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

Percentage Accurate: 99.8% → 100.0%

Time: 7.7s

Alternatives: 9

Speedup: 1.0×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (* 4.0 (/ (+ x (- (* y 0.25) z)) y))))

C

double code(double x, double y, double z) {
	return 1.0 + (4.0 * ((x + ((y * 0.25) - 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 * 0.25d0) - z)) / y))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (4.0 * ((x + ((y * 0.25) - z)) / y));
}

Python

def code(x, y, z):
	return 1.0 + (4.0 * ((x + ((y * 0.25) - z)) / y))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(4.0 * Float64(Float64(x + Float64(Float64(y * 0.25) - z)) / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (4.0 * ((x + ((y * 0.25) - z)) / y));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(4.0 * N[(N[(x + N[(N[(y * 0.25), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

   2. associate--l+ 100.0%

      \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto 1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y} \]
6. Add Preprocessing

Alternative 2: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -0.049:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+97}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))) (t_1 (* 4.0 (/ x y))))
   (if (<= y -0.049)
     2.0
     (if (<= y -7e-53)
       t_1
       (if (<= y -1.3e-74)
         t_0
         (if (<= y -2.7e-200)
           t_1
           (if (<= y -9.5e-298)
             t_0
             (if (<= y 6e-284) t_1 (if (<= y 4.8e+97) t_0 2.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (y <= -0.049) {
		tmp = 2.0;
	} else if (y <= -7e-53) {
		tmp = t_1;
	} else if (y <= -1.3e-74) {
		tmp = t_0;
	} else if (y <= -2.7e-200) {
		tmp = t_1;
	} else if (y <= -9.5e-298) {
		tmp = t_0;
	} else if (y <= 6e-284) {
		tmp = t_1;
	} else if (y <= 4.8e+97) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * ((-4.0d0) / y)
    t_1 = 4.0d0 * (x / y)
    if (y <= (-0.049d0)) then
        tmp = 2.0d0
    else if (y <= (-7d-53)) then
        tmp = t_1
    else if (y <= (-1.3d-74)) then
        tmp = t_0
    else if (y <= (-2.7d-200)) then
        tmp = t_1
    else if (y <= (-9.5d-298)) then
        tmp = t_0
    else if (y <= 6d-284) then
        tmp = t_1
    else if (y <= 4.8d+97) then
        tmp = t_0
    else
        tmp = 2.0d0
    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 t_1 = 4.0 * (x / y);
	double tmp;
	if (y <= -0.049) {
		tmp = 2.0;
	} else if (y <= -7e-53) {
		tmp = t_1;
	} else if (y <= -1.3e-74) {
		tmp = t_0;
	} else if (y <= -2.7e-200) {
		tmp = t_1;
	} else if (y <= -9.5e-298) {
		tmp = t_0;
	} else if (y <= 6e-284) {
		tmp = t_1;
	} else if (y <= 4.8e+97) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	t_1 = 4.0 * (x / y)
	tmp = 0
	if y <= -0.049:
		tmp = 2.0
	elif y <= -7e-53:
		tmp = t_1
	elif y <= -1.3e-74:
		tmp = t_0
	elif y <= -2.7e-200:
		tmp = t_1
	elif y <= -9.5e-298:
		tmp = t_0
	elif y <= 6e-284:
		tmp = t_1
	elif y <= 4.8e+97:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (y <= -0.049)
		tmp = 2.0;
	elseif (y <= -7e-53)
		tmp = t_1;
	elseif (y <= -1.3e-74)
		tmp = t_0;
	elseif (y <= -2.7e-200)
		tmp = t_1;
	elseif (y <= -9.5e-298)
		tmp = t_0;
	elseif (y <= 6e-284)
		tmp = t_1;
	elseif (y <= 4.8e+97)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	t_1 = 4.0 * (x / y);
	tmp = 0.0;
	if (y <= -0.049)
		tmp = 2.0;
	elseif (y <= -7e-53)
		tmp = t_1;
	elseif (y <= -1.3e-74)
		tmp = t_0;
	elseif (y <= -2.7e-200)
		tmp = t_1;
	elseif (y <= -9.5e-298)
		tmp = t_0;
	elseif (y <= 6e-284)
		tmp = t_1;
	elseif (y <= 4.8e+97)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.049], 2.0, If[LessEqual[y, -7e-53], t$95$1, If[LessEqual[y, -1.3e-74], t$95$0, If[LessEqual[y, -2.7e-200], t$95$1, If[LessEqual[y, -9.5e-298], t$95$0, If[LessEqual[y, 6e-284], t$95$1, If[LessEqual[y, 4.8e+97], t$95$0, 2.0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.049000000000000002 or 4.8e97 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.0%

      \[\leadsto \color{blue}{2} \]

   if -0.049000000000000002 < y < -6.99999999999999987e-53 or -1.3e-74 < y < -2.7000000000000001e-200 or -9.50000000000000012e-298 < y < 5.9999999999999999e-284

