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

Percentage Accurate: 99.7% → 100.0%

Time: 8.4s

Alternatives: 8

Speedup: 1.4×

• 20.9% 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, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto 4 + 4 \cdot \frac{x - z}{y} \]
5. Add Preprocessing

Alternative 2: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ \mathbf{if}\;y \leq -490000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-279}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)))
   (if (<= y -490000000.0)
     4.0
     (if (<= y -1.55e-74)
       t_0
       (if (<= y -1.15e-142)
         (* x (/ 4.0 y))
         (if (<= y -1.7e-279)
           t_0
           (if (<= y 5.2e-102)
             (/ 4.0 (/ y x))
             (if (<= y 1.8e+63) t_0 4.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double tmp;
	if (y <= -490000000.0) {
		tmp = 4.0;
	} else if (y <= -1.55e-74) {
		tmp = t_0;
	} else if (y <= -1.15e-142) {
		tmp = x * (4.0 / y);
	} else if (y <= -1.7e-279) {
		tmp = t_0;
	} else if (y <= 5.2e-102) {
		tmp = 4.0 / (y / x);
	} else if (y <= 1.8e+63) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    if (y <= (-490000000.0d0)) then
        tmp = 4.0d0
    else if (y <= (-1.55d-74)) then
        tmp = t_0
    else if (y <= (-1.15d-142)) then
        tmp = x * (4.0d0 / y)
    else if (y <= (-1.7d-279)) then
        tmp = t_0
    else if (y <= 5.2d-102) then
        tmp = 4.0d0 / (y / x)
    else if (y <= 1.8d+63) 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 * -4.0) / y;
	double tmp;
	if (y <= -490000000.0) {
		tmp = 4.0;
	} else if (y <= -1.55e-74) {
		tmp = t_0;
	} else if (y <= -1.15e-142) {
		tmp = x * (4.0 / y);
	} else if (y <= -1.7e-279) {
		tmp = t_0;
	} else if (y <= 5.2e-102) {
		tmp = 4.0 / (y / x);
	} else if (y <= 1.8e+63) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	tmp = 0
	if y <= -490000000.0:
		tmp = 4.0
	elif y <= -1.55e-74:
		tmp = t_0
	elif y <= -1.15e-142:
		tmp = x * (4.0 / y)
	elif y <= -1.7e-279:
		tmp = t_0
	elif y <= 5.2e-102:
		tmp = 4.0 / (y / x)
	elif y <= 1.8e+63:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	tmp = 0.0
	if (y <= -490000000.0)
		tmp = 4.0;
	elseif (y <= -1.55e-74)
		tmp = t_0;
	elseif (y <= -1.15e-142)
		tmp = Float64(x * Float64(4.0 / y));
	elseif (y <= -1.7e-279)
		tmp = t_0;
	elseif (y <= 5.2e-102)
		tmp = Float64(4.0 / Float64(y / x));
	elseif (y <= 1.8e+63)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	tmp = 0.0;
	if (y <= -490000000.0)
		tmp = 4.0;
	elseif (y <= -1.55e-74)
		tmp = t_0;
	elseif (y <= -1.15e-142)
		tmp = x * (4.0 / y);
	elseif (y <= -1.7e-279)
		tmp = t_0;
	elseif (y <= 5.2e-102)
		tmp = 4.0 / (y / x);
	elseif (y <= 1.8e+63)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -490000000.0], 4.0, If[LessEqual[y, -1.55e-74], t$95$0, If[LessEqual[y, -1.15e-142], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-279], t$95$0, If[LessEqual[y, 5.2e-102], N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+63], t$95$0, 4.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9e8 or 1.79999999999999999e63 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 65.4%

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

   if -4.9e8 < y < -1.5500000000000001e-74 or -1.15000000000000001e-142 < y < -1.70000000000000007e-279 or 5.19999999999999973e-102 < y < 1.79999999999999999e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.3%

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

      1. +-commutative 96.3%

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

      2. distribute-lft-out 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in y around 0 89.6%

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

   7. Taylor expanded in x around 0 62.3%

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

      1. associate-*r/ 62.3%

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

   9. Simplified 62.3%

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

   if -1.5500000000000001e-74 < y < -1.15000000000000001e-142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 76.8%

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

   7. Taylor expanded in x around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*l/ 61.0%

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

      3. associate-/l* 61.0%

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

   9. Simplified 61.0%

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

   if -1.70000000000000007e-279 < y < 5.19999999999999973e-102

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. distribute-lft-out 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in y around 0 91.1%

