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

Percentage Accurate: 99.7% → 100.0%

Time: 9.5s

Alternatives: 10

Speedup: 1.2×

• 20.4% 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, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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 98.8%

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

   1. associate--l+ 98.8%

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

   2. div-sub 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ t_1 := x \cdot \frac{4}{y}\\ \mathbf{if}\;y \leq -0.027:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-299}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)) (t_1 (* x (/ 4.0 y))))
   (if (<= y -0.027)
     4.0
     (if (<= y -1.45e-53)
       t_1
       (if (<= y -3.9e-81)
         t_0
         (if (<= y -5.5e-198)
           t_1
           (if (<= y -7.2e-299)
             t_0
             (if (<= y 6.1e-284) t_1 (if (<= y 7.2e+102) t_0 4.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double t_1 = x * (4.0 / y);
	double tmp;
	if (y <= -0.027) {
		tmp = 4.0;
	} else if (y <= -1.45e-53) {
		tmp = t_1;
	} else if (y <= -3.9e-81) {
		tmp = t_0;
	} else if (y <= -5.5e-198) {
		tmp = t_1;
	} else if (y <= -7.2e-299) {
		tmp = t_0;
	} else if (y <= 6.1e-284) {
		tmp = t_1;
	} else if (y <= 7.2e+102) {
		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) :: t_1
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    t_1 = x * (4.0d0 / y)
    if (y <= (-0.027d0)) then
        tmp = 4.0d0
    else if (y <= (-1.45d-53)) then
        tmp = t_1
    else if (y <= (-3.9d-81)) then
        tmp = t_0
    else if (y <= (-5.5d-198)) then
        tmp = t_1
    else if (y <= (-7.2d-299)) then
        tmp = t_0
    else if (y <= 6.1d-284) then
        tmp = t_1
    else if (y <= 7.2d+102) 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 = (z / y) * -4.0;
	double t_1 = x * (4.0 / y);
	double tmp;
	if (y <= -0.027) {
		tmp = 4.0;
	} else if (y <= -1.45e-53) {
		tmp = t_1;
	} else if (y <= -3.9e-81) {
		tmp = t_0;
	} else if (y <= -5.5e-198) {
		tmp = t_1;
	} else if (y <= -7.2e-299) {
		tmp = t_0;
	} else if (y <= 6.1e-284) {
		tmp = t_1;
	} else if (y <= 7.2e+102) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	t_1 = x * (4.0 / y)
	tmp = 0
	if y <= -0.027:
		tmp = 4.0
	elif y <= -1.45e-53:
		tmp = t_1
	elif y <= -3.9e-81:
		tmp = t_0
	elif y <= -5.5e-198:
		tmp = t_1
	elif y <= -7.2e-299:
		tmp = t_0
	elif y <= 6.1e-284:
		tmp = t_1
	elif y <= 7.2e+102:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	t_1 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (y <= -0.027)
		tmp = 4.0;
	elseif (y <= -1.45e-53)
		tmp = t_1;
	elseif (y <= -3.9e-81)
		tmp = t_0;
	elseif (y <= -5.5e-198)
		tmp = t_1;
	elseif (y <= -7.2e-299)
		tmp = t_0;
	elseif (y <= 6.1e-284)
		tmp = t_1;
	elseif (y <= 7.2e+102)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	t_1 = x * (4.0 / y);
	tmp = 0.0;
	if (y <= -0.027)
		tmp = 4.0;
	elseif (y <= -1.45e-53)
		tmp = t_1;
	elseif (y <= -3.9e-81)
		tmp = t_0;
	elseif (y <= -5.5e-198)
		tmp = t_1;
	elseif (y <= -7.2e-299)
		tmp = t_0;
	elseif (y <= 6.1e-284)
		tmp = t_1;
	elseif (y <= 7.2e+102)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.027], 4.0, If[LessEqual[y, -1.45e-53], t$95$1, If[LessEqual[y, -3.9e-81], t$95$0, If[LessEqual[y, -5.5e-198], t$95$1, If[LessEqual[y, -7.2e-299], t$95$0, If[LessEqual[y, 6.1e-284], t$95$1, If[LessEqual[y, 7.2e+102], t$95$0, 4.0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0269999999999999997 or 7.2000000000000003e102 < 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. 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 64.2%

      \[\leadsto 1 + 4 \cdot \color{blue}{0.75} \]

   if -0.0269999999999999997 < y < -1.4499999999999999e-53 or -3.89999999999999985e-81 < y < -5.5000000000000001e-198 or -7.2e-299 < y < 6.09999999999999976e-284

