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

Percentage Accurate: 99.8% → 100.0%

Time: 6.2s

Alternatives: 11

Speedup: 1.0×

• 20.5% 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: 99.8% 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 99.5%

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

   1. +-commutative 99.5%

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

   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. Add Preprocessing

Alternative 2: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+47} \lor \neg \left(y \leq 3.3 \cdot 10^{-32}\right) \land \left(y \leq 7.8 \cdot 10^{+44} \lor \neg \left(y \leq 3.8 \cdot 10^{+92}\right)\right):\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e+47)
         (and (not (<= y 3.3e-32)) (or (<= y 7.8e+44) (not (<= y 3.8e+92)))))
   (+ 4.0 (/ (* 4.0 x) y))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+47) || (!(y <= 3.3e-32) && ((y <= 7.8e+44) || !(y <= 3.8e+92)))) {
		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 ((y <= (-1.9d+47)) .or. (.not. (y <= 3.3d-32)) .and. (y <= 7.8d+44) .or. (.not. (y <= 3.8d+92))) 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 ((y <= -1.9e+47) || (!(y <= 3.3e-32) && ((y <= 7.8e+44) || !(y <= 3.8e+92)))) {
		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 (y <= -1.9e+47) or (not (y <= 3.3e-32) and ((y <= 7.8e+44) or not (y <= 3.8e+92))):
		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 ((y <= -1.9e+47) || (!(y <= 3.3e-32) && ((y <= 7.8e+44) || !(y <= 3.8e+92))))
		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 ((y <= -1.9e+47) || (~((y <= 3.3e-32)) && ((y <= 7.8e+44) || ~((y <= 3.8e+92)))))
		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[Or[LessEqual[y, -1.9e+47], And[N[Not[LessEqual[y, 3.3e-32]], $MachinePrecision], Or[LessEqual[y, 7.8e+44], N[Not[LessEqual[y, 3.8e+92]], $MachinePrecision]]]], 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 2 regimes

2. if y < -1.9000000000000002e47 or 3.30000000000000025e-32 < y < 7.8000000000000005e44 or 3.8e92 < y

   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. +-commutative 99.0%

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

      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 87.0%

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

      1. distribute-lft-in 87.0%

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

      2. metadata-eval 87.0%

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

      3. associate-+r+ 87.0%

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

      4. metadata-eval 87.0%

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

      5. *-commutative 87.0%

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

      6. associate-*l/ 87.0%

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

   7. Simplified 87.0%

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

   if -1.9000000000000002e47 < y < 3.30000000000000025e-32 or 7.8000000000000005e44 < y < 3.8e92

   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 0 91.5%

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

      1. *-commutative 91.5%

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

   7. Simplified 91.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+47} \lor \neg \left(y \leq 3.3 \cdot 10^{-32}\right) \land \left(y \leq 7.8 \cdot 10^{+44} \lor \neg \left(y \leq 3.8 \cdot 10^{+92}\right)\right):\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ t_1 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-142}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)) (t_1 (/ (* 4.0 x) y)))
   (if (<= z -6e+27)
     t_0
     (if (<= z 8.2e-275)
       t_1
       (if (<= z 3.3e-142) 4.0 (if (<= z 4.2e-20) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = (4.0 * x) / y;
	double tmp;
	if (z <= -6e+27) {
		tmp = t_0;
	} else if (z <= 8.2e-275) {
		tmp = t_1;
	} else if (z <= 3.3e-142) {
		tmp = 4.0;
	} else if (z <= 4.2e-20) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    t_1 = (4.0d0 * x) / y
    if (z <= (-6d+27)) then
        tmp = t_0
    else if (z <= 8.2d-275) then
        tmp = t_1
    else if (z <= 3.3d-142) then
        tmp = 4.0d0
    else if (z <= 4.2d-20) then
        tmp = t_1
    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 t_1 = (4.0 * x) / y;
	double tmp;
	if (z <= -6e+27) {
		tmp = t_0;
	} else if (z <= 8.2e-275) {
		tmp = t_1;
	} else if (z <= 3.3e-142) {
		tmp = 4.0;
	} else if (z <= 4.2e-20) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	t_1 = (4.0 * x) / y
	tmp = 0
	if z <= -6e+27:
		tmp = t_0
	elif z <= 8.2e-275:
		tmp = t_1
	elif z <= 3.3e-142:
		tmp = 4.0
	elif z <= 4.2e-20:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	t_1 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (z <= -6e+27)
		tmp = t_0;
	elseif (z <= 8.2e-275)
		tmp = t_1;
	elseif (z <= 3.3e-142)
		tmp = 4.0;
	elseif (z <= 4.2e-20)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	t_1 = (4.0 * x) / y;
	tmp = 0.0;
	if (z <= -6e+27)
		tmp = t_0;
	elseif (z <= 8.2e-275)
		tmp = t_1;
	elseif (z <= 3.3e-142)
		tmp = 4.0;
	elseif (z <= 4.2e-20)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -6e+27], t$95$0, If[LessEqual[z, 8.2e-275], t$95$1, If[LessEqual[z, 3.3e-142], 4.0, If[LessEqual[z, 4.2e-20], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999953e27 or 4.1999999999999998e-20 < z

