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

Percentage Accurate: 99.8% → 100.0%

Time: 5.8s

Alternatives: 9

Speedup: 1.4×

• 21.2% 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, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x - z}{y \cdot 0.25} + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (/ (- x z) (* y 0.25)) 2.0))

C

double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 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 = ((x - z) / (y * 0.25d0)) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 2.0;
}

Python

def code(x, y, z):
	return ((x - z) / (y * 0.25)) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - z) / Float64(y * 0.25)) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - z) / (y * 0.25)) + 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]

Derivation

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. Step-by-step derivation

   1. clear-num 99.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) + 2 \]

   2. div-inv 99.8%

      \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) + 2 \]

   3. metadata-eval 99.8%

      \[\leadsto \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) + 2 \]

   4. associate-*l/ 100.0%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} + 2 \]

   5. *-un-lft-identity 100.0%

      \[\leadsto \frac{\color{blue}{x - z}}{y \cdot 0.25} + 2 \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]
7. Add Preprocessing

Alternative 2: 56.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y} + 1\\ t_1 := \frac{x \cdot 4}{y} + 1\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-272}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-192}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-130}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 132000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+118}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* -4.0 (/ z y)) 1.0)) (t_1 (+ (/ (* x 4.0) y) 1.0)))
   (if (<= x -2.6e+82)
     t_1
     (if (<= x 5e-272)
       t_0
       (if (<= x 9.2e-192)
         2.0
         (if (<= x 1.42e-149)
           t_0
           (if (<= x 1.9e-130)
             2.0
             (if (<= x 8e-47)
               t_0
               (if (<= x 1.3e-9)
                 t_1
                 (if (<= x 132000000000.0)
                   t_0
                   (if (<= x 5e+118) 2.0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = ((x * 4.0) / y) + 1.0;
	double tmp;
	if (x <= -2.6e+82) {
		tmp = t_1;
	} else if (x <= 5e-272) {
		tmp = t_0;
	} else if (x <= 9.2e-192) {
		tmp = 2.0;
	} else if (x <= 1.42e-149) {
		tmp = t_0;
	} else if (x <= 1.9e-130) {
		tmp = 2.0;
	} else if (x <= 8e-47) {
		tmp = t_0;
	} else if (x <= 1.3e-9) {
		tmp = t_1;
	} else if (x <= 132000000000.0) {
		tmp = t_0;
	} else if (x <= 5e+118) {