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. *-commutative 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-*r/ 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. distribute-lft-in 99.9%

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

      12. neg-mul-1 99.9%

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

      13. remove-double-neg 99.9%

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

      14. neg-mul-1 99.9%

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

      15. distribute-rgt-neg-in 99.9%

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

      16. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. *-commutative 88.3%

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

      3. distribute-rgt-neg-in 88.3%

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

      4. sub-neg 88.3%

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

      5. metadata-eval 88.3%

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

      6. +-commutative 88.3%

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

   10. Simplified 88.3%

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

   11. Taylor expanded in x around inf 66.7%

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

       1. *-commutative 66.7%

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

       2. associate-*l/ 66.7%

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

       3. associate-/l* 66.5%

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

   13. Simplified 66.5%

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

   if -1.4499999999999999e-53 < y < -3.89999999999999985e-81 or -5.5000000000000001e-198 < y < -7.2e-299 or 6.09999999999999976e-284 < y < 7.2000000000000003e102

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 93.1%

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

      1. mul-1-neg 93.1%

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

      2. *-commutative 93.1%

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

      3. distribute-rgt-neg-in 93.1%

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

      4. sub-neg 93.1%

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

      5. metadata-eval 93.1%

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

      6. +-commutative 93.1%

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

      7. associate-*r/ 93.1%

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

      8. sub-neg 93.1%

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

      9. +-commutative 93.1%

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

      10. *-commutative 93.1%

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

      11. distribute-lft-in 93.1%

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

      12. neg-mul-1 93.1%

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

      13. remove-double-neg 93.1%

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

      14. neg-mul-1 93.1%

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

      15. distribute-rgt-neg-in 93.1%

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

      16. metadata-eval 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in y around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. sub-neg 88.5%

