Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A

Percentage Accurate: 99.7% → 100.0%

Time: 6.7s

Alternatives: 8

Speedup: 1.4×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma 4.0 (+ 0.75 (/ (- x z) y)) 1.0))

C

double code(double x, double y, double z) {
	return fma(4.0, (0.75 + ((x - z) / y)), 1.0);
}

Julia

function code(x, y, z)
	return fma(4.0, Float64(0.75 + Float64(Float64(x - z) / y)), 1.0)
end

Wolfram

code[x_, y_, z_] := N[(4.0 * N[(0.75 + N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.2%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} + 1} \]

   2. associate-/l* 100.0%

      \[\leadsto \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} + 1 \]

   3. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{\left(x + y \cdot 0.75\right) - z}{y}, 1\right)} \]

   4. associate--l+ 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y}, 1\right) \]

   5. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) + x}}{y}, 1\right) \]

   6. remove-double-neg 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{\left(y \cdot 0.75 - z\right) + \color{blue}{\left(-\left(-x\right)\right)}}{y}, 1\right) \]

   7. sub-neg 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) - \left(-x\right)}}{y}, 1\right) \]

   8. associate--r+ 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{y \cdot 0.75 - \left(z + \left(-x\right)\right)}}{y}, 1\right) \]

   9. div-sub 100.0%

      \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} - \frac{z + \left(-x\right)}{y}}, 1\right) \]

   10. sub-neg 100.0%

       \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} + \left(-\frac{z + \left(-x\right)}{y}\right)}, 1\right) \]

   11. associate-*l/ 100.0%

       \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y}{y} \cdot 0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

   12. *-inverses 100.0%

       \[\leadsto \mathsf{fma}\left(4, \color{blue}{1} \cdot 0.75 + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

   13. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \color{blue}{0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

   14. distribute-frac-neg2 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{z + \left(-x\right)}{-y}}, 1\right) \]

   15. remove-double-neg 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{\left(-\left(-z\right)\right)} + \left(-x\right)}{-y}, 1\right) \]

   16. distribute-neg-out 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{-\left(\left(-z\right) + x\right)}}{-y}, 1\right) \]

   17. +-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x + \left(-z\right)\right)}}{-y}, 1\right) \]

   18. sub-neg 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x - z\right)}}{-y}, 1\right) \]

   19. distribute-frac-neg 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\left(-\frac{x - z}{-y}\right)}, 1\right) \]

   20. distribute-frac-neg2 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{x - z}{-\left(-y\right)}}, 1\right) \]

   21. remove-double-neg 100.0%

       \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{x - z}{\color{blue}{y}}, 1\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right) \]
6. Add Preprocessing

Alternative 2: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-247}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)))
   (if (<= z -5.6e+68)
     t_0
     (if (<= z 3.1e-247) (* 4.0 (/ x y)) (if (<= z 4.6e+112) 4.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double tmp;
	if (z <= -5.6e+68) {
		tmp = t_0;
	} else if (z <= 3.1e-247) {
		tmp = 4.0 * (x / y);
	} else if (z <= 4.6e+112) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    if (z <= (-5.6d+68)) then
        tmp = t_0
    else if (z <= 3.1d-247) then
        tmp = 4.0d0 * (x / y)
    else if (z <= 4.6d+112) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double tmp;
	if (z <= -5.6e+68) {
		tmp = t_0;
	} else if (z <= 3.1e-247) {
		tmp = 4.0 * (x / y);
	} else if (z <= 4.6e+112) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	tmp = 0
	if z <= -5.6e+68:
		tmp = t_0
	elif z <= 3.1e-247:
		tmp = 4.0 * (x / y)
	elif z <= 4.6e+112:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	tmp = 0.0
	if (z <= -5.6e+68)
		tmp = t_0;
	elseif (z <= 3.1e-247)
		tmp = Float64(4.0 * Float64(x / y));
	elseif (z <= 4.6e+112)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	tmp = 0.0;
	if (z <= -5.6e+68)
		tmp = t_0;
	elseif (z <= 3.1e-247)
		tmp = 4.0 * (x / y);
	elseif (z <= 4.6e+112)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -5.6e+68], t$95$0, If[LessEqual[z, 3.1e-247], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+112], 4.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6e68 or 4.5999999999999999e112 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 79.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \color{blue}{\frac{z}{y} \cdot -4} \]