   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 z around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-*l/ 63.8%

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

   7. Simplified 63.8%

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

   if -5.99999999999999953e27 < z < 8.19999999999999949e-275 or 3.2999999999999997e-142 < z < 4.1999999999999998e-20

   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 x around inf 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-*l/ 53.2%

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

   7. Simplified 53.2%

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

   if 8.19999999999999949e-275 < z < 3.2999999999999997e-142

   1. Initial program 97.4%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 61.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+27}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-142}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ t_1 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+68}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-134}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))) (t_1 (/ (* 4.0 x) y)))
   (if (<= z -1e+68)
     t_0
     (if (<= z 2.9e-273)
       t_1
       (if (<= z 2.4e-134) 4.0 (if (<= z 4.5e-20) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = (4.0 * x) / y;
	double tmp;
	if (z <= -1e+68) {
		tmp = t_0;
	} else if (z <= 2.9e-273) {
		tmp = t_1;
	} else if (z <= 2.4e-134) {
		tmp = 4.0;
	} else if (z <= 4.5e-20) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * ((-4.0d0) / y)
    t_1 = (4.0d0 * x) / y
    if (z <= (-1d+68)) then
        tmp = t_0
    else if (z <= 2.9d-273) then
        tmp = t_1
    else if (z <= 2.4d-134) then
        tmp = 4.0d0
    else if (z <= 4.5d-20) then
        tmp = t_1
    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 t_1 = (4.0 * x) / y;
	double tmp;
	if (z <= -1e+68) {
		tmp = t_0;
	} else if (z <= 2.9e-273) {
		tmp = t_1;
	} else if (z <= 2.4e-134) {
		tmp = 4.0;
	} else if (z <= 4.5e-20) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	t_1 = (4.0 * x) / y
	tmp = 0
	if z <= -1e+68:
		tmp = t_0
	elif z <= 2.9e-273:
		tmp = t_1
	elif z <= 2.4e-134:
		tmp = 4.0
	elif z <= 4.5e-20:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	t_1 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (z <= -1e+68)
		tmp = t_0;
	elseif (z <= 2.9e-273)
		tmp = t_1;
	elseif (z <= 2.4e-134)
		tmp = 4.0;
	elseif (z <= 4.5e-20)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	t_1 = (4.0 * x) / y;
	tmp = 0.0;
	if (z <= -1e+68)
		tmp = t_0;
	elseif (z <= 2.9e-273)
		tmp = t_1;
	elseif (z <= 2.4e-134)
		tmp = 4.0;
	elseif (z <= 4.5e-20)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1e+68], t$95$0, If[LessEqual[z, 2.9e-273], t$95$1, If[LessEqual[z, 2.4e-134], 4.0, If[LessEqual[z, 4.5e-20], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999953e67 or 4.5000000000000001e-20 < z

   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 x around 0 94.1%

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

   6. Taylor expanded in z around inf 65.1%

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

      1. metadata-eval 65.1%

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

      2. distribute-lft-neg-in 65.1%

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

      3. *-lft-identity 65.1%

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

      4. associate-*l/ 64.8%

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

      5. associate-*l* 64.8%

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

      6. *-commutative 64.8%

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

      7. distribute-rgt-neg-in 64.8%

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

      8. associate-*r/ 64.8%

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

      9. metadata-eval 64.8%

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

      10. distribute-neg-frac 64.8%

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

      11. metadata-eval 64.8%

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

   8. Simplified 64.8%

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

   if -9.99999999999999953e67 < z < 2.89999999999999986e-273 or 2.4000000000000001e-134 < z < 4.5000000000000001e-20