		tmp = 2.0;
	} 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 = ((-4.0d0) * (z / y)) + 1.0d0
    t_1 = ((x * 4.0d0) / y) + 1.0d0
    if (x <= (-2.6d+82)) then
        tmp = t_1
    else if (x <= 5d-272) then
        tmp = t_0
    else if (x <= 9.2d-192) then
        tmp = 2.0d0
    else if (x <= 1.42d-149) then
        tmp = t_0
    else if (x <= 1.9d-130) then
        tmp = 2.0d0
    else if (x <= 8d-47) then
        tmp = t_0
    else if (x <= 1.3d-9) then
        tmp = t_1
    else if (x <= 132000000000.0d0) then
        tmp = t_0
    else if (x <= 5d+118) then
        tmp = 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = ((x * 4.0) / y) + 1.0;
	double tmp;
	if (x <= -2.6e+82) {
		tmp = t_1;
	} else if (x <= 5e-272) {
		tmp = t_0;
	} else if (x <= 9.2e-192) {
		tmp = 2.0;
	} else if (x <= 1.42e-149) {
		tmp = t_0;
	} else if (x <= 1.9e-130) {
		tmp = 2.0;
	} else if (x <= 8e-47) {
		tmp = t_0;
	} else if (x <= 1.3e-9) {
		tmp = t_1;
	} else if (x <= 132000000000.0) {
		tmp = t_0;
	} else if (x <= 5e+118) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * (z / y)) + 1.0
	t_1 = ((x * 4.0) / y) + 1.0
	tmp = 0
	if x <= -2.6e+82:
		tmp = t_1
	elif x <= 5e-272:
		tmp = t_0
	elif x <= 9.2e-192:
		tmp = 2.0
	elif x <= 1.42e-149:
		tmp = t_0
	elif x <= 1.9e-130:
		tmp = 2.0
	elif x <= 8e-47:
		tmp = t_0
	elif x <= 1.3e-9:
		tmp = t_1
	elif x <= 132000000000.0:
		tmp = t_0
	elif x <= 5e+118:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	t_1 = Float64(Float64(Float64(x * 4.0) / y) + 1.0)
	tmp = 0.0
	if (x <= -2.6e+82)
		tmp = t_1;
	elseif (x <= 5e-272)
		tmp = t_0;
	elseif (x <= 9.2e-192)
		tmp = 2.0;
	elseif (x <= 1.42e-149)
		tmp = t_0;
	elseif (x <= 1.9e-130)
		tmp = 2.0;
	elseif (x <= 8e-47)
		tmp = t_0;
	elseif (x <= 1.3e-9)
		tmp = t_1;
	elseif (x <= 132000000000.0)
		tmp = t_0;
	elseif (x <= 5e+118)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * (z / y)) + 1.0;
	t_1 = ((x * 4.0) / y) + 1.0;
	tmp = 0.0;
	if (x <= -2.6e+82)
		tmp = t_1;
	elseif (x <= 5e-272)
		tmp = t_0;
	elseif (x <= 9.2e-192)
		tmp = 2.0;
	elseif (x <= 1.42e-149)
		tmp = t_0;
	elseif (x <= 1.9e-130)
		tmp = 2.0;
	elseif (x <= 8e-47)
		tmp = t_0;
	elseif (x <= 1.3e-9)
		tmp = t_1;
	elseif (x <= 132000000000.0)
		tmp = t_0;
	elseif (x <= 5e+118)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, -2.6e+82], t$95$1, If[LessEqual[x, 5e-272], t$95$0, If[LessEqual[x, 9.2e-192], 2.0, If[LessEqual[x, 1.42e-149], t$95$0, If[LessEqual[x, 1.9e-130], 2.0, If[LessEqual[x, 8e-47], t$95$0, If[LessEqual[x, 1.3e-9], t$95$1, If[LessEqual[x, 132000000000.0], t$95$0, If[LessEqual[x, 5e+118], 2.0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999998e82 or 7.9999999999999998e-47 < x < 1.3000000000000001e-9 or 4.99999999999999972e118 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*l/ 81.5%