      2. associate-*l/ 79.6%

         \[\leadsto \color{blue}{\frac{z \cdot -4}{y}} \]

   7. Simplified 79.6%

      \[\leadsto \color{blue}{\frac{z \cdot -4}{y}} \]

   if -5.6e68 < z < 3.10000000000000015e-247

   1. Initial program 98.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

   7. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

   if 3.10000000000000015e-247 < z < 4.5999999999999999e112

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 51.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-247}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+119} \lor \neg \left(z \leq 5.6 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4e+119) (not (<= z 5.6e+113)))
   (/ (* z -4.0) y)
   (* 4.0 (/ (+ x y) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e+119) || !(z <= 5.6e+113)) {
		tmp = (z * -4.0) / y;
	} else {
		tmp = 4.0 * ((x + y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.4d+119)) .or. (.not. (z <= 5.6d+113))) then
        tmp = (z * (-4.0d0)) / y
    else
        tmp = 4.0d0 * ((x + y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e+119) || !(z <= 5.6e+113)) {
		tmp = (z * -4.0) / y;
	} else {
		tmp = 4.0 * ((x + y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4e+119) or not (z <= 5.6e+113):
		tmp = (z * -4.0) / y
	else:
		tmp = 4.0 * ((x + y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4e+119) || !(z <= 5.6e+113))
		tmp = Float64(Float64(z * -4.0) / y);
	else
		tmp = Float64(4.0 * Float64(Float64(x + y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.4e+119) || ~((z <= 5.6e+113)))
		tmp = (z * -4.0) / y;
	else
		tmp = 4.0 * ((x + y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4e+119], N[Not[LessEqual[z, 5.6e+113]], $MachinePrecision]], N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision], N[(4.0 * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3999999999999997e119 or 5.59999999999999995e113 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 82.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 82.4%

         \[\leadsto \color{blue}{\frac{z}{y} \cdot -4} \]

      2. associate-*l/ 82.4%

         \[\leadsto \color{blue}{\frac{z \cdot -4}{y}} \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{\frac{z \cdot -4}{y}} \]

   if -5.3999999999999997e119 < z < 5.59999999999999995e113

   1. Initial program 98.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.8%

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

      1. distribute-lft-out 98.8%

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

      2. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 87.1%

      \[\leadsto 4 \cdot \color{blue}{\frac{x + y}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+119} \lor \neg \left(z \leq 5.6 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+55} \lor \neg \left(z \leq 3.3 \cdot 10^{+111}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+55) (not (<= z 3.3e+111)))
   (* 4.0 (/ (- x z) y))
   (* 4.0 (/ (+ x y) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+55) || !(z <= 3.3e+111)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 * ((x + y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2d+55)) .or. (.not. (z <= 3.3d+111))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 * ((x + y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+55) || !(z <= 3.3e+111)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 * ((x + y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+55) or not (z <= 3.3e+111):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 * ((x + y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+55) || !(z <= 3.3e+111))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 * Float64(Float64(x + y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2e+55) || ~((z <= 3.3e+111)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 * ((x + y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+55], N[Not[LessEqual[z, 3.3e+111]], $MachinePrecision]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000002e55 or 3.3000000000000001e111 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 88.8%

      \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 88.8%

         \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4} \]

   7. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4} \]

   if -2.00000000000000002e55 < z < 3.3000000000000001e111

   1. Initial program 98.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.8%

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

      1. distribute-lft-out 98.8%

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

      2. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 88.7%

      \[\leadsto 4 \cdot \color{blue}{\frac{x + y}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+55} \lor \neg \left(z \leq 3.3 \cdot 10^{+111}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq 8.3 \cdot 10^{+52}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.8e+19)
   (+ 4.0 (/ (* 4.0 x) y))
   (if (<= x 8.3e+52) (+ 4.0 (/ (* z -4.0) y)) (* 4.0 (/ (- x z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+19) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if (x <= 8.3e+52) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.8d+19)) then
        tmp = 4.0d0 + ((4.0d0 * x) / y)
    else if (x <= 8.3d+52) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+19) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if (x <= 8.3e+52) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.8e+19:
		tmp = 4.0 + ((4.0 * x) / y)
	elif x <= 8.3e+52:
		tmp = 4.0 + ((z * -4.0) / y)
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.8e+19)
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / y));
	elseif (x <= 8.3e+52)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.8e+19)
		tmp = 4.0 + ((4.0 * x) / y);
	elseif (x <= 8.3e+52)
		tmp = 4.0 + ((z * -4.0) / y);
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.8e+19], N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.3e+52], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8e19

