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

Percentage Accurate: 99.7% → 100.0%

Time: 6.2s

Alternatives: 9

Speedup: 1.4×

• 21.3% 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: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+58} \lor \neg \left(y \leq -1.4 \cdot 10^{-35}\right) \land \left(y \leq -3.65 \cdot 10^{-113} \lor \neg \left(y \leq 2.5 \cdot 10^{+63}\right)\right):\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+58)
         (and (not (<= y -1.4e-35))
              (or (<= y -3.65e-113) (not (<= y 2.5e+63)))))
   (+ 4.0 (* z (/ -4.0 y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+58) || (!(y <= -1.4e-35) && ((y <= -3.65e-113) || !(y <= 2.5e+63)))) {
		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 ((y <= (-3d+58)) .or. (.not. (y <= (-1.4d-35))) .and. (y <= (-3.65d-113)) .or. (.not. (y <= 2.5d+63))) 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 ((y <= -3e+58) || (!(y <= -1.4e-35) && ((y <= -3.65e-113) || !(y <= 2.5e+63)))) {
		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 (y <= -3e+58) or (not (y <= -1.4e-35) and ((y <= -3.65e-113) or not (y <= 2.5e+63))):
		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 ((y <= -3e+58) || (!(y <= -1.4e-35) && ((y <= -3.65e-113) || !(y <= 2.5e+63))))
		tmp = Float64(4.0 + Float64(z * Float64(-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 ((y <= -3e+58) || (~((y <= -1.4e-35)) && ((y <= -3.65e-113) || ~((y <= 2.5e+63)))))
		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[Or[LessEqual[y, -3e+58], And[N[Not[LessEqual[y, -1.4e-35]], $MachinePrecision], Or[LessEqual[y, -3.65e-113], N[Not[LessEqual[y, 2.5e+63]], $MachinePrecision]]]], N[(4.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000002e58 or -1.4e-35 < y < -3.65000000000000006e-113 or 2.50000000000000005e63 < y

   1. Initial program 98.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 x around 0 87.0%

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

      1. +-commutative 87.0%

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

      2. fma-define 87.0%

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

      3. div-sub 87.0%

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

      4. *-commutative 87.0%

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

      5. *-lft-identity 87.0%

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

      6. associate-*l/ 87.0%

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

      7. associate-*r* 87.0%

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

      8. lft-mult-inverse 87.1%

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

      9. metadata-eval 87.1%

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

      10. fma-define 87.1%

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

      11. +-commutative 87.1%

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

      12. sub-neg 87.1%

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

      13. distribute-lft-in 87.1%

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

      14. metadata-eval 87.1%

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

      15. associate-+r+ 87.1%

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

      16. metadata-eval 87.1%

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

      17. distribute-rgt-neg-out 87.1%

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

      18. *-lft-identity 87.1%

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

      19. associate-*l/ 87.0%

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

      20. associate-*l* 87.0%

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

      21. *-commutative 87.0%

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

      22. distribute-rgt-neg-in 87.0%

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

      23. associate-*r/ 87.0%

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

   7. Simplified 87.0%

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

   if -3.0000000000000002e58 < y < -1.4e-35 or -3.65000000000000006e-113 < y < 2.50000000000000005e63