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

   5. Simplified 81.5%

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

   if -2.5999999999999998e82 < x < 4.99999999999999982e-272 or 9.20000000000000073e-192 < x < 1.42e-149 or 1.8999999999999999e-130 < x < 7.9999999999999998e-47 or 1.3000000000000001e-9 < x < 1.32e11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if 4.99999999999999982e-272 < x < 9.20000000000000073e-192 or 1.42e-149 < x < 1.8999999999999999e-130 or 1.32e11 < x < 4.99999999999999972e118

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{x \cdot 4}{y} + 1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-192}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-149}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-130}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-47}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;\frac{x \cdot 4}{y} + 1\\ \mathbf{elif}\;x \leq 132000000000:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+118}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 4}{y} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y} + 1\\ t_1 := 1 + x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-276}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-192}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-126}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 95000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+118}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* -4.0 (/ z y)) 1.0)) (t_1 (+ 1.0 (* x (/ 4.0 y)))))
   (if (<= x -3.1e+86)
     t_1
     (if (<= x 1.65e-276)
       t_0
       (if (<= x 7.2e-192)
         2.0
         (if (<= x 1.85e-150)
           t_0
           (if (<= x 4.5e-126)
             2.0
             (if (<= x 8e-47)
               t_0
               (if (<= x 1.2e-9)
                 t_1
                 (if (<= x 95000000000.0)
                   t_0
                   (if (<= x 5.2e+118) 2.0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -3.1e+86) {
		tmp = t_1;
	} else if (x <= 1.65e-276) {
		tmp = t_0;
	} else if (x <= 7.2e-192) {
		tmp = 2.0;
	} else if (x <= 1.85e-150) {
		tmp = t_0;
	} else if (x <= 4.5e-126) {
		tmp = 2.0;
	} else if (x <= 8e-47) {
		tmp = t_0;
	} else if (x <= 1.2e-9) {
		tmp = t_1;
	} else if (x <= 95000000000.0) {
		tmp = t_0;
	} else if (x <= 5.2e+118) {
		tmp = 2.0;
	} 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 = ((-4.0d0) * (z / y)) + 1.0d0
    t_1 = 1.0d0 + (x * (4.0d0 / y))
    if (x <= (-3.1d+86)) then
        tmp = t_1
    else if (x <= 1.65d-276) then
        tmp = t_0
    else if (x <= 7.2d-192) then
        tmp = 2.0d0
    else if (x <= 1.85d-150) then
        tmp = t_0
    else if (x <= 4.5d-126) then
        tmp = 2.0d0
    else if (x <= 8d-47) then
        tmp = t_0
    else if (x <= 1.2d-9) then
        tmp = t_1
    else if (x <= 95000000000.0d0) then
        tmp = t_0
    else if (x <= 5.2d+118) then
        tmp = 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -3.1e+86) {
		tmp = t_1;
	} else if (x <= 1.65e-276) {
		tmp = t_0;
	} else if (x <= 7.2e-192) {
		tmp = 2.0;
	} else if (x <= 1.85e-150) {
		tmp = t_0;
	} else if (x <= 4.5e-126) {
		tmp = 2.0;
	} else if (x <= 8e-47) {
		tmp = t_0;
	} else if (x <= 1.2e-9) {
		tmp = t_1;
	} else if (x <= 95000000000.0) {
		tmp = t_0;
	} else if (x <= 5.2e+118) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * (z / y)) + 1.0
	t_1 = 1.0 + (x * (4.0 / y))
	tmp = 0
	if x <= -3.1e+86:
		tmp = t_1
	elif x <= 1.65e-276:
		tmp = t_0
	elif x <= 7.2e-192:
		tmp = 2.0
	elif x <= 1.85e-150:
		tmp = t_0
	elif x <= 4.5e-126:
		tmp = 2.0
	elif x <= 8e-47:
		tmp = t_0
	elif x <= 1.2e-9:
		tmp = t_1
	elif x <= 95000000000.0:
		tmp = t_0
	elif x <= 5.2e+118:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(x * Float64(4.0 / y)))
	tmp = 0.0
	if (x <= -3.1e+86)
		tmp = t_1;
	elseif (x <= 1.65e-276)
		tmp = t_0;
	elseif (x <= 7.2e-192)
		tmp = 2.0;
	elseif (x <= 1.85e-150)
		tmp = t_0;
	elseif (x <= 4.5e-126)
		tmp = 2.0;
	elseif (x <= 8e-47)
		tmp = t_0;
	elseif (x <= 1.2e-9)
		tmp = t_1;
	elseif (x <= 95000000000.0)
		tmp = t_0;
	elseif (x <= 5.2e+118)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * (z / y)) + 1.0;
	t_1 = 1.0 + (x * (4.0 / y));
	tmp = 0.0;
	if (x <= -3.1e+86)
		tmp = t_1;
	elseif (x <= 1.65e-276)
		tmp = t_0;
	elseif (x <= 7.2e-192)
		tmp = 2.0;
	elseif (x <= 1.85e-150)
		tmp = t_0;
	elseif (x <= 4.5e-126)
		tmp = 2.0;
	elseif (x <= 8e-47)
		tmp = t_0;
	elseif (x <= 1.2e-9)
		tmp = t_1;
	elseif (x <= 95000000000.0)
		tmp = t_0;
	elseif (x <= 5.2e+118)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+86], t$95$1, If[LessEqual[x, 1.65e-276], t$95$0, If[LessEqual[x, 7.2e-192], 2.0, If[LessEqual[x, 1.85e-150], t$95$0, If[LessEqual[x, 4.5e-126], 2.0, If[LessEqual[x, 8e-47], t$95$0, If[LessEqual[x, 1.2e-9], t$95$1, If[LessEqual[x, 95000000000.0], t$95$0, If[LessEqual[x, 5.2e+118], 2.0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.1000000000000002e86 or 7.9999999999999998e-47 < x < 1.2e-9 or 5.20000000000000032e118 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.5%