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} + 1} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} + 1 \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{\left(x + y \cdot 0.75\right) - z}{y}, 1\right)} \]

      4. associate--l+ 99.9%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y}, 1\right) \]

      5. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) + x}}{y}, 1\right) \]

      6. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(4, \frac{\left(y \cdot 0.75 - z\right) + \color{blue}{\left(-\left(-x\right)\right)}}{y}, 1\right) \]

      7. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) - \left(-x\right)}}{y}, 1\right) \]

      8. associate--r+ 99.9%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{y \cdot 0.75 - \left(z + \left(-x\right)\right)}}{y}, 1\right) \]

      9. div-sub 99.9%

         \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} - \frac{z + \left(-x\right)}{y}}, 1\right) \]

      10. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} + \left(-\frac{z + \left(-x\right)}{y}\right)}, 1\right) \]

      11. associate-*l/ 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y}{y} \cdot 0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      12. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{1} \cdot 0.75 + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      14. distribute-frac-neg2 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{z + \left(-x\right)}{-y}}, 1\right) \]

      15. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{\left(-\left(-z\right)\right)} + \left(-x\right)}{-y}, 1\right) \]

      16. distribute-neg-out 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{-\left(\left(-z\right) + x\right)}}{-y}, 1\right) \]

      17. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x + \left(-z\right)\right)}}{-y}, 1\right) \]

      18. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x - z\right)}}{-y}, 1\right) \]

      19. distribute-frac-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\left(-\frac{x - z}{-y}\right)}, 1\right) \]

      20. distribute-frac-neg2 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{x - z}{-\left(-y\right)}}, 1\right) \]

      21. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{x - z}{\color{blue}{y}}, 1\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 88.4%

      \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-in 88.4%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.75 + 4 \cdot \frac{x}{y}\right)} \]

      2. metadata-eval 88.4%

         \[\leadsto 1 + \left(\color{blue}{3} + 4 \cdot \frac{x}{y}\right) \]

      3. associate-+r+ 88.4%

         \[\leadsto \color{blue}{\left(1 + 3\right) + 4 \cdot \frac{x}{y}} \]

      4. metadata-eval 88.4%

         \[\leadsto \color{blue}{4} + 4 \cdot \frac{x}{y} \]

      5. *-commutative 88.4%

         \[\leadsto 4 + \color{blue}{\frac{x}{y} \cdot 4} \]

      6. associate-*l/ 88.4%

         \[\leadsto 4 + \color{blue}{\frac{x \cdot 4}{y}} \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{4 + \frac{x \cdot 4}{y}} \]

   if -3.8e19 < x < 8.29999999999999994e52

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} + 1} \]

      2. associate-/l* 100.0%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} + 1 \]

      3. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{\left(x + y \cdot 0.75\right) - z}{y}, 1\right)} \]

      4. associate--l+ 100.0%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y}, 1\right) \]

      5. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) + x}}{y}, 1\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(4, \frac{\left(y \cdot 0.75 - z\right) + \color{blue}{\left(-\left(-x\right)\right)}}{y}, 1\right) \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) - \left(-x\right)}}{y}, 1\right) \]

      8. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{y \cdot 0.75 - \left(z + \left(-x\right)\right)}}{y}, 1\right) \]

      9. div-sub 100.0%

         \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} - \frac{z + \left(-x\right)}{y}}, 1\right) \]

      10. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} + \left(-\frac{z + \left(-x\right)}{y}\right)}, 1\right) \]

      11. associate-*l/ 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y}{y} \cdot 0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      12. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{1} \cdot 0.75 + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      14. distribute-frac-neg2 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{z + \left(-x\right)}{-y}}, 1\right) \]

      15. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{\left(-\left(-z\right)\right)} + \left(-x\right)}{-y}, 1\right) \]

