto \left(\frac{b}{z} + \color{blue}{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4} \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}\right) \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}}\right) \cdot \frac{1}{c} \]

      4. unpow3 82.8%

         \[\leadsto \left(\frac{b}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}\right) \cdot \frac{1}{c} \]

      5. +-commutative 82.8%

         \[\leadsto \color{blue}{\left({\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      6. unpow3 82.9%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4} \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}\right) \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}} + \frac{b}{z}\right) \cdot \frac{1}{c} \]

      7. add-cube-cbrt 83.3%

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

      8. associate-*r* 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -2.14999999999999991e151 < z < 1.4e114

   1. Initial program 89.4%

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

   if 1.4e114 < z

   1. Initial program 48.0%

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

      1. associate-/r* 60.3%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 80.9%

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

      1. associate-*r* 80.9%

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

      2. *-commutative 80.9%

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

      3. *-commutative 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+151}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b}{z}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 9: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) - z \cdot \left(\left(t \cdot a\right) \cdot 4\right)\right)}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.2e+45)
   (* (/ 1.0 c) (/ (+ b (- (* x (* 9.0 y)) (* z (* (* t a) 4.0)))) z))
   (if (<= z 1.35e+114)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (/ (+ (* t (* a -4.0)) (/ b z)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.2e+45) {
		tmp = (1.0 / c) * ((b + ((x * (9.0 * y)) - (z * ((t * a) * 4.0)))) / z);
	} else if (z <= 1.35e+114) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	}
	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) :: tmp
    if (z <= (-2.2d+45)) then
        tmp = (1.0d0 / c) * ((b + ((x * (9.0d0 * y)) - (z * ((t * a) * 4.0d0)))) / z)
    else if (z <= 1.35d+114) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    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 tmp;
	if (z <= -2.2e+45) {
		tmp = (1.0 / c) * ((b + ((x * (9.0 * y)) - (z * ((t * a) * 4.0)))) / z);
	} else if (z <= 1.35e+114) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -2.2e+45:
		tmp = (1.0 / c) * ((b + ((x * (9.0 * y)) - (z * ((t * a) * 4.0)))) / z)
	elif z <= 1.35e+114:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.2e+45)
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(Float64(t * a) * 4.0)))) / z));
	elseif (z <= 1.35e+114)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -2.2e+45)
		tmp = (1.0 / c) * ((b + ((x * (9.0 * y)) - (z * ((t * a) * 4.0)))) / z);
	elseif (z <= 1.35e+114)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.2e+45], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+114], 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], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e45

   1. Initial program 60.4%

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

      1. associate-*l* 60.4%

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

      2. associate-*l* 67.0%

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

   3. Simplified 67.0%

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

      1. *-un-lft-identity 67.0%

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

      2. *-commutative 67.0%

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

      3. times-frac 82.2%

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

      4. associate-*r* 82.2%

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

      5. associate-*r* 75.4%

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

      6. associate-*r* 75.4%

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

      7. associate-*r* 82.2%

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

      8. associate-*l* 82.2%

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

   5. Applied egg-rr 82.2%

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

   if -2.2e45 < z < 1.35e114

   1. Initial program 92.3%

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

   if 1.35e114 < z

   1. Initial program 48.0%

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

      1. associate-/r* 60.3%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 80.9%

