Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 88.4% → 99.9%

Time: 7.4s

Alternatives: 15

Speedup: 0.8×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10 \lor \neg \left(z \leq 3 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{1 + y}{z} \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -10.0) (not (<= z 3e-25)))
   (- (* (/ (+ 1.0 y) z) x) x)
   (* (/ x z) (+ 1.0 (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -10.0) || !(z <= 3e-25)) {
		tmp = (((1.0 + y) / z) * x) - x;
	} else {
		tmp = (x / z) * (1.0 + (y - 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 <= (-10.0d0)) .or. (.not. (z <= 3d-25))) then
        tmp = (((1.0d0 + y) / z) * x) - x
    else
        tmp = (x / z) * (1.0d0 + (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -10.0) || !(z <= 3e-25)) {
		tmp = (((1.0 + y) / z) * x) - x;
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -10.0) or not (z <= 3e-25):
		tmp = (((1.0 + y) / z) * x) - x
	else:
		tmp = (x / z) * (1.0 + (y - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -10.0) || !(z <= 3e-25))
		tmp = Float64(Float64(Float64(Float64(1.0 + y) / z) * x) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -10.0) || ~((z <= 3e-25)))
		tmp = (((1.0 + y) / z) * x) - x;
	else
		tmp = (x / z) * (1.0 + (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -10.0], N[Not[LessEqual[z, 3e-25]], $MachinePrecision]], N[(N[(N[(N[(1.0 + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -10 or 2.9999999999999998e-25 < z

   1. Initial program 77.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.8%

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

      1. neg-mul-1 93.8%

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

      2. +-commutative 93.8%

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

      3. unsub-neg 93.8%

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

      4. associate-/l* 96.0%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   if -10 < z < 2.9999999999999998e-25

   1. Initial program 99.9%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10 \lor \neg \left(z \leq 3 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{1 + y}{z} \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \]

