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

Percentage Accurate: 99.8% → 99.9%

Time: 9.0s

Alternatives: 8

Speedup: 1.4×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.4× speedup

Math

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

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

Derivation

1. Initial program 99.9%

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

   1. associate-*l/ 99.8%

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

   2. sub-neg 99.8%

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

   3. sub-neg 99.8%

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

   4. +-commutative 99.8%

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

   5. fma-def 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around 0 100.0%

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

   1. associate-*r/ 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 57.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot x}{y}\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -110000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-165}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-261}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-81}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 62000000000000:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 x) y))) (t_1 (+ 1.0 (* -4.0 (/ z y)))))
   (if (<= z -110000.0)
     t_1
     (if (<= z -3.6e-56)
       t_0
       (if (<= z -4e-165)
         4.0
         (if (<= z -1.2e-261)
           t_0
           (if (<= z 1.55e-81)
             4.0
             (if (<= z 2.7e-40)
               t_0
               (if (<= z 62000000000000.0) 4.0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * x) / y);
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -110000.0) {
		tmp = t_1;
	} else if (z <= -3.6e-56) {
		tmp = t_0;
	} else if (z <= -4e-165) {
		tmp = 4.0;
	} else if (z <= -1.2e-261) {
		tmp = t_0;
	} else if (z <= 1.55e-81) {
		tmp = 4.0;
	} else if (z <= 2.7e-40) {
		tmp = t_0;
	} else if (z <= 62000000000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	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 = 1.0d0 + ((4.0d0 * x) / y)
    t_1 = 1.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-110000.0d0)) then
        tmp = t_1
    else if (z <= (-3.6d-56)) then
        tmp = t_0
    else if (z <= (-4d-165)) then
        tmp = 4.0d0
    else if (z <= (-1.2d-261)) then
        tmp = t_0
    else if (z <= 1.55d-81) then
        tmp = 4.0d0
    else if (z <= 2.7d-40) then
        tmp = t_0
    else if (z <= 62000000000000.0d0) then
        tmp = 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * x) / y);
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -110000.0) {
		tmp = t_1;
	} else if (z <= -3.6e-56) {
		tmp = t_0;
	} else if (z <= -4e-165) {
		tmp = 4.0;
	} else if (z <= -1.2e-261) {
		tmp = t_0;
	} else if (z <= 1.55e-81) {
		tmp = 4.0;
	} else if (z <= 2.7e-40) {
		tmp = t_0;
	} else if (z <= 62000000000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * x) / y)
	t_1 = 1.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -110000.0:
		tmp = t_1
	elif z <= -3.6e-56:
		tmp = t_0
	elif z <= -4e-165:
		tmp = 4.0
	elif z <= -1.2e-261:
		tmp = t_0
	elif z <= 1.55e-81:
		tmp = 4.0
	elif z <= 2.7e-40:
		tmp = t_0
	elif z <= 62000000000000.0:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	t_1 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -110000.0)
		tmp = t_1;
	elseif (z <= -3.6e-56)
		tmp = t_0;
	elseif (z <= -4e-165)
		tmp = 4.0;
	elseif (z <= -1.2e-261)
		tmp = t_0;
	elseif (z <= 1.55e-81)
		tmp = 4.0;
	elseif (z <= 2.7e-40)
		tmp = t_0;
	elseif (z <= 62000000000000.0)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * x) / y);
	t_1 = 1.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -110000.0)
		tmp = t_1;
	elseif (z <= -3.6e-56)
		tmp = t_0;
	elseif (z <= -4e-165)
		tmp = 4.0;
	elseif (z <= -1.2e-261)
		tmp = t_0;
	elseif (z <= 1.55e-81)
		tmp = 4.0;
	elseif (z <= 2.7e-40)
		tmp = t_0;
	elseif (z <= 62000000000000.0)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -110000.0], t$95$1, If[LessEqual[z, -3.6e-56], t$95$0, If[LessEqual[z, -4e-165], 4.0, If[LessEqual[z, -1.2e-261], t$95$0, If[LessEqual[z, 1.55e-81], 4.0, If[LessEqual[z, 2.7e-40], t$95$0, If[LessEqual[z, 62000000000000.0], 4.0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e5 or 6.2e13 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.1%

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

      1. *-commutative 71.1%

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

   7. Simplified 71.1%

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

   if -1.1e5 < z < -3.59999999999999978e-56 or -4e-165 < z < -1.20000000000000007e-261 or 1.54999999999999994e-81 < z < 2.7e-40