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

      1. associate-*r* 80.9%

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

      2. *-commutative 80.9%

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

      3. *-commutative 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) - z \cdot \left(\left(t \cdot a\right) \cdot 4\right)\right)}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 10: 48.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.78 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))) (t_2 (* 9.0 (* (/ x z) (/ y c)))))
   (if (<= x -7.8e+87)
     t_2
     (if (<= x -9e-26)
       t_1
       (if (<= x -1.78e-127)
         (* b (/ (/ 1.0 z) c))
         (if (<= x 9e-299)
           (* -4.0 (/ a (/ c t)))
           (if (<= x 1.4e-209) (/ (/ b c) z) (if (<= x 1.6e-41) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double t_2 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -7.8e+87) {
		tmp = t_2;
	} else if (x <= -9e-26) {
		tmp = t_1;
	} else if (x <= -1.78e-127) {
		tmp = b * ((1.0 / z) / c);
	} else if (x <= 9e-299) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 1.4e-209) {
		tmp = (b / c) / z;
	} else if (x <= 1.6e-41) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    t_2 = 9.0d0 * ((x / z) * (y / c))
    if (x <= (-7.8d+87)) then
        tmp = t_2
    else if (x <= (-9d-26)) then
        tmp = t_1
    else if (x <= (-1.78d-127)) then
        tmp = b * ((1.0d0 / z) / c)
    else if (x <= 9d-299) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (x <= 1.4d-209) then
        tmp = (b / c) / z
    else if (x <= 1.6d-41) then
        tmp = t_1
    else
        tmp = 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 = -4.0 * (t * (a / c));
	double t_2 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -7.8e+87) {
		tmp = t_2;
	} else if (x <= -9e-26) {
		tmp = t_1;
	} else if (x <= -1.78e-127) {
		tmp = b * ((1.0 / z) / c);
	} else if (x <= 9e-299) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 1.4e-209) {
		tmp = (b / c) / z;
	} else if (x <= 1.6e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	t_2 = 9.0 * ((x / z) * (y / c))
	tmp = 0
	if x <= -7.8e+87:
		tmp = t_2
	elif x <= -9e-26:
		tmp = t_1
	elif x <= -1.78e-127:
		tmp = b * ((1.0 / z) / c)
	elif x <= 9e-299:
		tmp = -4.0 * (a / (c / t))
	elif x <= 1.4e-209:
		tmp = (b / c) / z
	elif x <= 1.6e-41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	t_2 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (x <= -7.8e+87)
		tmp = t_2;
	elseif (x <= -9e-26)
		tmp = t_1;
	elseif (x <= -1.78e-127)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (x <= 9e-299)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (x <= 1.4e-209)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 1.6e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	t_2 = 9.0 * ((x / z) * (y / c));
	tmp = 0.0;
	if (x <= -7.8e+87)
		tmp = t_2;
	elseif (x <= -9e-26)
		tmp = t_1;
	elseif (x <= -1.78e-127)
		tmp = b * ((1.0 / z) / c);
	elseif (x <= 9e-299)
		tmp = -4.0 * (a / (c / t));
	elseif (x <= 1.4e-209)
		tmp = (b / c) / z;
	elseif (x <= 1.6e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+87], t$95$2, If[LessEqual[x, -9e-26], t$95$1, If[LessEqual[x, -1.78e-127], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-299], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-209], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 1.6e-41], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.80000000000000039e87 or 1.60000000000000006e-41 < x

   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-/r* 74.0%

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

   3. Simplified 78.6%

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

      1. add-cube-cbrt 78.4%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 78.4%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 79.1%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in x around inf 48.4%

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

      1. times-frac 51.0%

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

   8. Simplified 51.0%

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

   if -7.80000000000000039e87 < x < -8.9999999999999998e-26 or 1.40000000000000006e-209 < x < 1.60000000000000006e-41

   1. Initial program 78.9%

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

      1. associate-*l* 78.9%

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

      2. associate-*l* 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in z around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-/l* 51.7%

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

      3. associate-/r/ 56.8%

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

   6. Simplified 56.8%

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

   if -8.9999999999999998e-26 < x < -1.77999999999999992e-127

   1. Initial program 82.1%

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

      1. associate-*l* 81.8%

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

      2. associate-*l* 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

      1. div-inv 45.2%

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

      2. associate-/r* 45.3%

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

   8. Applied egg-rr 45.3%

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

   if -1.77999999999999992e-127 < x < 9.00000000000000006e-299

   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%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   if 9.00000000000000006e-299 < x < 1.40000000000000006e-209

   1. Initial program 75.7%

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

      1. associate-/r* 91.8%

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

   3. Simplified 91.9%

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

      1. add-cube-cbrt 91.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 91.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 91.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 91.8%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in b around inf 59.2%