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.8%

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

   if -6.99999999999999987e-53 < y < -1.3e-74 or -2.7000000000000001e-200 < y < -9.50000000000000012e-298 or 5.9999999999999999e-284 < y < 4.8e97

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.5%

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

      1. associate-*r/ 62.5%

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

      2. metadata-eval 62.5%

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

      3. associate-*r* 62.5%

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

      4. neg-mul-1 62.5%

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

      5. associate-*l/ 62.3%

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

      6. distribute-rgt-neg-out 62.3%

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

      7. *-commutative 62.3%

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

      8. distribute-rgt-neg-in 62.3%

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

      9. distribute-neg-frac 62.3%

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

      10. metadata-eval 62.3%

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

   7. Simplified 62.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.049:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-53}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-200}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-284}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -0.037:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-298}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)) (t_1 (* 4.0 (/ x y))))
   (if (<= y -0.037)
     2.0
     (if (<= y -7.8e-54)
       t_1
       (if (<= y -2.8e-78)
         t_0
         (if (<= y -3e-201)
           t_1
           (if (<= y -1.85e-298)
             t_0
             (if (<= y 1.95e-283) t_1 (if (<= y 7.4e+102) t_0 2.0)))))))))

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 <= -0.037) {
		tmp = 2.0;
	} else if (y <= -7.8e-54) {
		tmp = t_1;
	} else if (y <= -2.8e-78) {
		tmp = t_0;
	} else if (y <= -3e-201) {
		tmp = t_1;
	} else if (y <= -1.85e-298) {
		tmp = t_0;
	} else if (y <= 1.95e-283) {
		tmp = t_1;
	} else if (y <= 7.4e+102) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	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 <= (-0.037d0)) then
        tmp = 2.0d0
    else if (y <= (-7.8d-54)) then
        tmp = t_1
    else if (y <= (-2.8d-78)) then
        tmp = t_0
    else if (y <= (-3d-201)) then
        tmp = t_1
    else if (y <= (-1.85d-298)) then
        tmp = t_0
    else if (y <= 1.95d-283) then
        tmp = t_1
    else if (y <= 7.4d+102) then
        tmp = t_0
    else
        tmp = 2.0d0
    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 <= -0.037) {
		tmp = 2.0;
	} else if (y <= -7.8e-54) {
		tmp = t_1;
	} else if (y <= -2.8e-78) {
		tmp = t_0;
	} else if (y <= -3e-201) {
		tmp = t_1;
	} else if (y <= -1.85e-298) {
		tmp = t_0;
	} else if (y <= 1.95e-283) {
		tmp = t_1;
	} else if (y <= 7.4e+102) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	t_1 = 4.0 * (x / y)
	tmp = 0
	if y <= -0.037:
		tmp = 2.0
	elif y <= -7.8e-54:
		tmp = t_1
	elif y <= -2.8e-78:
		tmp = t_0
	elif y <= -3e-201:
		tmp = t_1
	elif y <= -1.85e-298:
		tmp = t_0
	elif y <= 1.95e-283:
		tmp = t_1
	elif y <= 7.4e+102:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (y <= -0.037)
		tmp = 2.0;
	elseif (y <= -7.8e-54)
		tmp = t_1;
	elseif (y <= -2.8e-78)
		tmp = t_0;
	elseif (y <= -3e-201)
		tmp = t_1;
	elseif (y <= -1.85e-298)
		tmp = t_0;
	elseif (y <= 1.95e-283)
		tmp = t_1;
	elseif (y <= 7.4e+102)
		tmp = t_0;
	else
		tmp = 2.0;
	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 <= -0.037)
		tmp = 2.0;
	elseif (y <= -7.8e-54)
		tmp = t_1;
	elseif (y <= -2.8e-78)
		tmp = t_0;
	elseif (y <= -3e-201)
		tmp = t_1;
	elseif (y <= -1.85e-298)
		tmp = t_0;
	elseif (y <= 1.95e-283)
		tmp = t_1;
	elseif (y <= 7.4e+102)
		tmp = t_0;
	else
		tmp = 2.0;
	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[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.037], 2.0, If[LessEqual[y, -7.8e-54], t$95$1, If[LessEqual[y, -2.8e-78], t$95$0, If[LessEqual[y, -3e-201], t$95$1, If[LessEqual[y, -1.85e-298], t$95$0, If[LessEqual[y, 1.95e-283], t$95$1, If[LessEqual[y, 7.4e+102], t$95$0, 2.0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0369999999999999982 or 7.40000000000000045e102 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.0%