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

      5. metadata-eval 88.5%

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

      6. +-commutative 88.5%

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

   10. Simplified 88.5%

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

   11. Taylor expanded in z around inf 62.5%

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

       1. *-commutative 62.5%

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

   13. Simplified 62.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.027:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-299}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ t_1 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;y \leq -0.017:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-298}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)) (t_1 (/ (* 4.0 x) y)))
   (if (<= y -0.017)
     4.0
     (if (<= y -1.05e-54)
       t_1
       (if (<= y -2.2e-81)
         t_0
         (if (<= y -2.05e-199)
           t_1
           (if (<= y -1.65e-298)
             t_0
             (if (<= y 1.36e-283)
               (* x (/ 4.0 y))
               (if (<= y 1.45e+102) t_0 4.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double t_1 = (4.0 * x) / y;
	double tmp;
	if (y <= -0.017) {
		tmp = 4.0;
	} else if (y <= -1.05e-54) {
		tmp = t_1;
	} else if (y <= -2.2e-81) {
		tmp = t_0;
	} else if (y <= -2.05e-199) {
		tmp = t_1;
	} else if (y <= -1.65e-298) {
		tmp = t_0;
	} else if (y <= 1.36e-283) {
		tmp = x * (4.0 / y);
	} else if (y <= 1.45e+102) {
		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) :: t_1
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    t_1 = (4.0d0 * x) / y
    if (y <= (-0.017d0)) then
        tmp = 4.0d0
    else if (y <= (-1.05d-54)) then
        tmp = t_1
    else if (y <= (-2.2d-81)) then
        tmp = t_0
    else if (y <= (-2.05d-199)) then
        tmp = t_1
    else if (y <= (-1.65d-298)) then
        tmp = t_0
    else if (y <= 1.36d-283) then
        tmp = x * (4.0d0 / y)
    else if (y <= 1.45d+102) 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 = (z / y) * -4.0;
	double t_1 = (4.0 * x) / y;
	double tmp;
	if (y <= -0.017) {
		tmp = 4.0;
	} else if (y <= -1.05e-54) {
		tmp = t_1;
	} else if (y <= -2.2e-81) {
		tmp = t_0;
	} else if (y <= -2.05e-199) {
		tmp = t_1;
	} else if (y <= -1.65e-298) {
		tmp = t_0;
	} else if (y <= 1.36e-283) {
		tmp = x * (4.0 / y);
	} else if (y <= 1.45e+102) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	t_1 = (4.0 * x) / y
	tmp = 0
	if y <= -0.017:
		tmp = 4.0
	elif y <= -1.05e-54:
		tmp = t_1
	elif y <= -2.2e-81:
		tmp = t_0
	elif y <= -2.05e-199:
		tmp = t_1
	elif y <= -1.65e-298:
		tmp = t_0
	elif y <= 1.36e-283:
		tmp = x * (4.0 / y)
	elif y <= 1.45e+102:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	t_1 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (y <= -0.017)
		tmp = 4.0;
	elseif (y <= -1.05e-54)
		tmp = t_1;
	elseif (y <= -2.2e-81)
		tmp = t_0;
	elseif (y <= -2.05e-199)
		tmp = t_1;
	elseif (y <= -1.65e-298)
		tmp = t_0;
	elseif (y <= 1.36e-283)
		tmp = Float64(x * Float64(4.0 / y));
	elseif (y <= 1.45e+102)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	t_1 = (4.0 * x) / y;
	tmp = 0.0;
	if (y <= -0.017)
		tmp = 4.0;
	elseif (y <= -1.05e-54)
		tmp = t_1;
	elseif (y <= -2.2e-81)
		tmp = t_0;
	elseif (y <= -2.05e-199)
		tmp = t_1;
	elseif (y <= -1.65e-298)
		tmp = t_0;
	elseif (y <= 1.36e-283)
		tmp = x * (4.0 / y);
	elseif (y <= 1.45e+102)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -0.017], 4.0, If[LessEqual[y, -1.05e-54], t$95$1, If[LessEqual[y, -2.2e-81], t$95$0, If[LessEqual[y, -2.05e-199], t$95$1, If[LessEqual[y, -1.65e-298], t$95$0, If[LessEqual[y, 1.36e-283], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+102], t$95$0, 4.0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.017000000000000001 or 1.4500000000000001e102 < 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. 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 64.2%

      \[\leadsto 1 + 4 \cdot \color{blue}{0.75} \]

   if -0.017000000000000001 < y < -1.05e-54 or -2.1999999999999999e-81 < y < -2.05000000000000011e-199

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.3%

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

   6. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 63.1%

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

   8. Simplified 63.1%

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

   if -1.05e-54 < y < -2.1999999999999999e-81 or -2.05000000000000011e-199 < y < -1.6500000000000001e-298 or 1.35999999999999997e-283 < y < 1.4500000000000001e102

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 93.1%

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

      1. mul-1-neg 93.1%

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

      2. *-commutative 93.1%

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

      3. distribute-rgt-neg-in 93.1%

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

      4. sub-neg 93.1%

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

      5. metadata-eval 93.1%

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

      6. +-commutative 93.1%

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

      7. associate-*r/ 93.1%

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

      8. sub-neg 93.1%

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

      9. +-commutative 93.1%

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

      10. *-commutative 93.1%

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

      11. distribute-lft-in 93.1%

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

      12. neg-mul-1 93.1%

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

      13. remove-double-neg 93.1%

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

      14. neg-mul-1 93.1%

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

      15. distribute-rgt-neg-in 93.1%

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

      16. metadata-eval 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in y around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. sub-neg 88.5%