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

      1. associate-/r* 67.3%

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

   8. Simplified 67.3%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-26}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -1.78 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 11: 47.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= x -2.8e+87)
     (* 9.0 (/ (* x y) (* z c)))
     (if (<= x -3.5e-25)
       t_1
       (if (<= x -6e-128)
         (* b (/ (/ 1.0 z) c))
         (if (<= x 9.5e-299)
           (* -4.0 (/ a (/ c t)))
           (if (<= x 1.6e-209)
             (/ (/ b c) z)
             (if (<= x 6.2e-61) t_1 (* 9.0 (* (/ x z) (/ y c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (x <= -2.8e+87) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (x <= -3.5e-25) {
		tmp = t_1;
	} else if (x <= -6e-128) {
		tmp = b * ((1.0 / z) / c);
	} else if (x <= 9.5e-299) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 1.6e-209) {
		tmp = (b / c) / z;
	} else if (x <= 6.2e-61) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (x <= (-2.8d+87)) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (x <= (-3.5d-25)) then
        tmp = t_1
    else if (x <= (-6d-128)) then
        tmp = b * ((1.0d0 / z) / c)
    else if (x <= 9.5d-299) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (x <= 1.6d-209) then
        tmp = (b / c) / z
    else if (x <= 6.2d-61) then
        tmp = t_1
    else
        tmp = 9.0d0 * ((x / z) * (y / c))
    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 = -4.0 * (t * (a / c));
	double tmp;
	if (x <= -2.8e+87) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (x <= -3.5e-25) {
		tmp = t_1;
	} else if (x <= -6e-128) {
		tmp = b * ((1.0 / z) / c);
	} else if (x <= 9.5e-299) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 1.6e-209) {
		tmp = (b / c) / z;
	} else if (x <= 6.2e-61) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if x <= -2.8e+87:
		tmp = 9.0 * ((x * y) / (z * c))
	elif x <= -3.5e-25:
		tmp = t_1
	elif x <= -6e-128:
		tmp = b * ((1.0 / z) / c)
	elif x <= 9.5e-299:
		tmp = -4.0 * (a / (c / t))
	elif x <= 1.6e-209:
		tmp = (b / c) / z
	elif x <= 6.2e-61:
		tmp = t_1
	else:
		tmp = 9.0 * ((x / z) * (y / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (x <= -2.8e+87)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (x <= -3.5e-25)
		tmp = t_1;
	elseif (x <= -6e-128)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (x <= 9.5e-299)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (x <= 1.6e-209)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 6.2e-61)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (x <= -2.8e+87)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (x <= -3.5e-25)
		tmp = t_1;
	elseif (x <= -6e-128)
		tmp = b * ((1.0 / z) / c);
	elseif (x <= 9.5e-299)
		tmp = -4.0 * (a / (c / t));
	elseif (x <= 1.6e-209)
		tmp = (b / c) / z;
	elseif (x <= 6.2e-61)
		tmp = t_1;
	else
		tmp = 9.0 * ((x / z) * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+87], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-25], t$95$1, If[LessEqual[x, -6e-128], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-299], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-209], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 6.2e-61], t$95$1, N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.80000000000000015e87

   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%

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

      2. associate-*l* 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in x around inf 54.5%

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

   if -2.80000000000000015e87 < x < -3.5000000000000002e-25 or 1.6000000000000001e-209 < x < 6.1999999999999999e-61

   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%

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

      2. 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. Taylor expanded in z around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 52.6%

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

      3. associate-/r/ 57.9%

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

   6. Simplified 57.9%

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

   if -3.5000000000000002e-25 < x < -5.99999999999999956e-128

   1. Initial program 82.1%

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

      1. associate-*l* 81.8%

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

      2. associate-*l* 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

      1. div-inv 45.2%

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

      2. associate-/r* 45.3%

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

   8. Applied egg-rr 45.3%

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

   if -5.99999999999999956e-128 < x < 9.5000000000000001e-299

   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%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   if 9.5000000000000001e-299 < x < 1.6000000000000001e-209

   1. Initial program 75.7%

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

      1. associate-/r* 91.8%

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

   3. Simplified 91.9%

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

      1. add-cube-cbrt 91.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 91.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 91.8%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 91.8%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in b around inf 59.2%

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

      1. associate-/r* 67.3%

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

   8. Simplified 67.3%

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

   if 6.1999999999999999e-61 < x

   1. Initial program 76.8%

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

      1. associate-/r* 77.0%

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

   3. Simplified 82.4%

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

      1. add-cube-cbrt 82.2%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 82.3%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 83.6%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 83.6%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in x around inf 44.5%