Alternative 2: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))) (t_1 (* x (/ y z))))
   (if (<= z -3.4e+90)
     (- x)
     (if (<= z -2.05e-17)
       t_1
       (if (<= z -2.15e-135)
         (/ x z)
         (if (<= z -2e-200)
           t_0
           (if (<= z 4.8e-226)
             (/ x z)
             (if (<= z 1.85e-99)
               t_0
               (if (<= z 9.8e-74)
                 (/ x z)
                 (if (<= z 5.2e-41)
                   t_0
                   (if (<= z 1.4e-17)
                     (/ x z)
                     (if (<= z 1.08e+92) t_1 (- x)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -3.4e+90) {
		tmp = -x;
	} else if (z <= -2.05e-17) {
		tmp = t_1;
	} else if (z <= -2.15e-135) {
		tmp = x / z;
	} else if (z <= -2e-200) {
		tmp = t_0;
	} else if (z <= 4.8e-226) {
		tmp = x / z;
	} else if (z <= 1.85e-99) {
		tmp = t_0;
	} else if (z <= 9.8e-74) {
		tmp = x / z;
	} else if (z <= 5.2e-41) {
		tmp = t_0;
	} else if (z <= 1.4e-17) {
		tmp = x / z;
	} else if (z <= 1.08e+92) {
		tmp = t_1;
	} else {
		tmp = -x;
	}
	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 = y * (x / z)
    t_1 = x * (y / z)
    if (z <= (-3.4d+90)) then
        tmp = -x
    else if (z <= (-2.05d-17)) then
        tmp = t_1
    else if (z <= (-2.15d-135)) then
        tmp = x / z
    else if (z <= (-2d-200)) then
        tmp = t_0
    else if (z <= 4.8d-226) then
        tmp = x / z
    else if (z <= 1.85d-99) then
        tmp = t_0
    else if (z <= 9.8d-74) then
        tmp = x / z
    else if (z <= 5.2d-41) then
        tmp = t_0
    else if (z <= 1.4d-17) then
        tmp = x / z
    else if (z <= 1.08d+92) then
        tmp = t_1
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -3.4e+90) {
		tmp = -x;
	} else if (z <= -2.05e-17) {
		tmp = t_1;
	} else if (z <= -2.15e-135) {
		tmp = x / z;
	} else if (z <= -2e-200) {
		tmp = t_0;
	} else if (z <= 4.8e-226) {
		tmp = x / z;
	} else if (z <= 1.85e-99) {
		tmp = t_0;
	} else if (z <= 9.8e-74) {
		tmp = x / z;
	} else if (z <= 5.2e-41) {
		tmp = t_0;
	} else if (z <= 1.4e-17) {
		tmp = x / z;
	} else if (z <= 1.08e+92) {
		tmp = t_1;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	t_1 = x * (y / z)
	tmp = 0
	if z <= -3.4e+90:
		tmp = -x
	elif z <= -2.05e-17:
		tmp = t_1
	elif z <= -2.15e-135:
		tmp = x / z
	elif z <= -2e-200:
		tmp = t_0
	elif z <= 4.8e-226:
		tmp = x / z
	elif z <= 1.85e-99:
		tmp = t_0
	elif z <= 9.8e-74:
		tmp = x / z
	elif z <= 5.2e-41:
		tmp = t_0
	elif z <= 1.4e-17:
		tmp = x / z
	elif z <= 1.08e+92:
		tmp = t_1
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -3.4e+90)
		tmp = Float64(-x);
	elseif (z <= -2.05e-17)
		tmp = t_1;
	elseif (z <= -2.15e-135)
		tmp = Float64(x / z);
	elseif (z <= -2e-200)
		tmp = t_0;
	elseif (z <= 4.8e-226)
		tmp = Float64(x / z);
	elseif (z <= 1.85e-99)
		tmp = t_0;
	elseif (z <= 9.8e-74)
		tmp = Float64(x / z);
	elseif (z <= 5.2e-41)
		tmp = t_0;
	elseif (z <= 1.4e-17)
		tmp = Float64(x / z);
	elseif (z <= 1.08e+92)
		tmp = t_1;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -3.4e+90)
		tmp = -x;
	elseif (z <= -2.05e-17)
		tmp = t_1;
	elseif (z <= -2.15e-135)
		tmp = x / z;
	elseif (z <= -2e-200)
		tmp = t_0;
	elseif (z <= 4.8e-226)
		tmp = x / z;
	elseif (z <= 1.85e-99)
		tmp = t_0;
	elseif (z <= 9.8e-74)
		tmp = x / z;
	elseif (z <= 5.2e-41)
		tmp = t_0;
	elseif (z <= 1.4e-17)
		tmp = x / z;
	elseif (z <= 1.08e+92)
		tmp = t_1;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+90], (-x), If[LessEqual[z, -2.05e-17], t$95$1, If[LessEqual[z, -2.15e-135], N[(x / z), $MachinePrecision], If[LessEqual[z, -2e-200], t$95$0, If[LessEqual[z, 4.8e-226], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.85e-99], t$95$0, If[LessEqual[z, 9.8e-74], N[(x / z), $MachinePrecision], If[LessEqual[z, 5.2e-41], t$95$0, If[LessEqual[z, 1.4e-17], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.08e+92], t$95$1, (-x)]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000018e90 or 1.08e92 < z

   1. Initial program 68.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   5. Step-by-step derivation

      1. neg-mul-1 83.1%

         \[\leadsto \color{blue}{-x} \]

   6. Simplified 83.1%

      \[\leadsto \color{blue}{-x} \]

   if -3.40000000000000018e90 < z < -2.05e-17 or 1.3999999999999999e-17 < z < 1.08e92

   1. Initial program 95.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 59.1%

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

      1. associate-/l* 58.8%

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

      2. associate-/r/ 61.3%

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

   6. Simplified 61.3%

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

   if -2.05e-17 < z < -2.14999999999999999e-135 or -2e-200 < z < 4.7999999999999999e-226 or 1.85e-99 < z < 9.8000000000000006e-74 or 5.1999999999999999e-41 < z < 1.3999999999999999e-17

   1. Initial program 99.9%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in y around 0 71.3%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if -2.14999999999999999e-135 < z < -2e-200 or 4.7999999999999999e-226 < z < 1.85e-99 or 9.8000000000000006e-74 < z < 5.1999999999999999e-41