   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 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 2.89999999999999986e-273 < z < 2.4000000000000001e-134

   1. Initial program 97.4%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 61.1%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-273}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-134}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ t_1 := x \cdot \frac{4}{y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-143}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))) (t_1 (* x (/ 4.0 y))))
   (if (<= z -9.5e+67)
     t_0
     (if (<= z 2.35e-272)
       t_1
       (if (<= z 7.8e-143) 4.0 (if (<= z 3.7e-22) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = x * (4.0 / y);
	double tmp;
	if (z <= -9.5e+67) {
		tmp = t_0;
	} else if (z <= 2.35e-272) {
		tmp = t_1;
	} else if (z <= 7.8e-143) {
		tmp = 4.0;
	} else if (z <= 3.7e-22) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * ((-4.0d0) / y)
    t_1 = x * (4.0d0 / y)
    if (z <= (-9.5d+67)) then
        tmp = t_0
    else if (z <= 2.35d-272) then
        tmp = t_1
    else if (z <= 7.8d-143) then
        tmp = 4.0d0
    else if (z <= 3.7d-22) then
        tmp = t_1
    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 t_1 = x * (4.0 / y);
	double tmp;
	if (z <= -9.5e+67) {
		tmp = t_0;
	} else if (z <= 2.35e-272) {
		tmp = t_1;
	} else if (z <= 7.8e-143) {
		tmp = 4.0;
	} else if (z <= 3.7e-22) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	t_1 = x * (4.0 / y)
	tmp = 0
	if z <= -9.5e+67:
		tmp = t_0
	elif z <= 2.35e-272:
		tmp = t_1
	elif z <= 7.8e-143:
		tmp = 4.0
	elif z <= 3.7e-22:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	t_1 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (z <= -9.5e+67)
		tmp = t_0;
	elseif (z <= 2.35e-272)
		tmp = t_1;
	elseif (z <= 7.8e-143)
		tmp = 4.0;
	elseif (z <= 3.7e-22)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	t_1 = x * (4.0 / y);
	tmp = 0.0;
	if (z <= -9.5e+67)
		tmp = t_0;
	elseif (z <= 2.35e-272)
		tmp = t_1;
	elseif (z <= 7.8e-143)
		tmp = 4.0;
	elseif (z <= 3.7e-22)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+67], t$95$0, If[LessEqual[z, 2.35e-272], t$95$1, If[LessEqual[z, 7.8e-143], 4.0, If[LessEqual[z, 3.7e-22], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000002e67 or 3.7e-22 < z

   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 x around 0 94.1%

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

   6. Taylor expanded in z around inf 65.1%

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

      1. metadata-eval 65.1%

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

      2. distribute-lft-neg-in 65.1%

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

      3. *-lft-identity 65.1%

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

      4. associate-*l/ 64.8%

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

      5. associate-*l* 64.8%

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

      6. *-commutative 64.8%

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

      7. distribute-rgt-neg-in 64.8%

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

      8. associate-*r/ 64.8%

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

      9. metadata-eval 64.8%

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

      10. distribute-neg-frac 64.8%

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

      11. metadata-eval 64.8%

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

   8. Simplified 64.8%

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

   if -9.5000000000000002e67 < z < 2.3499999999999999e-272 or 7.80000000000000007e-143 < z < 3.7e-22

   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 x around 0 100.0%

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

   6. Taylor expanded in x around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*l/ 52.1%

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

      3. associate-*r/ 52.0%

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

   8. Simplified 52.0%

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

   if 2.3499999999999999e-272 < z < 7.80000000000000007e-143

   1. Initial program 97.4%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 61.1%

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

Alternative 6: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-14}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+49)
   (+ 4.0 (/ (* 4.0 x) y))
   (if (<= y 4.7e-14) (* 4.0 (/ (- x z) y)) (+ 4.0 (/ (* z -4.0) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+49) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if (y <= 4.7e-14) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + ((z * -4.0) / 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 <= (-3.3d+49)) then
        tmp = 4.0d0 + ((4.0d0 * x) / y)
    else if (y <= 4.7d-14) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+49) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if (y <= 4.7e-14) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.3e+49:
		tmp = 4.0 + ((4.0 * x) / y)
	elif y <= 4.7e-14:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e+49)
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / y));
	elseif (y <= 4.7e-14)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.3e+49)
		tmp = 4.0 + ((4.0 * x) / y);
	elseif (y <= 4.7e-14)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e+49], N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-14], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2999999999999998e49