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

      1. clear-num 91.1%

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

      2. un-div-inv 91.1%

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

   8. Applied egg-rr 91.1%

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

   9. Taylor expanded in x around inf 69.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -490000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-74}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-279}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+73} \lor \neg \left(y \leq 4.4 \cdot 10^{+119}\right) \land y \leq 3.3 \cdot 10^{+155}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+86)
   4.0
   (if (or (<= y 3.2e+73) (and (not (<= y 4.4e+119)) (<= y 3.3e+155)))
     (* 4.0 (/ (- x z) y))
     4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+86) {
		tmp = 4.0;
	} else if ((y <= 3.2e+73) || (!(y <= 4.4e+119) && (y <= 3.3e+155))) {
		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 <= (-1.2d+86)) then
        tmp = 4.0d0
    else if ((y <= 3.2d+73) .or. (.not. (y <= 4.4d+119)) .and. (y <= 3.3d+155)) 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 <= -1.2e+86) {
		tmp = 4.0;
	} else if ((y <= 3.2e+73) || (!(y <= 4.4e+119) && (y <= 3.3e+155))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+86:
		tmp = 4.0
	elif (y <= 3.2e+73) or (not (y <= 4.4e+119) and (y <= 3.3e+155)):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+86)
		tmp = 4.0;
	elseif ((y <= 3.2e+73) || (!(y <= 4.4e+119) && (y <= 3.3e+155)))
		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 <= -1.2e+86)
		tmp = 4.0;
	elseif ((y <= 3.2e+73) || (~((y <= 4.4e+119)) && (y <= 3.3e+155)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+86], 4.0, If[Or[LessEqual[y, 3.2e+73], And[N[Not[LessEqual[y, 4.4e+119]], $MachinePrecision], LessEqual[y, 3.3e+155]]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e86 or 3.19999999999999982e73 < y < 4.4000000000000003e119 or 3.2999999999999999e155 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.0%

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

   if -1.2e86 < y < 3.19999999999999982e73 or 4.4000000000000003e119 < y < 3.2999999999999999e155

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. distribute-lft-out 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around 0 84.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+73} \lor \neg \left(y \leq 4.4 \cdot 10^{+119}\right) \land y \leq 3.3 \cdot 10^{+155}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ \mathbf{if}\;y \leq -760000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-279}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)))
   (if (<= y -760000000.0)
     4.0
     (if (<= y -1.2e-279)
       t_0
       (if (<= y 8.8e-102) (/ (* 4.0 x) y) (if (<= y 3.25e+63) t_0 4.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double tmp;
	if (y <= -760000000.0) {
		tmp = 4.0;
	} else if (y <= -1.2e-279) {
		tmp = t_0;
	} else if (y <= 8.8e-102) {
		tmp = (4.0 * x) / y;
	} else if (y <= 3.25e+63) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    if (y <= (-760000000.0d0)) then
        tmp = 4.0d0
    else if (y <= (-1.2d-279)) then
        tmp = t_0
    else if (y <= 8.8d-102) then
        tmp = (4.0d0 * x) / y
    else if (y <= 3.25d+63) 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 * -4.0) / y;
	double tmp;
	if (y <= -760000000.0) {
		tmp = 4.0;
	} else if (y <= -1.2e-279) {
		tmp = t_0;
	} else if (y <= 8.8e-102) {
		tmp = (4.0 * x) / y;
	} else if (y <= 3.25e+63) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	tmp = 0
	if y <= -760000000.0:
		tmp = 4.0
	elif y <= -1.2e-279:
		tmp = t_0
	elif y <= 8.8e-102:
		tmp = (4.0 * x) / y
	elif y <= 3.25e+63:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	tmp = 0.0
	if (y <= -760000000.0)
		tmp = 4.0;
	elseif (y <= -1.2e-279)
		tmp = t_0;
	elseif (y <= 8.8e-102)
		tmp = Float64(Float64(4.0 * x) / y);
	elseif (y <= 3.25e+63)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	tmp = 0.0;
	if (y <= -760000000.0)
		tmp = 4.0;
	elseif (y <= -1.2e-279)
		tmp = t_0;
	elseif (y <= 8.8e-102)
		tmp = (4.0 * x) / y;
	elseif (y <= 3.25e+63)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -760000000.0], 4.0, If[LessEqual[y, -1.2e-279], t$95$0, If[LessEqual[y, 8.8e-102], N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.25e+63], t$95$0, 4.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6e8 or 3.24999999999999996e63 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 65.4%

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

   if -7.6e8 < y < -1.19999999999999995e-279 or 8.80000000000000052e-102 < y < 3.24999999999999996e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. distribute-lft-out 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in y around 0 87.9%