   1. Initial program 99.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 89.6%

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

      1. *-commutative 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+58} \lor \neg \left(y \leq -1.4 \cdot 10^{-35}\right) \land \left(y \leq -3.65 \cdot 10^{-113} \lor \neg \left(y \leq 2.5 \cdot 10^{+63}\right)\right):\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+55}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) y)))
   (if (<= y -7e+55)
     4.0
     (if (<= y 2.6e-61)
       t_0
       (if (<= y 1.8e+15) (* -4.0 (/ z y)) (if (<= y 9.8e+59) t_0 4.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double tmp;
	if (y <= -7e+55) {
		tmp = 4.0;
	} else if (y <= 2.6e-61) {
		tmp = t_0;
	} else if (y <= 1.8e+15) {
		tmp = -4.0 * (z / y);
	} else if (y <= 9.8e+59) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (4.0d0 * x) / y
    if (y <= (-7d+55)) then
        tmp = 4.0d0
    else if (y <= 2.6d-61) then
        tmp = t_0
    else if (y <= 1.8d+15) then
        tmp = (-4.0d0) * (z / y)
    else if (y <= 9.8d+59) then
        tmp = t_0
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double tmp;
	if (y <= -7e+55) {
		tmp = 4.0;
	} else if (y <= 2.6e-61) {
		tmp = t_0;
	} else if (y <= 1.8e+15) {
		tmp = -4.0 * (z / y);
	} else if (y <= 9.8e+59) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / y
	tmp = 0
	if y <= -7e+55:
		tmp = 4.0
	elif y <= 2.6e-61:
		tmp = t_0
	elif y <= 1.8e+15:
		tmp = -4.0 * (z / y)
	elif y <= 9.8e+59:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (y <= -7e+55)
		tmp = 4.0;
	elseif (y <= 2.6e-61)
		tmp = t_0;
	elseif (y <= 1.8e+15)
		tmp = Float64(-4.0 * Float64(z / y));
	elseif (y <= 9.8e+59)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / y;
	tmp = 0.0;
	if (y <= -7e+55)
		tmp = 4.0;
	elseif (y <= 2.6e-61)
		tmp = t_0;
	elseif (y <= 1.8e+15)
		tmp = -4.0 * (z / y);
	elseif (y <= 9.8e+59)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -7e+55], 4.0, If[LessEqual[y, 2.6e-61], t$95$0, If[LessEqual[y, 1.8e+15], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+59], t$95$0, 4.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000021e55 or 9.80000000000000015e59 < y

   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 inf 73.1%

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

   if -7.00000000000000021e55 < y < 2.6000000000000001e-61 or 1.8e15 < y < 9.80000000000000015e59

   1. Initial program 99.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*l/ 52.1%

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

   7. Simplified 52.1%

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

   if 2.6000000000000001e-61 < y < 1.8e15

   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 59.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+55}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+59}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+127}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+63}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.3e+127) 4.0 (if (<= y 1.12e+63) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.3e+127) {
		tmp = 4.0;
	} else if (y <= 1.12e+63) {
		tmp = 4.0 * ((x - z) / 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 <= (-4.3d+127)) then
        tmp = 4.0d0
    else if (y <= 1.12d+63) then
        tmp = 4.0d0 * ((x - z) / 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 <= -4.3e+127) {
		tmp = 4.0;
	} else if (y <= 1.12e+63) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.3e+127:
		tmp = 4.0
	elif y <= 1.12e+63:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.3e+127)
		tmp = 4.0;
	elseif (y <= 1.12e+63)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.3e+127)
		tmp = 4.0;
	elseif (y <= 1.12e+63)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.3e+127], 4.0, If[LessEqual[y, 1.12e+63], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.29999999999999984e127 or 1.12000000000000006e63 < y

   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 78.3%

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

   if -4.29999999999999984e127 < y < 1.12000000000000006e63

   1. Initial program 99.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 84.9%

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

      1. *-commutative 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+127}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+63}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+73}:\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.2e+73)
   (+ 4.0 (* z (/ -4.0 y)))
   (if (<= z 1.7e-72) (+ 4.0 (/ (* 4.0 x) y)) (* 4.0 (/ (- x z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e+73) {
		tmp = 4.0 + (z * (-4.0 / y));
	} else if (z <= 1.7e-72) {
		tmp = 4.0 + ((4.0 * x) / 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 (z <= (-4.2d+73)) then
        tmp = 4.0d0 + (z * ((-4.0d0) / y))
    else if (z <= 1.7d-72) then
        tmp = 4.0d0 + ((4.0d0 * x) / 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 (z <= -4.2e+73) {
		tmp = 4.0 + (z * (-4.0 / y));
	} else if (z <= 1.7e-72) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.2e+73:
		tmp = 4.0 + (z * (-4.0 / y))
	elif z <= 1.7e-72:
		tmp = 4.0 + ((4.0 * x) / y)
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.2e+73)
		tmp = Float64(4.0 + Float64(z * Float64(-4.0 / y)));
	elseif (z <= 1.7e-72)
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / 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 (z <= -4.2e+73)
		tmp = 4.0 + (z * (-4.0 / y));
	elseif (z <= 1.7e-72)
		tmp = 4.0 + ((4.0 * x) / y);
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.2e+73], N[(4.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-72], N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000003e73

