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

Percentage Accurate: 99.8% → 99.8%

Time: 8.3s

Alternatives: 12

Speedup: 1.4×

• 21.5% 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: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 100.0%

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

   1. distribute-lft-out 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 54.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-185}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-249}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-285}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-252}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+99}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -4.0 (/ z y))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= x -6.2e+74)
     t_1
     (if (<= x -4e-185)
       t_0
       (if (<= x -6.2e-249)
         4.0
         (if (<= x 1.56e-285)
           t_0
           (if (<= x 6.4e-252)
             4.0
             (if (<= x 3.9e-29) t_0 (if (<= x 1.1e+99) 4.0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * (z / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -6.2e+74) {
		tmp = t_1;
	} else if (x <= -4e-185) {
		tmp = t_0;
	} else if (x <= -6.2e-249) {
		tmp = 4.0;
	} else if (x <= 1.56e-285) {
		tmp = t_0;
	} else if (x <= 6.4e-252) {
		tmp = 4.0;
	} else if (x <= 3.9e-29) {
		tmp = t_0;
	} else if (x <= 1.1e+99) {
		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 = (-4.0d0) * (z / y)
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (x <= (-6.2d+74)) then
        tmp = t_1
    else if (x <= (-4d-185)) then
        tmp = t_0
    else if (x <= (-6.2d-249)) then
        tmp = 4.0d0
    else if (x <= 1.56d-285) then
        tmp = t_0
    else if (x <= 6.4d-252) then
        tmp = 4.0d0
    else if (x <= 3.9d-29) then
        tmp = t_0
    else if (x <= 1.1d+99) 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 = -4.0 * (z / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -6.2e+74) {
		tmp = t_1;
	} else if (x <= -4e-185) {
		tmp = t_0;
	} else if (x <= -6.2e-249) {
		tmp = 4.0;
	} else if (x <= 1.56e-285) {
		tmp = t_0;
	} else if (x <= 6.4e-252) {
		tmp = 4.0;
	} else if (x <= 3.9e-29) {
		tmp = t_0;
	} else if (x <= 1.1e+99) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * (z / y)
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -6.2e+74:
		tmp = t_1
	elif x <= -4e-185:
		tmp = t_0
	elif x <= -6.2e-249:
		tmp = 4.0
	elif x <= 1.56e-285:
		tmp = t_0
	elif x <= 6.4e-252:
		tmp = 4.0
	elif x <= 3.9e-29:
		tmp = t_0
	elif x <= 1.1e+99:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(z / y))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -6.2e+74)
		tmp = t_1;
	elseif (x <= -4e-185)
		tmp = t_0;
	elseif (x <= -6.2e-249)
		tmp = 4.0;
	elseif (x <= 1.56e-285)
		tmp = t_0;
	elseif (x <= 6.4e-252)
		tmp = 4.0;
	elseif (x <= 3.9e-29)
		tmp = t_0;
	elseif (x <= 1.1e+99)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * (z / y);
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -6.2e+74)
		tmp = t_1;
	elseif (x <= -4e-185)
		tmp = t_0;
	elseif (x <= -6.2e-249)
		tmp = 4.0;
	elseif (x <= 1.56e-285)
		tmp = t_0;
	elseif (x <= 6.4e-252)
		tmp = 4.0;
	elseif (x <= 3.9e-29)
		tmp = t_0;
	elseif (x <= 1.1e+99)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+74], t$95$1, If[LessEqual[x, -4e-185], t$95$0, If[LessEqual[x, -6.2e-249], 4.0, If[LessEqual[x, 1.56e-285], t$95$0, If[LessEqual[x, 6.4e-252], 4.0, If[LessEqual[x, 3.9e-29], t$95$0, If[LessEqual[x, 1.1e+99], 4.0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000043e74 or 1.09999999999999989e99 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if -6.20000000000000043e74 < x < -4e-185 or -6.19999999999999971e-249 < x < 1.55999999999999998e-285 or 6.4000000000000004e-252 < x < 3.8999999999999998e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

   8. Simplified 58.9%

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

   if -4e-185 < x < -6.19999999999999971e-249 or 1.55999999999999998e-285 < x < 6.4000000000000004e-252 or 3.8999999999999998e-29 < x < 1.09999999999999989e99