   1. Initial program 99.8%

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

      1. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in y around inf 81.2%

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

      1. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

      1. clear-num 81.0%

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

      2. associate-/r/ 81.1%

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

      3. clear-num 81.3%

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

   8. Applied egg-rr 81.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.35)
     (- x)
     (if (<= z -1.7e-136)
       (/ x z)
       (if (<= z -1.8e-200)
         t_0
         (if (<= z 5.5e-226)
           (/ x z)
           (if (<= z 2.1e-99)
             t_0
             (if (<= z 5.2e-76)
               (/ x z)
               (if (<= z 3.2e-41)
                 t_0
                 (if (<= z 2.3e-17)
                   (/ x z)
                   (if (<= z 1.08e+92) t_0 (- x))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.35) {
		tmp = -x;
	} else if (z <= -1.7e-136) {
		tmp = x / z;
	} else if (z <= -1.8e-200) {
		tmp = t_0;
	} else if (z <= 5.5e-226) {
		tmp = x / z;
	} else if (z <= 2.1e-99) {
		tmp = t_0;
	} else if (z <= 5.2e-76) {
		tmp = x / z;
	} else if (z <= 3.2e-41) {
		tmp = t_0;
	} else if (z <= 2.3e-17) {
		tmp = x / z;
	} else if (z <= 1.08e+92) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-1.35d0)) then
        tmp = -x
    else if (z <= (-1.7d-136)) then
        tmp = x / z
    else if (z <= (-1.8d-200)) then
        tmp = t_0
    else if (z <= 5.5d-226) then
        tmp = x / z
    else if (z <= 2.1d-99) then
        tmp = t_0
    else if (z <= 5.2d-76) then
        tmp = x / z
    else if (z <= 3.2d-41) then
        tmp = t_0
    else if (z <= 2.3d-17) then
        tmp = x / z
    else if (z <= 1.08d+92) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.35) {
		tmp = -x;
	} else if (z <= -1.7e-136) {
		tmp = x / z;
	} else if (z <= -1.8e-200) {
		tmp = t_0;
	} else if (z <= 5.5e-226) {
		tmp = x / z;
	} else if (z <= 2.1e-99) {
		tmp = t_0;
	} else if (z <= 5.2e-76) {
		tmp = x / z;
	} else if (z <= 3.2e-41) {
		tmp = t_0;
	} else if (z <= 2.3e-17) {
		tmp = x / z;
	} else if (z <= 1.08e+92) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.35:
		tmp = -x
	elif z <= -1.7e-136:
		tmp = x / z
	elif z <= -1.8e-200:
		tmp = t_0
	elif z <= 5.5e-226:
		tmp = x / z
	elif z <= 2.1e-99:
		tmp = t_0
	elif z <= 5.2e-76:
		tmp = x / z
	elif z <= 3.2e-41:
		tmp = t_0
	elif z <= 2.3e-17:
		tmp = x / z
	elif z <= 1.08e+92:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -1.35)
		tmp = Float64(-x);
	elseif (z <= -1.7e-136)
		tmp = Float64(x / z);
	elseif (z <= -1.8e-200)
		tmp = t_0;
	elseif (z <= 5.5e-226)
		tmp = Float64(x / z);
	elseif (z <= 2.1e-99)
		tmp = t_0;
	elseif (z <= 5.2e-76)
		tmp = Float64(x / z);
	elseif (z <= 3.2e-41)
		tmp = t_0;
	elseif (z <= 2.3e-17)
		tmp = Float64(x / z);
	elseif (z <= 1.08e+92)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -1.35)
		tmp = -x;
	elseif (z <= -1.7e-136)
		tmp = x / z;
	elseif (z <= -1.8e-200)
		tmp = t_0;
	elseif (z <= 5.5e-226)
		tmp = x / z;
	elseif (z <= 2.1e-99)
		tmp = t_0;
	elseif (z <= 5.2e-76)
		tmp = x / z;
	elseif (z <= 3.2e-41)
		tmp = t_0;
	elseif (z <= 2.3e-17)
		tmp = x / z;
	elseif (z <= 1.08e+92)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35], (-x), If[LessEqual[z, -1.7e-136], N[(x / z), $MachinePrecision], If[LessEqual[z, -1.8e-200], t$95$0, If[LessEqual[z, 5.5e-226], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.1e-99], t$95$0, If[LessEqual[z, 5.2e-76], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.2e-41], t$95$0, If[LessEqual[z, 2.3e-17], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.08e+92], t$95$0, (-x)]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001 or 1.08e92 < z

   1. Initial program 72.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.7%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   5. Step-by-step derivation

      1. neg-mul-1 76.7%

         \[\leadsto \color{blue}{-x} \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{-x} \]

   if -1.3500000000000001 < z < -1.7e-136 or -1.8000000000000001e-200 < z < 5.5e-226 or 2.09999999999999984e-99 < z < 5.1999999999999999e-76 or 3.20000000000000012e-41 < z < 2.30000000000000009e-17