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

      1. associate-*r/ 81.5%

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

      2. associate-*l/ 81.4%

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

      3. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -3.1000000000000002e86 < x < 1.64999999999999996e-276 or 7.1999999999999998e-192 < x < 1.85e-150 or 4.50000000000000025e-126 < x < 7.9999999999999998e-47 or 1.2e-9 < x < 9.5e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if 1.64999999999999996e-276 < x < 7.1999999999999998e-192 or 1.85e-150 < x < 4.50000000000000025e-126 or 9.5e10 < x < 5.20000000000000032e118

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+86}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-276}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-192}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-150}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-126}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-47}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-9}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq 95000000000:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+118}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + z \cdot \frac{-4}{y}\\ t_1 := 1 + x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{-274}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-192}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 96000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+118}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* z (/ -4.0 y)))) (t_1 (+ 1.0 (* x (/ 4.0 y)))))
   (if (<= x -1.4e+82)
     t_1
     (if (<= x 1.92e-274)
       t_0
       (if (<= x 7.8e-192)
         2.0
         (if (<= x 1.55e-149)
           t_0
           (if (<= x 5.2e-128)
             2.0
             (if (<= x 8e-47)
               t_0
               (if (<= x 7.5e-9)
                 t_1
                 (if (<= x 96000000000.0)
                   t_0
                   (if (<= x 5.2e+118) 2.0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (z * (-4.0 / y));
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -1.4e+82) {
		tmp = t_1;
	} else if (x <= 1.92e-274) {
		tmp = t_0;
	} else if (x <= 7.8e-192) {
		tmp = 2.0;
	} else if (x <= 1.55e-149) {
		tmp = t_0;
	} else if (x <= 5.2e-128) {
		tmp = 2.0;
	} else if (x <= 8e-47) {
		tmp = t_0;
	} else if (x <= 7.5e-9) {
		tmp = t_1;
	} else if (x <= 96000000000.0) {
		tmp = t_0;
	} else if (x <= 5.2e+118) {
		tmp = 2.0;
	} 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 + (z * ((-4.0d0) / y))
    t_1 = 1.0d0 + (x * (4.0d0 / y))
    if (x <= (-1.4d+82)) then
        tmp = t_1
    else if (x <= 1.92d-274) then
        tmp = t_0
    else if (x <= 7.8d-192) then
        tmp = 2.0d0
    else if (x <= 1.55d-149) then
        tmp = t_0
    else if (x <= 5.2d-128) then
        tmp = 2.0d0
    else if (x <= 8d-47) then
        tmp = t_0
    else if (x <= 7.5d-9) then
        tmp = t_1
    else if (x <= 96000000000.0d0) then
        tmp = t_0
    else if (x <= 5.2d+118) then
        tmp = 2.0d0
    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 + (z * (-4.0 / y));
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -1.4e+82) {
		tmp = t_1;
	} else if (x <= 1.92e-274) {
		tmp = t_0;
	} else if (x <= 7.8e-192) {
		tmp = 2.0;
	} else if (x <= 1.55e-149) {
		tmp = t_0;
	} else if (x <= 5.2e-128) {
		tmp = 2.0;
	} else if (x <= 8e-47) {
		tmp = t_0;
	} else if (x <= 7.5e-9) {
		tmp = t_1;
	} else if (x <= 96000000000.0) {
		tmp = t_0;
	} else if (x <= 5.2e+118) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (z * (-4.0 / y))
	t_1 = 1.0 + (x * (4.0 / y))
	tmp = 0
	if x <= -1.4e+82:
		tmp = t_1
	elif x <= 1.92e-274:
		tmp = t_0
	elif x <= 7.8e-192:
		tmp = 2.0
	elif x <= 1.55e-149:
		tmp = t_0
	elif x <= 5.2e-128:
		tmp = 2.0
	elif x <= 8e-47:
		tmp = t_0
	elif x <= 7.5e-9:
		tmp = t_1
	elif x <= 96000000000.0:
		tmp = t_0
	elif x <= 5.2e+118:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(z * Float64(-4.0 / y)))
	t_1 = Float64(1.0 + Float64(x * Float64(4.0 / y)))
	tmp = 0.0
	if (x <= -1.4e+82)
		tmp = t_1;
	elseif (x <= 1.92e-274)
		tmp = t_0;
	elseif (x <= 7.8e-192)
		tmp = 2.0;
	elseif (x <= 1.55e-149)
		tmp = t_0;
	elseif (x <= 5.2e-128)
		tmp = 2.0;
	elseif (x <= 8e-47)
		tmp = t_0;
	elseif (x <= 7.5e-9)
		tmp = t_1;
	elseif (x <= 96000000000.0)
		tmp = t_0;
	elseif (x <= 5.2e+118)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (z * (-4.0 / y));
	t_1 = 1.0 + (x * (4.0 / y));
	tmp = 0.0;
	if (x <= -1.4e+82)
		tmp = t_1;
	elseif (x <= 1.92e-274)
		tmp = t_0;
	elseif (x <= 7.8e-192)
		tmp = 2.0;
	elseif (x <= 1.55e-149)
		tmp = t_0;
	elseif (x <= 5.2e-128)
		tmp = 2.0;
	elseif (x <= 8e-47)
		tmp = t_0;
	elseif (x <= 7.5e-9)
		tmp = t_1;
	elseif (x <= 96000000000.0)
		tmp = t_0;
	elseif (x <= 5.2e+118)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+82], t$95$1, If[LessEqual[x, 1.92e-274], t$95$0, If[LessEqual[x, 7.8e-192], 2.0, If[LessEqual[x, 1.55e-149], t$95$0, If[LessEqual[x, 5.2e-128], 2.0, If[LessEqual[x, 8e-47], t$95$0, If[LessEqual[x, 7.5e-9], t$95$1, If[LessEqual[x, 96000000000.0], t$95$0, If[LessEqual[x, 5.2e+118], 2.0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e82 or 7.9999999999999998e-47 < x < 7.49999999999999933e-9 or 5.20000000000000032e118 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.5%