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-185}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-249}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-285}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-252}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+99}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ t_1 := -4 \cdot \frac{z}{y}\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-239}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-252}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) y)) (t_1 (* -4.0 (/ z y))))
   (if (<= x -1.18e+75)
     t_0
     (if (<= x -1.35e-184)
       t_1
       (if (<= x -4.5e-239)
         4.0
         (if (<= x 3.5e-284)
           t_1
           (if (<= x 7.4e-252)
             4.0
             (if (<= x 4.3e-32) t_1 (if (<= x 1.15e+99) 4.0 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double t_1 = -4.0 * (z / y);
	double tmp;
	if (x <= -1.18e+75) {
		tmp = t_0;
	} else if (x <= -1.35e-184) {
		tmp = t_1;
	} else if (x <= -4.5e-239) {
		tmp = 4.0;
	} else if (x <= 3.5e-284) {
		tmp = t_1;
	} else if (x <= 7.4e-252) {
		tmp = 4.0;
	} else if (x <= 4.3e-32) {
		tmp = t_1;
	} else if (x <= 1.15e+99) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * x) / y
    t_1 = (-4.0d0) * (z / y)
    if (x <= (-1.18d+75)) then
        tmp = t_0
    else if (x <= (-1.35d-184)) then
        tmp = t_1
    else if (x <= (-4.5d-239)) then
        tmp = 4.0d0
    else if (x <= 3.5d-284) then
        tmp = t_1
    else if (x <= 7.4d-252) then
        tmp = 4.0d0
    else if (x <= 4.3d-32) then
        tmp = t_1
    else if (x <= 1.15d+99) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double t_1 = -4.0 * (z / y);
	double tmp;
	if (x <= -1.18e+75) {
		tmp = t_0;
	} else if (x <= -1.35e-184) {
		tmp = t_1;
	} else if (x <= -4.5e-239) {
		tmp = 4.0;
	} else if (x <= 3.5e-284) {
		tmp = t_1;
	} else if (x <= 7.4e-252) {
		tmp = 4.0;
	} else if (x <= 4.3e-32) {
		tmp = t_1;
	} else if (x <= 1.15e+99) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / y
	t_1 = -4.0 * (z / y)
	tmp = 0
	if x <= -1.18e+75:
		tmp = t_0
	elif x <= -1.35e-184:
		tmp = t_1
	elif x <= -4.5e-239:
		tmp = 4.0
	elif x <= 3.5e-284:
		tmp = t_1
	elif x <= 7.4e-252:
		tmp = 4.0
	elif x <= 4.3e-32:
		tmp = t_1
	elif x <= 1.15e+99:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / y)
	t_1 = Float64(-4.0 * Float64(z / y))
	tmp = 0.0
	if (x <= -1.18e+75)
		tmp = t_0;
	elseif (x <= -1.35e-184)
		tmp = t_1;
	elseif (x <= -4.5e-239)
		tmp = 4.0;
	elseif (x <= 3.5e-284)
		tmp = t_1;
	elseif (x <= 7.4e-252)
		tmp = 4.0;
	elseif (x <= 4.3e-32)
		tmp = t_1;
	elseif (x <= 1.15e+99)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / y;
	t_1 = -4.0 * (z / y);
	tmp = 0.0;
	if (x <= -1.18e+75)
		tmp = t_0;
	elseif (x <= -1.35e-184)
		tmp = t_1;
	elseif (x <= -4.5e-239)
		tmp = 4.0;
	elseif (x <= 3.5e-284)
		tmp = t_1;
	elseif (x <= 7.4e-252)
		tmp = 4.0;
	elseif (x <= 4.3e-32)
		tmp = t_1;
	elseif (x <= 1.15e+99)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.18e+75], t$95$0, If[LessEqual[x, -1.35e-184], t$95$1, If[LessEqual[x, -4.5e-239], 4.0, If[LessEqual[x, 3.5e-284], t$95$1, If[LessEqual[x, 7.4e-252], 4.0, If[LessEqual[x, 4.3e-32], t$95$1, If[LessEqual[x, 1.15e+99], 4.0, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.18e75 or 1.1500000000000001e99 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 74.3%

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

   if -1.18e75 < x < -1.35e-184 or -4.50000000000000013e-239 < x < 3.49999999999999975e-284 or 7.4000000000000002e-252 < x < 4.2999999999999999e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

   8. Simplified 58.9%

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

   if -1.35e-184 < x < -4.50000000000000013e-239 or 3.49999999999999975e-284 < x < 7.4000000000000002e-252 or 4.2999999999999999e-32 < x < 1.1500000000000001e99