      \[\leadsto \color{blue}{2} \]

   if -0.0369999999999999982 < y < -7.8e-54 or -2.80000000000000024e-78 < y < -3.00000000000000002e-201 or -1.8499999999999999e-298 < y < 1.9500000000000001e-283

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.8%

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

   if -7.8e-54 < y < -2.80000000000000024e-78 or -3.00000000000000002e-201 < y < -1.8499999999999999e-298 or 1.9500000000000001e-283 < y < 7.40000000000000045e102

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.5%

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

      1. *-commutative 62.5%

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

   7. Simplified 62.5%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.037:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-54}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-201}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-298}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-283}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+171}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+115} \lor \neg \left(y \leq -1.15 \cdot 10^{+60}\right) \land y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+171)
   2.0
   (if (or (<= y -1.3e+115) (and (not (<= y -1.15e+60)) (<= y 2.5e+129)))
     (* 4.0 (/ (- x z) y))
     2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+171) {
		tmp = 2.0;
	} else if ((y <= -1.3e+115) || (!(y <= -1.15e+60) && (y <= 2.5e+129))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	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 <= (-7.5d+171)) then
        tmp = 2.0d0
    else if ((y <= (-1.3d+115)) .or. (.not. (y <= (-1.15d+60))) .and. (y <= 2.5d+129)) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+171) {
		tmp = 2.0;
	} else if ((y <= -1.3e+115) || (!(y <= -1.15e+60) && (y <= 2.5e+129))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+171:
		tmp = 2.0
	elif (y <= -1.3e+115) or (not (y <= -1.15e+60) and (y <= 2.5e+129)):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+171)
		tmp = 2.0;
	elseif ((y <= -1.3e+115) || (!(y <= -1.15e+60) && (y <= 2.5e+129)))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.5e+171)
		tmp = 2.0;
	elseif ((y <= -1.3e+115) || (~((y <= -1.15e+60)) && (y <= 2.5e+129)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+171], 2.0, If[Or[LessEqual[y, -1.3e+115], And[N[Not[LessEqual[y, -1.15e+60]], $MachinePrecision], LessEqual[y, 2.5e+129]]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999998e171 or -1.3e115 < y < -1.15000000000000008e60 or 2.5000000000000001e129 < y

   1. Initial program 98.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.3%

      \[\leadsto \color{blue}{2} \]

   if -7.4999999999999998e171 < y < -1.3e115 or -1.15000000000000008e60 < y < 2.5000000000000001e129

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. 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 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+171}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+115} \lor \neg \left(y \leq -1.15 \cdot 10^{+60}\right) \land y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-63}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 2.0 (* 4.0 (/ x y)))))
   (if (<= x -3.2e+69)
     t_0
     (if (<= x 1.65e-63)
       (+ 2.0 (* (/ z y) -4.0))
       (if (<= x 2.4e+41) t_0 (* 4.0 (/ (- x z) y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 2.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -3.2e+69) {
		tmp = t_0;
	} else if (x <= 1.65e-63) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else if (x <= 2.4e+41) {
		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 = 2.0d0 + (4.0d0 * (x / y))
    if (x <= (-3.2d+69)) then
        tmp = t_0
    else if (x <= 1.65d-63) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else if (x <= 2.4d+41) 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 = 2.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -3.2e+69) {
		tmp = t_0;
	} else if (x <= 1.65e-63) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else if (x <= 2.4e+41) {
		tmp = t_0;
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 2.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -3.2e+69:
		tmp = t_0
	elif x <= 1.65e-63:
		tmp = 2.0 + ((z / y) * -4.0)
	elif x <= 2.4e+41:
		tmp = t_0
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(2.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -3.2e+69)
		tmp = t_0;
	elseif (x <= 1.65e-63)
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	elseif (x <= 2.4e+41)
		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 = 2.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -3.2e+69)
		tmp = t_0;
	elseif (x <= 1.65e-63)
		tmp = 2.0 + ((z / y) * -4.0);
	elseif (x <= 2.4e+41)
		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[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+69], t$95$0, If[LessEqual[x, 1.65e-63], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+41], t$95$0, N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $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%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \color{blue}{2} \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 90.2%