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 66.3%

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

      1. associate-*r/ 66.3%

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

   7. Simplified 66.3%

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

   if -3.59999999999999978e-56 < z < -4e-165 or -1.20000000000000007e-261 < z < 1.54999999999999994e-81 or 2.7e-40 < z < 6.2e13

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 66.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -110000:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-165}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-261}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-81}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-40}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 62000000000000:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4}{\frac{y}{x - z}}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+110}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-17} \lor \neg \left(z \leq 2.55 \cdot 10^{+14}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ 4.0 (/ y (- x z))))))
   (if (<= z -3.1e+204)
     t_0
     (if (<= z -7.4e+110)
       (+ 4.0 (* -4.0 (/ z y)))
       (if (or (<= z -1.4e-17) (not (<= z 2.55e+14)))
         t_0
         (+ 4.0 (* 4.0 (/ x y))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 / (y / (x - z)));
	double tmp;
	if (z <= -3.1e+204) {
		tmp = t_0;
	} else if (z <= -7.4e+110) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else if ((z <= -1.4e-17) || !(z <= 2.55e+14)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (4.0d0 / (y / (x - z)))
    if (z <= (-3.1d+204)) then
        tmp = t_0
    else if (z <= (-7.4d+110)) then
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    else if ((z <= (-1.4d-17)) .or. (.not. (z <= 2.55d+14))) then
        tmp = t_0
    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 t_0 = 1.0 + (4.0 / (y / (x - z)));
	double tmp;
	if (z <= -3.1e+204) {
		tmp = t_0;
	} else if (z <= -7.4e+110) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else if ((z <= -1.4e-17) || !(z <= 2.55e+14)) {
		tmp = t_0;
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 / (y / (x - z)))
	tmp = 0
	if z <= -3.1e+204:
		tmp = t_0
	elif z <= -7.4e+110:
		tmp = 4.0 + (-4.0 * (z / y))
	elif (z <= -1.4e-17) or not (z <= 2.55e+14):
		tmp = t_0
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 / Float64(y / Float64(x - z))))
	tmp = 0.0
	if (z <= -3.1e+204)
		tmp = t_0;
	elseif (z <= -7.4e+110)
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	elseif ((z <= -1.4e-17) || !(z <= 2.55e+14))
		tmp = t_0;
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (4.0 / (y / (x - z)));
	tmp = 0.0;
	if (z <= -3.1e+204)
		tmp = t_0;
	elseif (z <= -7.4e+110)
		tmp = 4.0 + (-4.0 * (z / y));
	elseif ((z <= -1.4e-17) || ~((z <= 2.55e+14)))
		tmp = t_0;
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+204], t$95$0, If[LessEqual[z, -7.4e+110], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.4e-17], N[Not[LessEqual[z, 2.55e+14]], $MachinePrecision]], t$95$0, N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000002e204 or -7.40000000000000024e110 < z < -1.3999999999999999e-17 or 2.55e14 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 87.8%

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

      1. associate-*r/ 87.8%

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

      2. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   if -3.1000000000000002e204 < z < -7.40000000000000024e110

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -1.3999999999999999e-17 < z < 2.55e14

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 96.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+110}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-17} \lor \neg \left(z \leq 2.55 \cdot 10^{+14}\right):\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+156} \lor \neg \left(x \leq 1.2 \cdot 10^{+139}\right) \land \left(x \leq 4.2 \cdot 10^{+168} \lor \neg \left(x \leq 2.8 \cdot 10^{+188}\right)\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e+156)
         (and (not (<= x 1.2e+139))
              (or (<= x 4.2e+168) (not (<= x 2.8e+188)))))
   (+ 1.0 (/ (* 4.0 x) y))
   (+ 4.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+156) || (!(x <= 1.2e+139) && ((x <= 4.2e+168) || !(x <= 2.8e+188)))) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else {
		tmp = 4.0 + (-4.0 * (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 ((x <= (-1.4d+156)) .or. (.not. (x <= 1.2d+139)) .and. (x <= 4.2d+168) .or. (.not. (x <= 2.8d+188))) then
        tmp = 1.0d0 + ((4.0d0 * x) / y)
    else
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+156) || (!(x <= 1.2e+139) && ((x <= 4.2e+168) || !(x <= 2.8e+188)))) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else {
		tmp = 4.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e+156) or (not (x <= 1.2e+139) and ((x <= 4.2e+168) or not (x <= 2.8e+188))):
		tmp = 1.0 + ((4.0 * x) / y)
	else:
		tmp = 4.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e+156) || (!(x <= 1.2e+139) && ((x <= 4.2e+168) || !(x <= 2.8e+188))))
		tmp = Float64(1.0 + Float64(Float64(4.0 * x) / y));
	else
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e+156) || (~((x <= 1.2e+139)) && ((x <= 4.2e+168) || ~((x <= 2.8e+188)))))
		tmp = 1.0 + ((4.0 * x) / y);
	else
		tmp = 4.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e+156], And[N[Not[LessEqual[x, 1.2e+139]], $MachinePrecision], Or[LessEqual[x, 4.2e+168], N[Not[LessEqual[x, 2.8e+188]], $MachinePrecision]]]], N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999994e156 or 1.20000000000000004e139 < x < 4.20000000000000006e168 or 2.7999999999999998e188 < x