   1. Initial program 97.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 x around 0 93.6%

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

      1. +-commutative 93.6%

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

      2. fma-define 93.6%

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

      3. div-sub 93.6%

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

      4. *-commutative 93.6%

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

      5. *-lft-identity 93.6%

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

      6. associate-*l/ 93.6%

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

      7. associate-*r* 93.6%

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

      8. lft-mult-inverse 93.7%

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

      9. metadata-eval 93.7%

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

      10. fma-define 93.7%

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

      11. +-commutative 93.7%

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

      12. sub-neg 93.7%

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

      13. distribute-lft-in 93.7%

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

      14. metadata-eval 93.7%

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

      15. associate-+r+ 93.7%

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

      16. metadata-eval 93.7%

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

      17. distribute-rgt-neg-out 93.7%

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

      18. *-lft-identity 93.7%

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

      19. associate-*l/ 93.5%

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

      20. associate-*l* 93.5%

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

      21. *-commutative 93.5%

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

      22. distribute-rgt-neg-in 93.5%

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

      23. associate-*r/ 93.5%

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

   7. Simplified 93.5%

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

   if -4.2000000000000003e73 < z < 1.6999999999999999e-72

   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 91.5%

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

      1. distribute-lft-in 91.5%

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

      2. metadata-eval 91.5%

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

      3. associate-+r+ 91.6%

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

      4. metadata-eval 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*l/ 91.6%

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

   7. Simplified 91.6%

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

   if 1.6999999999999999e-72 < z

   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* 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 84.9%

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

      1. *-commutative 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+73}:\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+57) 4.0 (if (<= y 5e+39) (* -4.0 (/ z y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+57) {
		tmp = 4.0;
	} else if (y <= 5e+39) {
		tmp = -4.0 * (z / 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 <= (-2.7d+57)) then
        tmp = 4.0d0
    else if (y <= 5d+39) then
        tmp = (-4.0d0) * (z / 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 <= -2.7e+57) {
		tmp = 4.0;
	} else if (y <= 5e+39) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+57:
		tmp = 4.0
	elif y <= 5e+39:
		tmp = -4.0 * (z / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+57)
		tmp = 4.0;
	elseif (y <= 5e+39)
		tmp = Float64(-4.0 * Float64(z / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+57)
		tmp = 4.0;
	elseif (y <= 5e+39)
		tmp = -4.0 * (z / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+57], 4.0, If[LessEqual[y, 5e+39], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999998e57 or 5.00000000000000015e39 < y

   1. Initial program 98.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 69.7%

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

   if -2.6999999999999998e57 < y < 5.00000000000000015e39

   1. Initial program 99.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 46.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + (4.0 * ((x + ((0.75 * y) - 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 + ((0.75d0 * y) - z)) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(4.0 * N[(N[(x + N[(N[(0.75 * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $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. Final simplification 100.0%

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

Alternative 8: 99.8% accurate, 1.4× speedup

Math

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

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(Float64(4.0 * 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[(N[(4.0 * N[(N[(x - z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] / y), $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 98.9%

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

   1. distribute-lft-out 98.9%

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

7. Simplified 98.9%

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

8. Final simplification 98.9%

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

Alternative 9: 34.7% 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 33.0%

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

6. Final simplification 33.0%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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)))