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+75}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-184}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-239}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-252}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+134} \lor \neg \left(z \leq 5 \cdot 10^{+126}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4e+134) (not (<= z 5e+126)))
   (* -4.0 (/ z y))
   (+ 4.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e+134) || !(z <= 5e+126)) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0 + (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 <= (-5.4d+134)) .or. (.not. (z <= 5d+126))) then
        tmp = (-4.0d0) * (z / y)
    else
        tmp = 4.0d0 + (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 <= -5.4e+134) || !(z <= 5e+126)) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4e+134) or not (z <= 5e+126):
		tmp = -4.0 * (z / y)
	else:
		tmp = 4.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4e+134) || !(z <= 5e+126))
		tmp = Float64(-4.0 * Float64(z / y));
	else
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.4e+134) || ~((z <= 5e+126)))
		tmp = -4.0 * (z / y);
	else
		tmp = 4.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4e+134], N[Not[LessEqual[z, 5e+126]], $MachinePrecision]], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e134 or 4.99999999999999977e126 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 81.5%

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

      1. *-commutative 81.5%

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

   8. Simplified 81.5%

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

   if -5.4e134 < z < 4.99999999999999977e126

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. distribute-lft-in 87.0%

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

      2. metadata-eval 87.0%

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

      3. associate-+r+ 87.0%

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

      4. metadata-eval 87.0%

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

      5. *-commutative 87.0%

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

      6. associate-*l/ 87.0%

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

      7. associate-*r/ 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+134} \lor \neg \left(z \leq 5 \cdot 10^{+126}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+76} \lor \neg \left(x \leq 5.6 \cdot 10^{-83}\right):\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+76) (not (<= x 5.6e-83)))
   (+ 4.0 (* x (/ 4.0 y)))
   (+ 4.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+76) || !(x <= 5.6e-83)) {
		tmp = 4.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0 + ((z * -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 ((x <= (-5.2d+76)) .or. (.not. (x <= 5.6d-83))) then
        tmp = 4.0d0 + (x * (4.0d0 / y))
    else
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+76) || !(x <= 5.6e-83)) {
		tmp = 4.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+76) or not (x <= 5.6e-83):
		tmp = 4.0 + (x * (4.0 / y))
	else:
		tmp = 4.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e+76) || !(x <= 5.6e-83))
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.2e+76) || ~((x <= 5.6e-83)))
		tmp = 4.0 + (x * (4.0 / y));
	else
		tmp = 4.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+76], N[Not[LessEqual[x, 5.6e-83]], $MachinePrecision]], N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1999999999999999e76 or 5.6000000000000002e-83 < 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. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 87.8%

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

      1. distribute-lft-in 87.8%

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

      2. metadata-eval 87.8%

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

      3. associate-+r+ 87.8%

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

      4. metadata-eval 87.8%

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

      5. *-commutative 87.8%

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

      6. associate-*l/ 87.8%

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

      7. associate-*r/ 87.6%

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

   7. Simplified 87.6%

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

   if -5.1999999999999999e76 < x < 5.6000000000000002e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. fma-define 92.0%

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

      3. div-sub 92.0%

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

      4. associate-/l* 92.1%

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

      5. *-inverses 92.1%

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

      6. metadata-eval 92.1%

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

      7. fma-define 92.1%

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

      8. +-commutative 92.1%

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

      9. sub-neg 92.1%

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

      10. distribute-lft-in 92.1%

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

      11. metadata-eval 92.1%

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

      12. associate-+r+ 92.1%

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

      13. metadata-eval 92.1%

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

      14. neg-mul-1 92.1%

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

      15. associate-*r* 92.1%

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

      16. metadata-eval 92.1%

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

      17. *-commutative 92.1%

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

      18. associate-*l/ 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+76} \lor \neg \left(x \leq 5.6 \cdot 10^{-83}\right):\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+23}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{\frac{y}{x - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+129)
   (+ 4.0 (/ (* z -4.0) y))
   (if (<= z 2.7e+23) (+ 4.0 (* x (/ 4.0 y))) (/ 4.0 (/ y (- x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+129) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (z <= 2.7e+23) {
		tmp = 4.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0 / (y / (x - z));
	}
	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 <= (-1.9d+129)) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else if (z <= 2.7d+23) then
        tmp = 4.0d0 + (x * (4.0d0 / y))
    else
        tmp = 4.0d0 / (y / (x - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+129) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (z <= 2.7e+23) {
		tmp = 4.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0 / (y / (x - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+129:
		tmp = 4.0 + ((z * -4.0) / y)
	elif z <= 2.7e+23:
		tmp = 4.0 + (x * (4.0 / y))
	else:
		tmp = 4.0 / (y / (x - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+129)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	elseif (z <= 2.7e+23)
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = Float64(4.0 / Float64(y / Float64(x - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+129)
		tmp = 4.0 + ((z * -4.0) / y);
	elseif (z <= 2.7e+23)
		tmp = 4.0 + (x * (4.0 / y));
	else
		tmp = 4.0 / (y / (x - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+129], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+23], N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000003e129