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 87.0%

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

      1. associate-*r/ 87.0%

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

   7. Simplified 87.0%

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

   if -1.39999999999999994e156 < x < 1.20000000000000004e139 or 4.20000000000000006e168 < x < 2.7999999999999998e188

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 85.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+156} \lor \neg \left(x \leq 1.2 \cdot 10^{+139}\right) \land \left(x \leq 4.2 \cdot 10^{+168} \lor \neg \left(x \leq 2.8 \cdot 10^{+188}\right)\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-17} \lor \neg \left(z \leq 62000000000000\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.56e-17) (not (<= z 62000000000000.0)))
   (+ 1.0 (* -4.0 (/ z y)))
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-17) || !(z <= 62000000000000.0)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.56d-17)) .or. (.not. (z <= 62000000000000.0d0))) then
        tmp = 1.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-17) || !(z <= 62000000000000.0)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.56e-17) or not (z <= 62000000000000.0):
		tmp = 1.0 + (-4.0 * (z / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.56e-17) || !(z <= 62000000000000.0))
		tmp = Float64(1.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.56e-17) || ~((z <= 62000000000000.0)))
		tmp = 1.0 + (-4.0 * (z / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.56e-17], N[Not[LessEqual[z, 62000000000000.0]], $MachinePrecision]], N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -1.56000000000000002e-17 or 6.2e13 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   if -1.56000000000000002e-17 < z < 6.2e13

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 53.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-17} \lor \neg \left(z \leq 62000000000000\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -116000 \lor \neg \left(z \leq 4.3 \cdot 10^{+88}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -116000.0) (not (<= z 4.3e+88)))
   (+ 4.0 (* -4.0 (/ z y)))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -116000.0) || !(z <= 4.3e+88)) {
		tmp = 4.0 + (-4.0 * (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 <= (-116000.0d0)) .or. (.not. (z <= 4.3d+88))) then
        tmp = 4.0d0 + ((-4.0d0) * (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 <= -116000.0) || !(z <= 4.3e+88)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -116000.0) or not (z <= 4.3e+88):
		tmp = 4.0 + (-4.0 * (z / y))
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -116000.0) || !(z <= 4.3e+88))
		tmp = Float64(4.0 + Float64(-4.0 * Float64(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 <= -116000.0) || ~((z <= 4.3e+88)))
		tmp = 4.0 + (-4.0 * (z / y));
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -116000.0], N[Not[LessEqual[z, 4.3e+88]], $MachinePrecision]], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -116000 or 4.29999999999999974e88 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 86.9%

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

   if -116000 < z < 4.29999999999999974e88

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 92.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -116000 \lor \neg \left(z \leq 4.3 \cdot 10^{+88}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-17} \lor \neg \left(z \leq 1.8 \cdot 10^{+14}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.56e-17) (not (<= z 1.8e+14))) (* -4.0 (/ z y)) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-17) || !(z <= 1.8e+14)) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.56d-17)) .or. (.not. (z <= 1.8d+14))) then
        tmp = (-4.0d0) * (z / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-17) || !(z <= 1.8e+14)) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.56e-17) or not (z <= 1.8e+14):
		tmp = -4.0 * (z / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.56e-17) || !(z <= 1.8e+14))
		tmp = Float64(-4.0 * Float64(z / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.56e-17) || ~((z <= 1.8e+14)))
		tmp = -4.0 * (z / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.56e-17], N[Not[LessEqual[z, 1.8e+14]], $MachinePrecision]], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -1.56000000000000002e-17 or 1.8e14 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 81.9%

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

   9. Taylor expanded in z around inf 66.1%

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

   if -1.56000000000000002e-17 < z < 1.8e14

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 53.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-17} \lor \neg \left(z \leq 1.8 \cdot 10^{+14}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

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

   1. associate-*l/ 99.8%

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

   2. sub-neg 99.8%

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

   3. sub-neg 99.8%

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

   4. +-commutative 99.8%

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

   5. fma-def 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 34.7%

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

6. Final simplification 34.7%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))