   1. Initial program 99.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in y around 0 69.6%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if -1.7e-136 < z < -1.8000000000000001e-200 or 5.5e-226 < z < 2.09999999999999984e-99 or 5.1999999999999999e-76 < z < 3.20000000000000012e-41 or 2.30000000000000009e-17 < z < 1.08e92

   1. Initial program 98.4%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in y around inf 73.5%

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

      1. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

      1. clear-num 74.6%

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

      2. associate-/r/ 74.7%

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

      3. clear-num 74.9%

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

   8. Applied egg-rr 74.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 94.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z} - x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+212}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (/ y z)) x)))
   (if (<= y -1.0)
     t_0
     (if (<= y 0.15)
       (- (/ x z) x)
       (if (<= y 4.5e+212) t_0 (* (* y x) (/ 1.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y / z)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.15) {
		tmp = (x / z) - x;
	} else if (y <= 4.5e+212) {
		tmp = t_0;
	} else {
		tmp = (y * x) * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = (x * (y / z)) - x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 0.15d0) then
        tmp = (x / z) - x
    else if (y <= 4.5d+212) then
        tmp = t_0
    else
        tmp = (y * x) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y / z)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.15) {
		tmp = (x / z) - x;
	} else if (y <= 4.5e+212) {
		tmp = t_0;
	} else {
		tmp = (y * x) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y / z)) - x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 0.15:
		tmp = (x / z) - x
	elif y <= 4.5e+212:
		tmp = t_0
	else:
		tmp = (y * x) * (1.0 / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y / z)) - x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.15)
		tmp = Float64(Float64(x / z) - x);
	elseif (y <= 4.5e+212)
		tmp = t_0;
	else
		tmp = Float64(Float64(y * x) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y / z)) - x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.15)
		tmp = (x / z) - x;
	elseif (y <= 4.5e+212)
		tmp = t_0;
	else
		tmp = (y * x) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 0.15], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 4.5e+212], t$95$0, N[(N[(y * x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.149999999999999994 < y < 4.5000000000000002e212

   1. Initial program 88.9%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 92.2%

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

      1. neg-mul-1 92.2%

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

      2. +-commutative 92.2%

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

      3. unsub-neg 92.2%

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

      4. associate-/l* 95.9%

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

      5. associate-/r/ 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in y around inf 90.5%

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

      1. associate-*l/ 90.6%

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

      2. *-commutative 90.6%

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

   9. Simplified 90.6%

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

   if -1 < y < 0.149999999999999994

   1. Initial program 84.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 97.9%

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

   if 4.5000000000000002e212 < y

   1. Initial program 99.7%

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

      1. associate-/l* 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in y around inf 99.7%

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

      1. associate-/l* 95.1%

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

   6. Simplified 95.1%

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

      1. div-inv 94.8%

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

      2. clear-num 95.0%

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

      3. div-inv 94.9%

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

      4. associate-*r* 99.8%

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

   8. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \]

Alternative 5: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{z}{y}} - x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+210}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ x (/ z y)) x)))
   (if (<= y -1.0)
     t_0
     (if (<= y 0.15)
       (- (/ x z) x)
       (if (<= y 9.5e+210) t_0 (* (* y x) (/ 1.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / (z / y)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.15) {
		tmp = (x / z) - x;
	} else if (y <= 9.5e+210) {
		tmp = t_0;
	} else {
		tmp = (y * x) * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = (x / (z / y)) - x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 0.15d0) then
        tmp = (x / z) - x
    else if (y <= 9.5d+210) then
        tmp = t_0
    else
        tmp = (y * x) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / (z / y)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.15) {
		tmp = (x / z) - x;
	} else if (y <= 9.5e+210) {
		tmp = t_0;
	} else {
		tmp = (y * x) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / (z / y)) - x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 0.15:
		tmp = (x / z) - x
	elif y <= 9.5e+210:
		tmp = t_0
	else:
		tmp = (y * x) * (1.0 / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / Float64(z / y)) - x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.15)
		tmp = Float64(Float64(x / z) - x);
	elseif (y <= 9.5e+210)
		tmp = t_0;
	else
		tmp = Float64(Float64(y * x) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / (z / y)) - x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.15)
		tmp = (x / z) - x;
	elseif (y <= 9.5e+210)
		tmp = t_0;
	else
		tmp = (y * x) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 0.15], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 9.5e+210], t$95$0, N[(N[(y * x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.149999999999999994 < y < 9.5000000000000004e210