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

      5. metadata-eval 88.5%

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

      6. +-commutative 88.5%

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

   10. Simplified 88.5%

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

   11. Taylor expanded in z around inf 62.5%

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

       1. *-commutative 62.5%

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

   13. Simplified 62.5%

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

   if -1.6500000000000001e-298 < y < 1.35999999999999997e-283

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-*r/ 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. *-commutative 100.0%

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

      11. distribute-lft-in 100.0%

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

      12. neg-mul-1 100.0%

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

      13. remove-double-neg 100.0%

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

      14. neg-mul-1 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. +-commutative 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in x around inf 86.5%

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

       1. *-commutative 86.5%

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

       2. associate-*l/ 86.5%

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

       3. associate-/l* 86.5%

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

   13. Simplified 86.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.017:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-298}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+171}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+112} \lor \neg \left(y \leq -1.15 \cdot 10^{+60}\right) \land y \leq 6.2 \cdot 10^{+130}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+171)
   4.0
   (if (or (<= y -7.8e+112) (and (not (<= y -1.15e+60)) (<= y 6.2e+130)))
     (* 4.0 (/ (- x z) y))
     4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+171) {
		tmp = 4.0;
	} else if ((y <= -7.8e+112) || (!(y <= -1.15e+60) && (y <= 6.2e+130))) {
		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 <= (-8.5d+171)) then
        tmp = 4.0d0
    else if ((y <= (-7.8d+112)) .or. (.not. (y <= (-1.15d+60))) .and. (y <= 6.2d+130)) 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 <= -8.5e+171) {
		tmp = 4.0;
	} else if ((y <= -7.8e+112) || (!(y <= -1.15e+60) && (y <= 6.2e+130))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+171:
		tmp = 4.0
	elif (y <= -7.8e+112) or (not (y <= -1.15e+60) and (y <= 6.2e+130)):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+171)
		tmp = 4.0;
	elseif ((y <= -7.8e+112) || (!(y <= -1.15e+60) && (y <= 6.2e+130)))
		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 <= -8.5e+171)
		tmp = 4.0;
	elseif ((y <= -7.8e+112) || (~((y <= -1.15e+60)) && (y <= 6.2e+130)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+171], 4.0, If[Or[LessEqual[y, -7.8e+112], And[N[Not[LessEqual[y, -1.15e+60]], $MachinePrecision], LessEqual[y, 6.2e+130]]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999995e171 or -7.79999999999999937e112 < y < -1.15000000000000008e60 or 6.1999999999999999e130 < y

   1. Initial program 98.6%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   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 76.6%

      \[\leadsto 1 + 4 \cdot \color{blue}{0.75} \]

   if -8.4999999999999995e171 < y < -7.79999999999999937e112 or -1.15000000000000008e60 < y < 6.1999999999999999e130

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.8%

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

   6. Taylor expanded in y around 0 84.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+171}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+112} \lor \neg \left(y \leq -1.15 \cdot 10^{+60}\right) \land y \leq 6.2 \cdot 10^{+130}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-66}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 4.0 (+ 0.75 (/ x y))))))
   (if (<= x -3e+69)
     t_0
     (if (<= x 8.6e-66)
       (+ 1.0 (* 4.0 (- 0.75 (/ z y))))
       (if (<= x 4.2e+39) t_0 (* 4.0 (/ (- x z) y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (0.75 + (x / y)));
	double tmp;
	if (x <= -3e+69) {
		tmp = t_0;
	} else if (x <= 8.6e-66) {
		tmp = 1.0 + (4.0 * (0.75 - (z / y)));
	} else if (x <= 4.2e+39) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (4.0d0 * (0.75d0 + (x / y)))
    if (x <= (-3d+69)) then
        tmp = t_0
    else if (x <= 8.6d-66) then
        tmp = 1.0d0 + (4.0d0 * (0.75d0 - (z / y)))
    else if (x <= 4.2d+39) then
        tmp = t_0
    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 t_0 = 1.0 + (4.0 * (0.75 + (x / y)));
	double tmp;
	if (x <= -3e+69) {
		tmp = t_0;
	} else if (x <= 8.6e-66) {
		tmp = 1.0 + (4.0 * (0.75 - (z / y)));
	} else if (x <= 4.2e+39) {
		tmp = t_0;
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 * (0.75 + (x / y)))
	tmp = 0
	if x <= -3e+69:
		tmp = t_0
	elif x <= 8.6e-66:
		tmp = 1.0 + (4.0 * (0.75 - (z / y)))
	elif x <= 4.2e+39:
		tmp = t_0
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 * Float64(0.75 + Float64(x / y))))
	tmp = 0.0
	if (x <= -3e+69)
		tmp = t_0;
	elseif (x <= 8.6e-66)
		tmp = Float64(1.0 + Float64(4.0 * Float64(0.75 - Float64(z / y))));
	elseif (x <= 4.2e+39)
		tmp = t_0;
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (4.0 * (0.75 + (x / y)));
	tmp = 0.0;
	if (x <= -3e+69)
		tmp = t_0;
	elseif (x <= 8.6e-66)
		tmp = 1.0 + (4.0 * (0.75 - (z / y)));
	elseif (x <= 4.2e+39)
		tmp = t_0;
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(4.0 * N[(0.75 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+69], t$95$0, If[LessEqual[x, 8.6e-66], N[(1.0 + N[(4.0 * N[(0.75 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+39], t$95$0, N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.99999999999999983e69 or 8.60000000000000027e-66 < x < 4.1999999999999997e39