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

      1. associate-*r/ 81.5%

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

      2. associate-*l/ 81.4%

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

      3. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -1.4e82 < x < 1.91999999999999992e-274 or 7.8000000000000005e-192 < x < 1.54999999999999994e-149 or 5.19999999999999961e-128 < x < 7.9999999999999998e-47 or 7.49999999999999933e-9 < x < 9.6e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. metadata-eval 66.0%

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

      3. associate-*r* 66.0%

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

      4. neg-mul-1 66.0%

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

      5. *-commutative 66.0%

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

      6. associate-*r/ 65.8%

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

      7. distribute-lft-neg-out 65.8%

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

      8. distribute-rgt-neg-in 65.8%

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

      9. distribute-neg-frac 65.8%

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

      10. metadata-eval 65.8%

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

   5. Simplified 65.8%

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

   if 1.91999999999999992e-274 < x < 7.8000000000000005e-192 or 1.54999999999999994e-149 < x < 5.19999999999999961e-128 or 9.6e10 < x < 5.20000000000000032e118

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

Alternative 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1010000000000 \lor \neg \left(z \leq 10^{-79}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{x \cdot 4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1010000000000.0) (not (<= z 1e-79)))
   (+ 2.0 (* -4.0 (/ z y)))
   (+ 2.0 (/ (* x 4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1010000000000.0) || !(z <= 1e-79)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + ((x * 4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1010000000000.0d0)) .or. (.not. (z <= 1d-79))) then
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 2.0d0 + ((x * 4.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1010000000000.0) || !(z <= 1e-79)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + ((x * 4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1010000000000.0) or not (z <= 1e-79):
		tmp = 2.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0 + ((x * 4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1010000000000.0) || !(z <= 1e-79))
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(2.0 + Float64(Float64(x * 4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1010000000000.0) || ~((z <= 1e-79)))
		tmp = 2.0 + (-4.0 * (z / y));
	else
		tmp = 2.0 + ((x * 4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1010000000000.0], N[Not[LessEqual[z, 1e-79]], $MachinePrecision]], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01e12 or 1e-79 < z

   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. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) + 2 \]

      2. div-inv 99.8%

         \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) + 2 \]

      3. metadata-eval 99.8%

         \[\leadsto \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) + 2 \]