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

      1. times-frac 47.2%

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

   8. Simplified 47.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-25}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 12: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+68}:\\ \;\;\;\;-4 \cdot \left(\left(t \cdot a\right) \cdot \frac{1}{c}\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= z -3.4e+14)
     (* -4.0 (* t (/ a c)))
     (if (<= z 1.45e+45)
       t_1
       (if (<= z 6.4e+68)
         (* -4.0 (* (* t a) (/ 1.0 c)))
         (if (<= z 5.2e+134) t_1 (* -4.0 (/ (* t a) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -3.4e+14) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 1.45e+45) {
		tmp = t_1;
	} else if (z <= 6.4e+68) {
		tmp = -4.0 * ((t * a) * (1.0 / c));
	} else if (z <= 5.2e+134) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	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) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    if (z <= (-3.4d+14)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= 1.45d+45) then
        tmp = t_1
    else if (z <= 6.4d+68) then
        tmp = (-4.0d0) * ((t * a) * (1.0d0 / c))
    else if (z <= 5.2d+134) then
        tmp = t_1
    else
        tmp = (-4.0d0) * ((t * a) / c)
    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 + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -3.4e+14) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 1.45e+45) {
		tmp = t_1;
	} else if (z <= 6.4e+68) {
		tmp = -4.0 * ((t * a) * (1.0 / c));
	} else if (z <= 5.2e+134) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if z <= -3.4e+14:
		tmp = -4.0 * (t * (a / c))
	elif z <= 1.45e+45:
		tmp = t_1
	elif z <= 6.4e+68:
		tmp = -4.0 * ((t * a) * (1.0 / c))
	elif z <= 5.2e+134:
		tmp = t_1
	else:
		tmp = -4.0 * ((t * a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (z <= -3.4e+14)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= 1.45e+45)
		tmp = t_1;
	elseif (z <= 6.4e+68)
		tmp = Float64(-4.0 * Float64(Float64(t * a) * Float64(1.0 / c)));
	elseif (z <= 5.2e+134)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (z <= -3.4e+14)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= 1.45e+45)
		tmp = t_1;
	elseif (z <= 6.4e+68)
		tmp = -4.0 * ((t * a) * (1.0 / c));
	elseif (z <= 5.2e+134)
		tmp = t_1;
	else
		tmp = -4.0 * ((t * a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+14], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+45], t$95$1, If[LessEqual[z, 6.4e+68], N[(-4.0 * N[(N[(t * a), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+134], t$95$1, N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4e14

   1. Initial program 64.0%

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

      1. associate-*l* 64.0%

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

      2. associate-*l* 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in z around inf 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-/l* 64.2%

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

      3. associate-/r/ 63.0%

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

   6. Simplified 63.0%

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

   if -3.4e14 < z < 1.4499999999999999e45 or 6.39999999999999989e68 < z < 5.2000000000000003e134

   1. Initial program 92.0%

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

      1. associate-*l* 91.9%

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

      2. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around inf 79.0%

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

   if 1.4499999999999999e45 < z < 6.39999999999999989e68

   1. Initial program 83.7%

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

      1. associate-*l* 83.7%

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

      2. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in z around inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 81.6%

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

      3. associate-/r/ 65.5%

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

   6. Simplified 65.5%

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

   7. Taylor expanded in a around 0 81.6%

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

      1. div-inv 81.6%

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

      2. *-commutative 81.6%

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

   9. Applied egg-rr 81.6%

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

   if 5.2000000000000003e134 < z

   1. Initial program 43.6%

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

      1. associate-*l* 43.6%

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

      2. associate-*l* 46.7%

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

   3. Simplified 46.7%

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

   4. Taylor expanded in z around inf 64.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+68}:\\ \;\;\;\;-4 \cdot \left(\left(t \cdot a\right) \cdot \frac{1}{c}\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]