      16. distribute-neg-out 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{-\left(\left(-z\right) + x\right)}}{-y}, 1\right) \]

      17. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x + \left(-z\right)\right)}}{-y}, 1\right) \]

      18. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x - z\right)}}{-y}, 1\right) \]

      19. distribute-frac-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\left(-\frac{x - z}{-y}\right)}, 1\right) \]

      20. distribute-frac-neg2 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{x - z}{-\left(-y\right)}}, 1\right) \]

      21. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{x - z}{\color{blue}{y}}, 1\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 93.1%

      \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 93.1%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(0.75 + \left(-\frac{z}{y}\right)\right)} \]

      2. distribute-rgt-in 93.1%

         \[\leadsto 1 + \color{blue}{\left(0.75 \cdot 4 + \left(-\frac{z}{y}\right) \cdot 4\right)} \]

      3. metadata-eval 93.1%

         \[\leadsto 1 + \left(\color{blue}{3} + \left(-\frac{z}{y}\right) \cdot 4\right) \]

      4. associate-+r+ 93.1%

         \[\leadsto \color{blue}{\left(1 + 3\right) + \left(-\frac{z}{y}\right) \cdot 4} \]

      5. metadata-eval 93.1%

         \[\leadsto \color{blue}{4} + \left(-\frac{z}{y}\right) \cdot 4 \]

      6. neg-mul-1 93.1%

         \[\leadsto 4 + \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \cdot 4 \]

      7. *-commutative 93.1%

         \[\leadsto 4 + \color{blue}{\left(\frac{z}{y} \cdot -1\right)} \cdot 4 \]

      8. associate-*l* 93.1%

         \[\leadsto 4 + \color{blue}{\frac{z}{y} \cdot \left(-1 \cdot 4\right)} \]

      9. metadata-eval 93.1%

         \[\leadsto 4 + \frac{z}{y} \cdot \color{blue}{-4} \]

      10. associate-*l/ 93.1%

          \[\leadsto 4 + \color{blue}{\frac{z \cdot -4}{y}} \]

   7. Simplified 93.1%

      \[\leadsto \color{blue}{4 + \frac{z \cdot -4}{y}} \]

   if 8.29999999999999994e52 < x

   1. Initial program 98.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.3%

      \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4} \]

   7. Simplified 83.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq 8.3 \cdot 10^{+52}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+95}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+35) 4.0 (if (<= y 1.35e+95) (* 4.0 (/ x y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+35) {
		tmp = 4.0;
	} else if (y <= 1.35e+95) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.8d+35)) then
        tmp = 4.0d0
    else if (y <= 1.35d+95) then
        tmp = 4.0d0 * (x / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+35) {
		tmp = 4.0;
	} else if (y <= 1.35e+95) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+35:
		tmp = 4.0
	elif y <= 1.35e+95:
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+35)
		tmp = 4.0;
	elseif (y <= 1.35e+95)
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+35)
		tmp = 4.0;
	elseif (y <= 1.35e+95)
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+35], 4.0, If[LessEqual[y, 1.35e+95], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e35 or 1.35e95 < y

   1. Initial program 98.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.6%

      \[\leadsto \color{blue}{4} \]

   if -3.8e35 < y < 1.35e95

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.4%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 49.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

   7. Simplified 49.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+95}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.4× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* 4.0 (/ (+ (- x z) y) y)))

C

double code(double x, double y, double z) {
	return 4.0 * (((x - z) + y) / y);
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	return 4.0 * (((x - z) + y) / y);
}

Python

def code(x, y, z):
	return 4.0 * (((x - z) + y) / y)

Julia

function code(x, y, z)
	return Float64(4.0 * Float64(Float64(Float64(x - z) + y) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0 * (((x - z) + y) / y);
end

Wolfram

code[x_, y_, z_] := N[(4.0 * N[(N[(N[(x - z), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

   2. associate--l+ 100.0%

      \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 99.2%

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

   1. distribute-lft-out 99.2%

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

   2. associate-/l* 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{\left(x - z\right) + y}{y} \]
9. Add Preprocessing

Alternative 8: 33.9% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 4.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.2%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} \]

   2. associate--l+ 100.0%

      \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.75 - z\right)}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 32.6%

   \[\leadsto \color{blue}{4} \]

6. Final simplification 32.6%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024074 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))