      \[\leadsto \color{blue}{2 + 4 \cdot \frac{x}{y}} \]

   if -3.19999999999999985e69 < x < 1.64999999999999997e-63

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.7%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.7%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.7%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \color{blue}{2} \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.4%

      \[\leadsto \color{blue}{2 + -4 \cdot \frac{z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 93.4%

         \[\leadsto 2 + \color{blue}{\frac{z}{y} \cdot -4} \]

   7. Simplified 93.4%

      \[\leadsto \color{blue}{2 + \frac{z}{y} \cdot -4} \]

   if 2.4000000000000002e41 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+69}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-63}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-5} \lor \neg \left(y \leq 6.2 \cdot 10^{+92}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e-5) (not (<= y 6.2e+92)))
   (+ 2.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-5) || !(y <= 6.2e+92)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2d-5)) .or. (.not. (y <= 6.2d+92))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-5) || !(y <= 6.2e+92)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e-5) or not (y <= 6.2e+92):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e-5) || !(y <= 6.2e+92))
		tmp = Float64(2.0 + Float64(4.0 * 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 <= -2e-5) || ~((y <= 6.2e+92)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e-5], N[Not[LessEqual[y, 6.2e+92]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000016e-5 or 6.2000000000000004e92 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.1%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \color{blue}{2} \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 86.4%

      \[\leadsto \color{blue}{2 + 4 \cdot \frac{x}{y}} \]

   if -2.00000000000000016e-5 < y < 6.2000000000000004e92

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. 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 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-5} \lor \neg \left(y \leq 6.2 \cdot 10^{+92}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+115} \lor \neg \left(x \leq 6 \cdot 10^{+39}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e+115) (not (<= x 6e+39))) (* 4.0 (/ x y)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e+115) || !(x <= 6e+39)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	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 <= (-1.6d+115)) .or. (.not. (x <= 6d+39))) then
        tmp = 4.0d0 * (x / y)
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e+115) || !(x <= 6e+39)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e+115) or not (x <= 6e+39):
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.6e+115) || !(x <= 6e+39))
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.6e+115) || ~((x <= 6e+39)))
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e+115], N[Not[LessEqual[x, 6e+39]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e115 or 5.9999999999999999e39 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.1%

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

   if -1.6e115 < x < 5.9999999999999999e39

   1. Initial program 99.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 46.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+115} \lor \neg \left(x \leq 6 \cdot 10^{+39}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{4}{y} \cdot \left(x - z\right) + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (/ 4.0 y) (- x z)) 2.0))

C

double code(double x, double y, double z) {
	return ((4.0 / y) * (x - z)) + 2.0;
}

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 / y) * (x - z)) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return ((4.0 / y) * (x - z)) + 2.0;
}

Python

def code(x, y, z):
	return ((4.0 / y) * (x - z)) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(Float64(4.0 / y) * Float64(x - z)) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((4.0 / y) * (x - z)) + 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

   2. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

   3. +-commutative 99.7%

      \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

   4. associate--l+ 99.7%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

   5. +-commutative 99.7%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

   6. distribute-lft-in 99.7%

      \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

   7. associate-+l+ 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

   8. associate-*l/ 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

   9. *-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

   10. associate-*l* 99.8%

       \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

       \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \color{blue}{2} \]

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 9: 34.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.25\right) - z}{y}} \]

   2. associate--l+ 100.0%

      \[\leadsto 1 + 4 \cdot \frac{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}{y} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \left(y \cdot 0.25 - z\right)}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 34.4%

   \[\leadsto \color{blue}{2} \]

6. Final simplification 34.4%

   \[\leadsto 2 \]
7. 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, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))