Alternative 13: 50.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-44}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-290}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-63}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 14000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5.2e-44)
   (* -4.0 (* t (/ a c)))
   (if (<= z 7.6e-290)
     (* 9.0 (/ (* x y) (* z c)))
     (if (<= z 3.7e-63)
       (/ b (* z c))
       (if (<= z 14000000000.0)
         (* (/ x z) (/ (* 9.0 y) c))
         (if (<= z 1.5e+40) (/ (/ b z) c) (* -4.0 (/ (* t a) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.2e-44) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 7.6e-290) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 3.7e-63) {
		tmp = b / (z * c);
	} else if (z <= 14000000000.0) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else if (z <= 1.5e+40) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	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) :: tmp
    if (z <= (-5.2d-44)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= 7.6d-290) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (z <= 3.7d-63) then
        tmp = b / (z * c)
    else if (z <= 14000000000.0d0) then
        tmp = (x / z) * ((9.0d0 * y) / c)
    else if (z <= 1.5d+40) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * ((t * a) / c)
    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 tmp;
	if (z <= -5.2e-44) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 7.6e-290) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 3.7e-63) {
		tmp = b / (z * c);
	} else if (z <= 14000000000.0) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else if (z <= 1.5e+40) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -5.2e-44:
		tmp = -4.0 * (t * (a / c))
	elif z <= 7.6e-290:
		tmp = 9.0 * ((x * y) / (z * c))
	elif z <= 3.7e-63:
		tmp = b / (z * c)
	elif z <= 14000000000.0:
		tmp = (x / z) * ((9.0 * y) / c)
	elif z <= 1.5e+40:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * ((t * a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.2e-44)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= 7.6e-290)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (z <= 3.7e-63)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= 14000000000.0)
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	elseif (z <= 1.5e+40)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -5.2e-44)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= 7.6e-290)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (z <= 3.7e-63)
		tmp = b / (z * c);
	elseif (z <= 14000000000.0)
		tmp = (x / z) * ((9.0 * y) / c);
	elseif (z <= 1.5e+40)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * ((t * a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -5.2e-44], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-290], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-63], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 14000000000.0], N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+40], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.1999999999999996e-44

   1. Initial program 68.0%

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

      1. associate-*l* 68.0%

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

      2. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/l* 61.6%

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

      3. associate-/r/ 60.5%

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

   6. Simplified 60.5%

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

   if -5.1999999999999996e-44 < z < 7.5999999999999995e-290

   1. Initial program 98.0%

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

      1. associate-*l* 97.9%

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

      2. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around inf 62.9%

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

   if 7.5999999999999995e-290 < z < 3.70000000000000012e-63

   1. Initial program 92.8%

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

      1. associate-*l* 92.7%

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

      2. 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. Taylor expanded in b around inf 63.5%

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

      1. *-commutative 63.5%

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

   6. Simplified 63.5%

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

   if 3.70000000000000012e-63 < z < 1.4e10

   1. Initial program 85.0%

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

      1. associate-*l* 84.7%

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

      2. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 55.6%

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

      1. associate-*r/ 55.6%

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

      2. associate-*r* 55.4%

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

      3. times-frac 56.0%

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

      4. *-commutative 56.0%

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

   6. Simplified 56.0%

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

   if 1.4e10 < z < 1.5000000000000001e40

   1. Initial program 79.7%

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

      1. associate-/r* 80.7%

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

   3. Simplified 80.7%

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

      1. add-cube-cbrt 80.7%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)} \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}\right) \cdot \sqrt[3]{t \cdot \left(a \cdot -4\right)}}}{c} \]

      2. pow3 80.7%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{t \cdot \left(a \cdot -4\right)}\right)}^{3}}}{c} \]

      3. associate-*r* 80.7%

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + {\left(\sqrt[3]{\color{blue}{\left(t \cdot a\right) \cdot -4}}\right)}^{3}}{c} \]

   5. Applied egg-rr 80.7%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}}{c} \]

   6. Taylor expanded in b around inf 61.3%

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

   if 1.5000000000000001e40 < z

   1. Initial program 56.6%

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

      1. associate-*l* 56.6%

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

      2. associate-*l* 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in z around inf 56.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-44}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-290}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-63}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 14000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]

Alternative 14: 75.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-51} \lor \neg \left(z \leq 1.75 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1e-51) (not (<= z 1.75e-6)))
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e-51) || !(z <= 1.75e-6)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	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) :: tmp
    if ((z <= (-1d-51)) .or. (.not. (z <= 1.75d-6))) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    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 tmp;
	if ((z <= -1e-51) || !(z <= 1.75e-6)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1e-51) or not (z <= 1.75e-6):
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1e-51) || !(z <= 1.75e-6))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1e-51) || ~((z <= 1.75e-6)))
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1e-51], N[Not[LessEqual[z, 1.75e-6]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-51 or 1.74999999999999997e-6 < z

   1. Initial program 65.2%

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

      1. associate-/r* 75.0%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around 0 77.3%