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.2%

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

      1. associate--l+ 97.2%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 90.2%

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

   if -2.99999999999999983e69 < x < 8.60000000000000027e-66

   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* 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 93.3%

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

      1. div-sub 93.3%

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

      2. *-commutative 93.3%

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

      3. *-lft-identity 93.3%

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

      4. associate-*l/ 93.2%

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

      5. associate-*r* 93.2%

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

      6. lft-mult-inverse 93.4%

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

      7. metadata-eval 93.4%

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

   7. Simplified 93.4%

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

   if 4.1999999999999997e39 < 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 y around 0 90.4%

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

   6. Taylor expanded in y around 0 89.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+69}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-66}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+39}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-63}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 4.0 (+ 0.75 (/ x y))))))
   (if (<= x -3.2e+69)
     t_0
     (if (<= x 1.65e-63)
       (+ 1.0 (* 4.0 (- 0.75 (/ z y))))
       (if (<= x 2.4e+41) t_0 (+ 1.0 (* 4.0 (/ (- x z) y))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (0.75 + (x / y)));
	double tmp;
	if (x <= -3.2e+69) {
		tmp = t_0;
	} else if (x <= 1.65e-63) {
		tmp = 1.0 + (4.0 * (0.75 - (z / y)));
	} else if (x <= 2.4e+41) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (4.0d0 * (0.75d0 + (x / y)))
    if (x <= (-3.2d+69)) then
        tmp = t_0
    else if (x <= 1.65d-63) then
        tmp = 1.0d0 + (4.0d0 * (0.75d0 - (z / y)))
    else if (x <= 2.4d+41) then
        tmp = t_0
    else
        tmp = 1.0d0 + (4.0d0 * ((x - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (0.75 + (x / y)));
	double tmp;
	if (x <= -3.2e+69) {
		tmp = t_0;
	} else if (x <= 1.65e-63) {
		tmp = 1.0 + (4.0 * (0.75 - (z / y)));
	} else if (x <= 2.4e+41) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (4.0 * ((x - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 * (0.75 + (x / y)))
	tmp = 0
	if x <= -3.2e+69:
		tmp = t_0
	elif x <= 1.65e-63:
		tmp = 1.0 + (4.0 * (0.75 - (z / y)))
	elif x <= 2.4e+41:
		tmp = t_0
	else:
		tmp = 1.0 + (4.0 * ((x - z) / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 * Float64(0.75 + Float64(x / y))))
	tmp = 0.0
	if (x <= -3.2e+69)
		tmp = t_0;
	elseif (x <= 1.65e-63)
		tmp = Float64(1.0 + Float64(4.0 * Float64(0.75 - Float64(z / y))));
	elseif (x <= 2.4e+41)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(4.0 * Float64(Float64(x - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (4.0 * (0.75 + (x / y)));
	tmp = 0.0;
	if (x <= -3.2e+69)
		tmp = t_0;
	elseif (x <= 1.65e-63)
		tmp = 1.0 + (4.0 * (0.75 - (z / y)));
	elseif (x <= 2.4e+41)
		tmp = t_0;
	else
		tmp = 1.0 + (4.0 * ((x - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(4.0 * N[(0.75 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+69], t$95$0, If[LessEqual[x, 1.65e-63], N[(1.0 + N[(4.0 * N[(0.75 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+41], t$95$0, N[(1.0 + N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999985e69 or 1.64999999999999997e-63 < x < 2.4000000000000002e41