      4. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} + 2 \]

      5. *-un-lft-identity 100.0%

         \[\leadsto \frac{\color{blue}{x - z}}{y \cdot 0.25} + 2 \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   7. Taylor expanded in x around 0 82.7%

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

   if -1.01e12 < z < 1e-79

   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. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) + 2 \]

      2. div-inv 99.8%

         \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) + 2 \]

      3. metadata-eval 99.8%

         \[\leadsto \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) + 2 \]

      4. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} + 2 \]

      5. *-un-lft-identity 100.0%

         \[\leadsto \frac{\color{blue}{x - z}}{y \cdot 0.25} + 2 \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   7. Taylor expanded in x around inf 98.1%

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

      1. associate-*r/ 98.1%

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

   9. Simplified 98.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1010000000000 \lor \neg \left(z \leq 10^{-79}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{x \cdot 4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+90} \lor \neg \left(x \leq 3.4 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x \cdot 4}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e+90) (not (<= x 3.4e+124)))
   (+ (/ (* x 4.0) y) 1.0)
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e+90) || !(x <= 3.4e+124)) {
		tmp = ((x * 4.0) / y) + 1.0;
	} else {
		tmp = 2.0 + (-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 <= (-3.3d+90)) .or. (.not. (x <= 3.4d+124))) then
        tmp = ((x * 4.0d0) / y) + 1.0d0
    else
        tmp = 2.0d0 + ((-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 <= -3.3e+90) || !(x <= 3.4e+124)) {
		tmp = ((x * 4.0) / y) + 1.0;
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e+90) or not (x <= 3.4e+124):
		tmp = ((x * 4.0) / y) + 1.0
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e+90) || !(x <= 3.4e+124))
		tmp = Float64(Float64(Float64(x * 4.0) / y) + 1.0);
	else
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.3e+90) || ~((x <= 3.4e+124)))
		tmp = ((x * 4.0) / y) + 1.0;
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e+90], N[Not[LessEqual[x, 3.4e+124]], $MachinePrecision]], N[(N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000008e90 or 3.4e124 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*l/ 83.0%

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

   5. Simplified 83.0%

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

   if -3.30000000000000008e90 < x < 3.4e124

   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. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) + 2 \]

      2. div-inv 99.8%

         \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) + 2 \]

      3. metadata-eval 99.8%

         \[\leadsto \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) + 2 \]

      4. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} + 2 \]

      5. *-un-lft-identity 100.0%

         \[\leadsto \frac{\color{blue}{x - z}}{y \cdot 0.25} + 2 \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   7. Taylor expanded in x around 0 88.2%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+90} \lor \neg \left(x \leq 3.4 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x \cdot 4}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+66}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+121}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.25e+66) 2.0 (if (<= y 6.8e+121) (+ 1.0 (* x (/ 4.0 y))) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.25e+66) {
		tmp = 2.0;
	} else if (y <= 6.8e+121) {
		tmp = 1.0 + (x * (4.0 / 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 <= (-3.25d+66)) then
        tmp = 2.0d0
    else if (y <= 6.8d+121) then
        tmp = 1.0d0 + (x * (4.0d0 / 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 <= -3.25e+66) {
		tmp = 2.0;
	} else if (y <= 6.8e+121) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.25e+66:
		tmp = 2.0
	elif y <= 6.8e+121:
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.25e+66)
		tmp = 2.0;
	elseif (y <= 6.8e+121)
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.25e+66)
		tmp = 2.0;
	elseif (y <= 6.8e+121)
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.25e+66], 2.0, If[LessEqual[y, 6.8e+121], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2500000000000001e66 or 6.80000000000000021e121 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.9%

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

   if -3.2500000000000001e66 < y < 6.80000000000000021e121

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.5%

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

      1. associate-*r/ 48.5%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

   5. Simplified 48.4%

      \[\leadsto 1 + \color{blue}{x \cdot \frac{4}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 + ((x - z) * (4.0d0 / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.8%

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

Alternative 9: 34.0% 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 100.0%

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

3. Taylor expanded in y around inf 30.9%

   \[\leadsto \color{blue}{2} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(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)))