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

      1. associate-*r* 76.7%

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

      2. *-commutative 76.7%

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

      3. *-commutative 76.7%

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

   6. Simplified 76.7%

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

   if -1e-51 < z < 1.74999999999999997e-6

   1. Initial program 93.8%

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

      1. associate-*l* 93.8%

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

      2. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in x around inf 84.4%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-51} \lor \neg \left(z \leq 1.75 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 15: 75.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + \frac{b}{z}\\ \mathbf{if}\;z \leq -3.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{1}{c} \cdot t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* t (* a -4.0)) (/ b z))))
   (if (<= z -3.65e-50)
     (* (/ 1.0 c) t_1)
     (if (<= z 1.55e-6) (/ (+ b (* 9.0 (* x y))) (* z c)) (/ t_1 c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -3.65e-50) {
		tmp = (1.0 / c) * t_1;
	} else if (z <= 1.55e-6) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1 / c;
	}
	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) :: tmp
    t_1 = (t * (a * (-4.0d0))) + (b / z)
    if (z <= (-3.65d-50)) then
        tmp = (1.0d0 / c) * t_1
    else if (z <= 1.55d-6) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t_1 / c
    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 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -3.65e-50) {
		tmp = (1.0 / c) * t_1;
	} else if (z <= 1.55e-6) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1 / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * (a * -4.0)) + (b / z)
	tmp = 0
	if z <= -3.65e-50:
		tmp = (1.0 / c) * t_1
	elif z <= 1.55e-6:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t_1 / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z))
	tmp = 0.0
	if (z <= -3.65e-50)
		tmp = Float64(Float64(1.0 / c) * t_1);
	elseif (z <= 1.55e-6)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(t_1 / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * (a * -4.0)) + (b / z);
	tmp = 0.0;
	if (z <= -3.65e-50)
		tmp = (1.0 / c) * t_1;
	elseif (z <= 1.55e-6)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t_1 / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.65e-50], N[(N[(1.0 / c), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[z, 1.55e-6], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.65000000000000018e-50

   1. Initial program 68.8%

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

      1. associate-/r* 80.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around 0 78.7%

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

      1. associate-*r* 77.4%

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

      2. *-commutative 77.4%

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

      3. *-commutative 77.4%

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

   6. Simplified 77.4%

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

      1. div-inv 77.5%

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

      2. associate-*r* 78.7%

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

      3. add-cube-cbrt 78.3%

         \[\leadsto \left(\frac{b}{z} + \color{blue}{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4} \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}\right) \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}}\right) \cdot \frac{1}{c} \]

      4. unpow3 78.3%

         \[\leadsto \left(\frac{b}{z} + \color{blue}{{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3}}\right) \cdot \frac{1}{c} \]

      5. +-commutative 78.3%

         \[\leadsto \color{blue}{\left({\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4}\right)}^{3} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      6. unpow3 78.3%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(t \cdot a\right) \cdot -4} \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}\right) \cdot \sqrt[3]{\left(t \cdot a\right) \cdot -4}} + \frac{b}{z}\right) \cdot \frac{1}{c} \]

      7. add-cube-cbrt 78.7%

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

      8. associate-*r* 77.5%

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

   8. Applied egg-rr 77.5%

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

   if -3.65000000000000018e-50 < z < 1.55e-6

   1. Initial program 93.9%

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

      1. associate-*l* 93.8%

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

      2. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in x around inf 84.5%

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

   if 1.55e-6 < z

   1. Initial program 60.4%

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

      1. associate-/r* 68.4%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around 0 75.3%

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

      1. associate-*r* 75.3%

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

      2. *-commutative 75.3%

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

      3. *-commutative 75.3%

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

   6. Simplified 75.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b}{z}\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 16: 47.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-80} \lor \neg \left(a \leq 1.16 \cdot 10^{+64}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -2.4e-80) (not (<= a 1.16e+64)))
   (* -4.0 (/ (* t a) c))
   (/ b (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.4e-80) || !(a <= 1.16e+64)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = b / (z * c);
	}
	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) :: tmp
    if ((a <= (-2.4d-80)) .or. (.not. (a <= 1.16d+64))) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = b / (z * c)
    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 tmp;
	if ((a <= -2.4e-80) || !(a <= 1.16e+64)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -2.4e-80) or not (a <= 1.16e+64):
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -2.4e-80) || !(a <= 1.16e+64))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -2.4e-80) || ~((a <= 1.16e+64)))
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -2.4e-80], N[Not[LessEqual[a, 1.16e+64]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3999999999999999e-80 or 1.16e64 < a