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. fma-define 93.8%

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

      3. div-sub 93.8%

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

      4. associate-/l* 93.8%

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

      5. *-inverses 93.8%

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

      6. metadata-eval 93.8%

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

      7. fma-define 93.8%

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

      8. +-commutative 93.8%

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

      9. sub-neg 93.8%

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

      10. distribute-lft-in 93.8%

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

      11. metadata-eval 93.8%

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

      12. associate-+r+ 93.9%

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

      13. metadata-eval 93.9%

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

      14. neg-mul-1 93.9%

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

      15. associate-*r* 93.9%

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

      16. metadata-eval 93.9%

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

      17. *-commutative 93.9%

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

      18. associate-*l/ 93.9%

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

   5. Simplified 93.9%

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

   if -1.90000000000000003e129 < z < 2.6999999999999999e23

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 90.5%

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

      1. distribute-lft-in 90.5%

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

      2. metadata-eval 90.5%

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

      3. associate-+r+ 90.5%

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

      4. metadata-eval 90.5%

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

      5. *-commutative 90.5%

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

      6. associate-*l/ 90.5%

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

      7. associate-*r/ 90.3%

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

   7. Simplified 90.3%

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

   if 2.6999999999999999e23 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. times-frac 99.8%

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

      5. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{{\left(0.25 \cdot \frac{y}{y + \left(x - z\right)}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 99.8%

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

      2. associate-/r* 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+r- 99.8%

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

      5. +-commutative 99.8%

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

      6. associate--l+ 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in y around 0 88.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+23}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{\frac{y}{x - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{4 \cdot \left(y + x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{\frac{y}{x - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.22e+129)
   (+ 4.0 (/ (* z -4.0) y))
   (if (<= z 9.6e+22) (/ (* 4.0 (+ y x)) y) (/ 4.0 (/ y (- x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.22e+129) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (z <= 9.6e+22) {
		tmp = (4.0 * (y + x)) / y;
	} else {
		tmp = 4.0 / (y / (x - z));
	}
	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 <= (-1.22d+129)) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else if (z <= 9.6d+22) then
        tmp = (4.0d0 * (y + x)) / y
    else
        tmp = 4.0d0 / (y / (x - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.22e+129) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (z <= 9.6e+22) {
		tmp = (4.0 * (y + x)) / y;
	} else {
		tmp = 4.0 / (y / (x - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.22e+129:
		tmp = 4.0 + ((z * -4.0) / y)
	elif z <= 9.6e+22:
		tmp = (4.0 * (y + x)) / y
	else:
		tmp = 4.0 / (y / (x - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.22e+129)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	elseif (z <= 9.6e+22)
		tmp = Float64(Float64(4.0 * Float64(y + x)) / y);
	else
		tmp = Float64(4.0 / Float64(y / Float64(x - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.22e+129)
		tmp = 4.0 + ((z * -4.0) / y);
	elseif (z <= 9.6e+22)
		tmp = (4.0 * (y + x)) / y;
	else
		tmp = 4.0 / (y / (x - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.22e+129], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+22], N[(N[(4.0 * N[(y + x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2200000000000001e129

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. fma-define 93.8%

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

      3. div-sub 93.8%

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

      4. associate-/l* 93.8%

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

      5. *-inverses 93.8%

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

      6. metadata-eval 93.8%

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

      7. fma-define 93.8%

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

      8. +-commutative 93.8%

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

      9. sub-neg 93.8%

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

      10. distribute-lft-in 93.8%

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

      11. metadata-eval 93.8%

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

      12. associate-+r+ 93.9%

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

      13. metadata-eval 93.9%

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

      14. neg-mul-1 93.9%

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

      15. associate-*r* 93.9%

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

      16. metadata-eval 93.9%

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

      17. *-commutative 93.9%

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

      18. associate-*l/ 93.9%

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

   5. Simplified 93.9%

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

   if -1.2200000000000001e129 < z < 9.6e22

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 90.5%

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

   if 9.6e22 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. times-frac 99.8%

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

      5. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{{\left(0.25 \cdot \frac{y}{y + \left(x - z\right)}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 99.8%