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

   7. Taylor expanded in x around 0 56.5%

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

      1. associate-*r/ 56.5%

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

   9. Simplified 56.5%

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

   if -1.19999999999999995e-279 < y < 8.80000000000000052e-102

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. distribute-lft-out 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in y around 0 91.1%

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

   7. Taylor expanded in x around inf 69.6%

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

      1. associate-*r/ 69.6%

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

   9. Simplified 69.6%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -760000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-279}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+63}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+54} \lor \neg \left(z \leq 2.7 \cdot 10^{+57}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.5e+54) (not (<= z 2.7e+57)))
   (* 4.0 (/ (- x z) y))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e+54) || !(z <= 2.7e+57)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.5d+54)) .or. (.not. (z <= 2.7d+57))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e+54) || !(z <= 2.7e+57)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.5e+54) or not (z <= 2.7e+57):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.5e+54) || !(z <= 2.7e+57))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.5e+54) || ~((z <= 2.7e+57)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.5e+54], N[Not[LessEqual[z, 2.7e+57]], $MachinePrecision]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e54 or 2.6999999999999998e57 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.6%

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

      1. +-commutative 94.6%

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

      2. distribute-lft-out 94.6%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in y around 0 80.9%

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

   if -9.4999999999999999e54 < z < 2.6999999999999998e57

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 94.7%

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

      1. distribute-lft-in 94.7%

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

      2. metadata-eval 94.7%

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

      3. associate-+r+ 94.7%

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

      4. metadata-eval 94.7%

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

   7. Simplified 94.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+54} \lor \neg \left(z \leq 2.7 \cdot 10^{+57}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+60} \lor \neg \left(z \leq 9.2 \cdot 10^{+51}\right):\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.75e+60) (not (<= z 9.2e+51)))
   (+ 4.0 (/ (* z -4.0) y))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.75e+60) || !(z <= 9.2e+51)) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.75d+60)) .or. (.not. (z <= 9.2d+51))) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.75e+60) || !(z <= 9.2e+51)) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.75e+60) or not (z <= 9.2e+51):
		tmp = 4.0 + ((z * -4.0) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.75e+60) || !(z <= 9.2e+51))
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.75e+60) || ~((z <= 9.2e+51)))
		tmp = 4.0 + ((z * -4.0) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.75e+60], N[Not[LessEqual[z, 9.2e+51]], $MachinePrecision]], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e60 or 9.2000000000000002e51 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

      4. associate--l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r+ 100.0%

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

      9. div-sub 100.0%

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

      10. sub-neg 100.0%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.8%

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

      1. sub-neg 91.8%

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

      2. distribute-lft-in 91.8%

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

      3. metadata-eval 91.8%

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

      4. associate-+r+ 91.8%

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

      5. metadata-eval 91.8%

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

      6. neg-mul-1 91.8%

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

      7. associate-*r* 91.8%

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

      8. metadata-eval 91.8%

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

      9. *-commutative 91.8%

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

      10. associate-*l/ 91.8%

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

   7. Simplified 91.8%

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

   if -2.75e60 < z < 9.2000000000000002e51

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 94.6%

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

      1. distribute-lft-in 94.6%

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

      2. metadata-eval 94.6%

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

      3. associate-+r+ 94.6%

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

      4. metadata-eval 94.6%

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

   7. Simplified 94.6%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+60} \lor \neg \left(z \leq 9.2 \cdot 10^{+51}\right):\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+47) 4.0 (if (<= y 6.1e-58) (* x (/ 4.0 y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+47) {
		tmp = 4.0;
	} else if (y <= 6.1e-58) {
		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 (y <= (-1.4d+47)) then
        tmp = 4.0d0
    else if (y <= 6.1d-58) 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 (y <= -1.4e+47) {
		tmp = 4.0;
	} else if (y <= 6.1e-58) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+47:
		tmp = 4.0
	elif y <= 6.1e-58:
		tmp = x * (4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+47)
		tmp = 4.0;
	elseif (y <= 6.1e-58)
		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 (y <= -1.4e+47)
		tmp = 4.0;
	elseif (y <= 6.1e-58)
		tmp = x * (4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+47], 4.0, If[LessEqual[y, 6.1e-58], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999994e47 or 6.1000000000000003e-58 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 62.1%

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

   if -1.39999999999999994e47 < y < 6.1000000000000003e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.1%

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

      1. +-commutative 96.1%

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

      2. distribute-lft-out 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in y around 0 89.5%

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

   7. Taylor expanded in x around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-*l/ 52.0%

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

      3. associate-/l* 51.9%

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

   9. Simplified 51.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 35.7%

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

4. Final simplification 35.7%

   \[\leadsto 4 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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)))