   1. Initial program 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate-*l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around inf 56.6%

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

   if -2.3999999999999999e-80 < a < 1.16e64

   1. Initial program 81.8%

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

      1. associate-*l* 81.7%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in b around inf 48.0%

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

      1. *-commutative 48.0%

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

   6. Simplified 48.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-80} \lor \neg \left(a \leq 1.16 \cdot 10^{+64}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 17: 47.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-80} \lor \neg \left(a \leq 1.15 \cdot 10^{+64}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.45e-80) (not (<= a 1.15e+64)))
   (* -4.0 (/ (* t a) c))
   (* b (/ (/ 1.0 z) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.45e-80) || !(a <= 1.15e+64)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	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) :: tmp
    if ((a <= (-1.45d-80)) .or. (.not. (a <= 1.15d+64))) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = b * ((1.0d0 / z) / c)
    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 tmp;
	if ((a <= -1.45e-80) || !(a <= 1.15e+64)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.45e-80) or not (a <= 1.15e+64):
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = b * ((1.0 / z) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.45e-80) || !(a <= 1.15e+64))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.45e-80) || ~((a <= 1.15e+64)))
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = b * ((1.0 / z) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.45e-80], N[Not[LessEqual[a, 1.15e+64]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.44999999999999999e-80 or 1.15e64 < a

   1. Initial program 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate-*l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around inf 56.6%

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

   if -1.44999999999999999e-80 < a < 1.15e64

   1. Initial program 81.8%

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

      1. associate-*l* 81.7%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in b around inf 48.0%

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

      1. *-commutative 48.0%

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

   6. Simplified 48.0%

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

      1. div-inv 48.6%

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

      2. associate-/r* 48.7%

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

   8. Applied egg-rr 48.7%

      \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{z}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-80} \lor \neg \left(a \leq 1.15 \cdot 10^{+64}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \]

Alternative 18: 48.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -2.5e-113)
   (* -4.0 (* a (/ t c)))
   (if (<= a 3e+64) (* b (/ (/ 1.0 z) c)) (* -4.0 (/ (* t a) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.5e-113) {
		tmp = -4.0 * (a * (t / c));
	} else if (a <= 3e+64) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	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) :: tmp
    if (a <= (-2.5d-113)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (a <= 3d+64) then
        tmp = b * ((1.0d0 / z) / c)
    else
        tmp = (-4.0d0) * ((t * a) / c)
    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 tmp;
	if (a <= -2.5e-113) {
		tmp = -4.0 * (a * (t / c));
	} else if (a <= 3e+64) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.5e-113:
		tmp = -4.0 * (a * (t / c))
	elif a <= 3e+64:
		tmp = b * ((1.0 / z) / c)
	else:
		tmp = -4.0 * ((t * a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.5e-113)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (a <= 3e+64)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.5e-113)
		tmp = -4.0 * (a * (t / c));
	elseif (a <= 3e+64)
		tmp = b * ((1.0 / z) / c);
	else
		tmp = -4.0 * ((t * a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.5e-113], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+64], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4999999999999999e-113

   1. Initial program 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate-*l* 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. associate-/l* 53.5%

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

      3. associate-/r/ 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in a around 0 50.4%

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

      1. expm1-log1p-u 31.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)\right)} \cdot -4 \]

      2. expm1-udef 24.4%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)} - 1\right)} \cdot -4 \]

      3. associate-/l* 27.1%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{c}{t}}}\right)} - 1\right) \cdot -4 \]

   9. Applied egg-rr 27.1%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)} - 1\right)} \cdot -4 \]
   10. Step-by-step derivation

       1. expm1-def 31.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)\right)} \cdot -4 \]

       2. expm1-log1p 53.5%

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

       3. associate-/l* 50.4%

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

       4. associate-*r/ 53.5%

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

   11. Simplified 53.5%

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

   if -2.4999999999999999e-113 < a < 3.0000000000000002e64

   1. Initial program 82.1%

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

      1. associate-*l* 82.0%

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

      2. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in b around inf 48.7%

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

      1. *-commutative 48.7%

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

   6. Simplified 48.7%

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

      1. div-inv 49.4%

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

      2. associate-/r* 49.5%

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

   8. Applied egg-rr 49.5%

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

   if 3.0000000000000002e64 < a

   1. Initial program 75.0%

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

      1. associate-*l* 75.0%

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

      2. associate-*l* 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 61.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]