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      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 86.3%

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

      1. distribute-lft-in 86.3%

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

      2. metadata-eval 86.3%

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

      3. associate-+r+ 86.3%

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

      4. metadata-eval 86.3%

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

      5. *-commutative 86.3%

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

      6. associate-*l/ 86.3%

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

   7. Simplified 86.3%

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

   if -3.2999999999999998e49 < y < 4.7000000000000002e-14

   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 0 92.4%

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

      1. *-commutative 92.4%

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

   7. Simplified 92.4%

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

   if 4.7000000000000002e-14 < 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 x around 0 83.8%

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

      1. div-sub 83.8%

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

      2. *-commutative 83.8%

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

      3. *-lft-identity 83.8%

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

      4. associate-*l/ 83.7%

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

      5. associate-*r* 83.8%

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

      6. lft-mult-inverse 83.9%

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

      7. metadata-eval 83.9%

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

      8. sub-neg 83.9%

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

      9. distribute-lft-in 83.9%

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

      10. metadata-eval 83.9%

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

      11. associate-+r+ 83.9%

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

      12. metadata-eval 83.9%

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

      13. neg-mul-1 83.9%

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

      14. associate-*r* 83.9%

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

      15. metadata-eval 83.9%

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

      16. *-commutative 83.9%

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

      17. associate-*l/ 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-14}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+181}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.8e+181) 4.0 (if (<= y 2.6e+109) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.8e+181) {
		tmp = 4.0;
	} else if (y <= 2.6e+109) {
		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 <= (-8.8d+181)) then
        tmp = 4.0d0
    else if (y <= 2.6d+109) 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 <= -8.8e+181) {
		tmp = 4.0;
	} else if (y <= 2.6e+109) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.8e+181:
		tmp = 4.0
	elif y <= 2.6e+109:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.8e+181)
		tmp = 4.0;
	elseif (y <= 2.6e+109)
		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 <= -8.8e+181)
		tmp = 4.0;
	elseif (y <= 2.6e+109)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.8e+181], 4.0, If[LessEqual[y, 2.6e+109], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000004e181 or 2.5999999999999998e109 < y

   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* 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 83.0%

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

   if -8.8000000000000004e181 < y < 2.5999999999999998e109

   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 0 82.7%

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

      1. *-commutative 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+181}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+141} \lor \neg \left(x \leq 3.8 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+141) (not (<= x 3.8e-8))) (* x (/ 4.0 y)) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+141) || !(x <= 3.8e-8)) {
		tmp = x * (4.0 / 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 ((x <= (-9.5d+141)) .or. (.not. (x <= 3.8d-8))) then
        tmp = x * (4.0d0 / 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 ((x <= -9.5e+141) || !(x <= 3.8e-8)) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+141) or not (x <= 3.8e-8):
		tmp = x * (4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+141) || !(x <= 3.8e-8))
		tmp = Float64(x * Float64(4.0 / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.5e+141) || ~((x <= 3.8e-8)))
		tmp = x * (4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+141], N[Not[LessEqual[x, 3.8e-8]], $MachinePrecision]], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999974e141 or 3.80000000000000028e-8 < x

   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 x around 0 95.8%

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

   6. Taylor expanded in x around inf 69.3%

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

      1. *-commutative 69.3%

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

      2. associate-*l/ 69.3%

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

      3. associate-*r/ 69.2%

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

   8. Simplified 69.2%

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

   if -9.49999999999999974e141 < x < 3.80000000000000028e-8

   1. Initial program 99.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 45.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+141} \lor \neg \left(x \leq 3.8 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 99.5%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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. Final simplification 99.9%

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

Alternative 10: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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 97.3%

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

Alternative 11: 34.8% 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 99.5%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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 34.0%

   \[\leadsto \color{blue}{4} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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)))