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.2%

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

      1. associate--l+ 97.2%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 90.2%

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

   if -3.19999999999999985e69 < x < 1.64999999999999997e-63

   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* 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 93.3%

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

      1. div-sub 93.3%

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

      2. *-commutative 93.3%

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

      3. *-lft-identity 93.3%

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

      4. associate-*l/ 93.2%

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

      5. associate-*r* 93.2%

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

      6. lft-mult-inverse 93.4%

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

      7. metadata-eval 93.4%

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

   7. Simplified 93.4%

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

   if 2.4000000000000002e41 < 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 y around 0 90.4%

      \[\leadsto 1 + 4 \cdot \color{blue}{\frac{x - z}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+69}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-63}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-5} \lor \neg \left(y \leq 6.5 \cdot 10^{+92}\right):\\ \;\;\;\;1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.36e-5) (not (<= y 6.5e+92)))
   (+ 1.0 (* 4.0 (+ 0.75 (/ x y))))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.36e-5) || !(y <= 6.5e+92)) {
		tmp = 1.0 + (4.0 * (0.75 + (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 <= (-1.36d-5)) .or. (.not. (y <= 6.5d+92))) then
        tmp = 1.0d0 + (4.0d0 * (0.75d0 + (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 <= -1.36e-5) || !(y <= 6.5e+92)) {
		tmp = 1.0 + (4.0 * (0.75 + (x / y)));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.36e-5) or not (y <= 6.5e+92):
		tmp = 1.0 + (4.0 * (0.75 + (x / y)))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.36e-5) || !(y <= 6.5e+92))
		tmp = Float64(1.0 + Float64(4.0 * Float64(0.75 + Float64(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 <= -1.36e-5) || ~((y <= 6.5e+92)))
		tmp = 1.0 + (4.0 * (0.75 + (x / y)));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.36e-5], N[Not[LessEqual[y, 6.5e+92]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(0.75 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.36000000000000002e-5 or 6.49999999999999999e92 < y

   1. Initial program 99.1%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 86.6%

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

   if -1.36000000000000002e-5 < y < 6.49999999999999999e92

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 91.5%

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

   6. Taylor expanded in y around 0 90.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-5} \lor \neg \left(y \leq 6.5 \cdot 10^{+92}\right):\\ \;\;\;\;1 + 4 \cdot \left(0.75 + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+69} \lor \neg \left(x \leq 2.95 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e+69) (not (<= x 2.95e-64)))
   (* x (/ 4.0 y))
   (* (/ z y) -4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e+69) || !(x <= 2.95e-64)) {
		tmp = x * (4.0 / y);
	} else {
		tmp = (z / y) * -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 <= (-3.7d+69)) .or. (.not. (x <= 2.95d-64))) then
        tmp = x * (4.0d0 / y)
    else
        tmp = (z / y) * (-4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e+69) || !(x <= 2.95e-64)) {
		tmp = x * (4.0 / y);
	} else {
		tmp = (z / y) * -4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e+69) or not (x <= 2.95e-64):
		tmp = x * (4.0 / y)
	else:
		tmp = (z / y) * -4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e+69) || !(x <= 2.95e-64))
		tmp = Float64(x * Float64(4.0 / y));
	else
		tmp = Float64(Float64(z / y) * -4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.7e+69) || ~((x <= 2.95e-64)))
		tmp = x * (4.0 / y);
	else
		tmp = (z / y) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e+69], N[Not[LessEqual[x, 2.95e-64]], $MachinePrecision]], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999999e69 or 2.94999999999999997e-64 < 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 -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. *-commutative 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-*r/ 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. distribute-lft-in 99.9%