Alternative 19: 49.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -2.5e-113)
   (* -4.0 (* a (/ t c)))
   (if (<= a 2.9e+38) (* b (/ (/ 1.0 z) c)) (* -4.0 (* t (/ a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.5e-113) {
		tmp = -4.0 * (a * (t / c));
	} else if (a <= 2.9e+38) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	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) :: tmp
    if (a <= (-2.5d-113)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (a <= 2.9d+38) then
        tmp = b * ((1.0d0 / z) / c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    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 tmp;
	if (a <= -2.5e-113) {
		tmp = -4.0 * (a * (t / c));
	} else if (a <= 2.9e+38) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.5e-113:
		tmp = -4.0 * (a * (t / c))
	elif a <= 2.9e+38:
		tmp = b * ((1.0 / z) / c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.5e-113)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (a <= 2.9e+38)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.5e-113)
		tmp = -4.0 * (a * (t / c));
	elseif (a <= 2.9e+38)
		tmp = b * ((1.0 / z) / c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.5e-113], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+38], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4999999999999999e-113

   1. Initial program 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate-*l* 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. associate-/l* 53.5%

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

      3. associate-/r/ 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in a around 0 50.4%

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

      1. expm1-log1p-u 31.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)\right)} \cdot -4 \]

      2. expm1-udef 24.4%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)} - 1\right)} \cdot -4 \]

      3. associate-/l* 27.1%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{c}{t}}}\right)} - 1\right) \cdot -4 \]

   9. Applied egg-rr 27.1%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)} - 1\right)} \cdot -4 \]
   10. Step-by-step derivation

       1. expm1-def 31.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)\right)} \cdot -4 \]

       2. expm1-log1p 53.5%

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

       3. associate-/l* 50.4%

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

       4. associate-*r/ 53.5%

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

   11. Simplified 53.5%

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

   if -2.4999999999999999e-113 < a < 2.90000000000000007e38

   1. Initial program 81.2%

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

      1. associate-*l* 81.1%

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

      2. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   6. Simplified 49.1%

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

      1. div-inv 49.8%

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

      2. associate-/r* 49.9%

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

   8. Applied egg-rr 49.9%

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

   if 2.90000000000000007e38 < a

   1. Initial program 76.9%

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

      1. associate-*l* 76.9%

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

      2. associate-*l* 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-/l* 57.5%

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

      3. associate-/r/ 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 20: 49.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{-114}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -2.95e-114)
   (* -4.0 (/ a (/ c t)))
   (if (<= a 1.15e+38) (* b (/ (/ 1.0 z) c)) (* -4.0 (* t (/ a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.95e-114) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= 1.15e+38) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	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) :: tmp
    if (a <= (-2.95d-114)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= 1.15d+38) then
        tmp = b * ((1.0d0 / z) / c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    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 tmp;
	if (a <= -2.95e-114) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= 1.15e+38) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.95e-114:
		tmp = -4.0 * (a / (c / t))
	elif a <= 1.15e+38:
		tmp = b * ((1.0 / z) / c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.95e-114)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= 1.15e+38)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.95e-114)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= 1.15e+38)
		tmp = b * ((1.0 / z) / c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.95e-114], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+38], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9500000000000001e-114

   1. Initial program 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate-*l* 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. associate-/l* 53.5%

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

   6. Simplified 53.5%

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

   if -2.9500000000000001e-114 < a < 1.1500000000000001e38

   1. Initial program 81.2%

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

      1. associate-*l* 81.1%

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

      2. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   6. Simplified 49.1%

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

      1. div-inv 49.8%

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

      2. associate-/r* 49.9%

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

   8. Applied egg-rr 49.9%

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

   if 1.1500000000000001e38 < a

   1. Initial program 76.9%

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

      1. associate-*l* 76.9%

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

      2. associate-*l* 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-/l* 57.5%

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

      3. associate-/r/ 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{-114}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 21: 35.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return 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 = 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 b / (z * c);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.9%

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

   1. associate-*l* 77.8%

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

   2. associate-*l* 78.5%

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

3. Simplified 78.5%

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

4. Taylor expanded in b around inf 35.1%

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

   1. *-commutative 35.1%

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

6. Simplified 35.1%

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

7. Final simplification 35.1%

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

Developer target: 80.2% accurate, 0.2× 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 2023199 
(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)))