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

      2. associate-/r* 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+r- 99.8%

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

      5. +-commutative 99.8%

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

      6. associate--l+ 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in y around 0 88.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{4 \cdot \left(y + x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{\frac{y}{x - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+129}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+22}:\\ \;\;\;\;\frac{4 \cdot \left(y + x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e+129)
   (+ 4.0 (/ (* z -4.0) y))
   (if (<= z 2.7e+22) (/ (* 4.0 (+ y x)) y) (/ (* 4.0 (- x z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+129) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (z <= 2.7e+22) {
		tmp = (4.0 * (y + x)) / y;
	} else {
		tmp = (4.0 * (x - z)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.85d+129)) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else if (z <= 2.7d+22) then
        tmp = (4.0d0 * (y + x)) / y
    else
        tmp = (4.0d0 * (x - z)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+129) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (z <= 2.7e+22) {
		tmp = (4.0 * (y + x)) / y;
	} else {
		tmp = (4.0 * (x - z)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e+129:
		tmp = 4.0 + ((z * -4.0) / y)
	elif z <= 2.7e+22:
		tmp = (4.0 * (y + x)) / y
	else:
		tmp = (4.0 * (x - z)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e+129)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	elseif (z <= 2.7e+22)
		tmp = Float64(Float64(4.0 * Float64(y + x)) / y);
	else
		tmp = Float64(Float64(4.0 * Float64(x - z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.85e+129)
		tmp = 4.0 + ((z * -4.0) / y);
	elseif (z <= 2.7e+22)
		tmp = (4.0 * (y + x)) / y;
	else
		tmp = (4.0 * (x - z)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e+129], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+22], N[(N[(4.0 * N[(y + x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999989e129

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. fma-define 93.8%

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

      3. div-sub 93.8%

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

      4. associate-/l* 93.8%

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

      5. *-inverses 93.8%

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

      6. metadata-eval 93.8%

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

      7. fma-define 93.8%

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

      8. +-commutative 93.8%

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

      9. sub-neg 93.8%

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

      10. distribute-lft-in 93.8%

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

      11. metadata-eval 93.8%

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

      12. associate-+r+ 93.9%

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

      13. metadata-eval 93.9%

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

      14. neg-mul-1 93.9%

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

      15. associate-*r* 93.9%

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

      16. metadata-eval 93.9%

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

      17. *-commutative 93.9%

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

      18. associate-*l/ 93.9%

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

   5. Simplified 93.9%

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

   if -1.84999999999999989e129 < z < 2.7000000000000002e22

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 90.5%

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

   if 2.7000000000000002e22 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 88.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+129}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+22}:\\ \;\;\;\;\frac{4 \cdot \left(y + x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+133} \lor \neg \left(z \leq 1.2 \cdot 10^{+23}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+133) (not (<= z 1.2e+23))) (* -4.0 (/ z y)) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+133) || !(z <= 1.2e+23)) {
		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 <= (-5.8d+133)) .or. (.not. (z <= 1.2d+23))) 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 <= -5.8e+133) || !(z <= 1.2e+23)) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+133) or not (z <= 1.2e+23):
		tmp = -4.0 * (z / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+133) || !(z <= 1.2e+23))
		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 <= -5.8e+133) || ~((z <= 1.2e+23)))
		tmp = -4.0 * (z / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+133], N[Not[LessEqual[z, 1.2e+23]], $MachinePrecision]], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000002e133 or 1.2e23 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. *-commutative 70.3%

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

   8. Simplified 70.3%

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

   if -5.8000000000000002e133 < z < 1.2e23

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 43.6%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+133} \lor \neg \left(z \leq 1.2 \cdot 10^{+23}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 100.0%

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

   1. distribute-lft-out 100.0%

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

5. Simplified 100.0%

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

   1. clear-num 99.8%

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

   2. inv-pow 99.8%

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

   3. *-un-lft-identity 99.8%

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

   4. times-frac 99.8%

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

   5. metadata-eval 99.8%

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

7. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{{\left(0.25 \cdot \frac{y}{y + \left(x - z\right)}\right)}^{-1}} \]
8. Step-by-step derivation

   1. unpow-1 99.8%

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

   2. associate-/r* 99.8%

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

   3. metadata-eval 99.8%

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

   4. associate-+r- 99.8%

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

   5. +-commutative 99.8%

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

   6. associate--l+ 99.8%

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

9. Simplified 99.8%

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

10. Final simplification 99.8%

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

Alternative 11: 7.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 42.6%

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

   1. *-commutative 42.6%

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

5. Simplified 42.6%

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

6. Taylor expanded in x around 0 7.1%

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

7. Final simplification 7.1%

   \[\leadsto 1 \]
8. Add Preprocessing

Alternative 12: 33.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 31.7%

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

4. Final simplification 31.7%

   \[\leadsto 4 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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)))