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

      12. neg-mul-1 99.9%

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

      13. remove-double-neg 99.9%

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

      14. neg-mul-1 99.9%

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

      15. distribute-rgt-neg-in 99.9%

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

      16. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. *-commutative 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

      4. sub-neg 79.9%

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

      5. metadata-eval 79.9%

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

      6. +-commutative 79.9%

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

   10. Simplified 79.9%

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

   11. Taylor expanded in x around inf 62.1%

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

       1. *-commutative 62.1%

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

       2. associate-*l/ 62.1%

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

       3. associate-/l* 61.9%

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

   13. Simplified 61.9%

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

   if -3.6999999999999999e69 < x < 2.94999999999999997e-64

   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* 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 72.1%

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

      1. mul-1-neg 72.1%

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

      2. *-commutative 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. sub-neg 72.1%

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

      5. metadata-eval 72.1%

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

      6. +-commutative 72.1%

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

      7. associate-*r/ 72.1%

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

      8. sub-neg 72.1%

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

      9. +-commutative 72.1%

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

      10. *-commutative 72.1%

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

      11. distribute-lft-in 72.1%

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

      12. neg-mul-1 72.1%

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

      13. remove-double-neg 72.1%

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

      14. neg-mul-1 72.1%

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

      15. distribute-rgt-neg-in 72.1%

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

      16. metadata-eval 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. *-commutative 55.4%

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

      3. distribute-rgt-neg-in 55.4%

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

      4. sub-neg 55.4%

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

      5. metadata-eval 55.4%

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

      6. +-commutative 55.4%

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

   10. Simplified 55.4%

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

   11. Taylor expanded in z around inf 50.1%

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

       1. *-commutative 50.1%

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

   13. Simplified 50.1%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+69} \lor \neg \left(x \leq 2.95 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{4}{y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x * (4.0 / 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 = x * (4.0d0 / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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 85.6%

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

   1. mul-1-neg 85.6%

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

   2. *-commutative 85.6%

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

   3. distribute-rgt-neg-in 85.6%

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

   4. sub-neg 85.6%

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

   5. metadata-eval 85.6%

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

   6. +-commutative 85.6%

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

   7. associate-*r/ 85.6%

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

   8. sub-neg 85.6%

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

   9. +-commutative 85.6%

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

   10. *-commutative 85.6%

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

   11. distribute-lft-in 85.6%

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

   12. neg-mul-1 85.6%

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

   13. remove-double-neg 85.6%

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

   14. neg-mul-1 85.6%

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

   15. distribute-rgt-neg-in 85.6%

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

   16. metadata-eval 85.6%

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

7. Simplified 85.6%

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

8. Taylor expanded in y around 0 67.3%

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

   1. mul-1-neg 67.3%

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

   2. *-commutative 67.3%

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

   3. distribute-rgt-neg-in 67.3%

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

   4. sub-neg 67.3%

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

   5. metadata-eval 67.3%

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

   6. +-commutative 67.3%

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

10. Simplified 67.3%

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

11. Taylor expanded in x around inf 34.6%

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

    1. *-commutative 34.6%

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

    2. associate-*l/ 34.6%

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

    3. associate-/l* 34.5%

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

13. Simplified 34.5%

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

14. Final simplification 34.5%

    \[\leadsto x \cdot \frac{4}{y} \]
15. Add Preprocessing

Alternative 10: 7.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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 38.3%

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

   1. neg-mul-1 38.3%

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

   2. distribute-neg-frac2 38.3%

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

7. Simplified 38.3%

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

8. Taylor expanded in z around 0 7.8%

   \[\leadsto \color{blue}{1} \]

9. Final simplification 7.8%

   \[\leadsto 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(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)))