   1. Initial program 88.9%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 92.2%

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

      1. neg-mul-1 92.2%

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

      2. +-commutative 92.2%

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

      3. unsub-neg 92.2%

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

      4. associate-/l* 95.9%

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

      5. associate-/r/ 92.3%

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

   6. Simplified 92.3%

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

      1. *-commutative 92.3%

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

      2. clear-num 92.2%

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

      3. un-div-inv 94.7%

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

   8. Applied egg-rr 94.7%

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

   9. Taylor expanded in y around inf 93.0%

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

   if -1 < y < 0.149999999999999994

   1. Initial program 84.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 97.9%

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

   if 9.5000000000000004e210 < y

   1. Initial program 99.7%

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

      1. associate-/l* 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in y around inf 99.7%

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

      1. associate-/l* 95.1%

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

   6. Simplified 95.1%

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

      1. div-inv 94.8%

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

      2. clear-num 95.0%

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

      3. div-inv 94.9%

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

      4. associate-*r* 99.8%

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

   8. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \]

Alternative 6: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+22} \lor \neg \left(z \leq 6.5 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e+22) (not (<= z 6.5e+61)))
   (- (* x (/ y z)) x)
   (* (/ x z) (+ 1.0 (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+22) || !(z <= 6.5e+61)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * (1.0 + (y - 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 <= (-1.4d+22)) .or. (.not. (z <= 6.5d+61))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) * (1.0d0 + (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+22) || !(z <= 6.5e+61)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e+22) or not (z <= 6.5e+61):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) * (1.0 + (y - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e+22) || !(z <= 6.5e+61))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e+22) || ~((z <= 6.5e+61)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) * (1.0 + (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e+22], N[Not[LessEqual[z, 6.5e+61]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e22 or 6.4999999999999996e61 < z

   1. Initial program 73.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.3%

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

      1. neg-mul-1 93.3%

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

      2. +-commutative 93.3%

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

      3. unsub-neg 93.3%

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

      4. associate-/l* 95.3%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 93.3%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   9. Simplified 99.9%

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

   if -1.4e22 < z < 6.4999999999999996e61

   1. Initial program 99.2%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+22} \lor \neg \left(z \leq 6.5 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \]

Alternative 7: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13.2 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -13.2) (not (<= z 1.0)))
   (- (* x (/ y z)) x)
   (/ (+ x (* y x)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13.2) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x + (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 <= (-13.2d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x + (y * x)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13.2) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x + (y * x)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -13.2) or not (z <= 1.0):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x + (y * x)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -13.2) || !(z <= 1.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x + Float64(y * x)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -13.2) || ~((z <= 1.0)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x + (y * x)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -13.2], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -13.199999999999999 or 1 < z

   1. Initial program 75.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.1%

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

      1. neg-mul-1 93.1%

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

      2. +-commutative 93.1%

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

      3. unsub-neg 93.1%

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

      4. associate-/l* 95.7%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 92.2%

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

      1. associate-*l/ 99.0%

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

      2. *-commutative 99.0%

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

   9. Simplified 99.0%

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

   if -13.199999999999999 < z < 1

   1. Initial program 99.8%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around 0 99.5%

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

      1. *-commutative 99.5%

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

      2. distribute-lft-in 99.5%

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

      3. *-rgt-identity 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13.2 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot x}{z}\\ \end{array} \]

Alternative 8: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -900.0)
   (* y (/ x z))
   (if (<= y 1e+61) (- (/ x z) x) (* (* y x) (/ 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -900.0) {
		tmp = y * (x / z);
	} else if (y <= 1e+61) {
		tmp = (x / z) - x;
	} else {
		tmp = (y * x) * (1.0 / 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 (y <= (-900.0d0)) then
        tmp = y * (x / z)
    else if (y <= 1d+61) then
        tmp = (x / z) - x
    else
        tmp = (y * x) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -900.0) {
		tmp = y * (x / z);
	} else if (y <= 1e+61) {
		tmp = (x / z) - x;
	} else {
		tmp = (y * x) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -900.0:
		tmp = y * (x / z)
	elif y <= 1e+61:
		tmp = (x / z) - x
	else:
		tmp = (y * x) * (1.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -900.0)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1e+61)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(y * x) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -900.0)
		tmp = y * (x / z);
	elseif (y <= 1e+61)
		tmp = (x / z) - x;
	else
		tmp = (y * x) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -900.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+61], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -900

   1. Initial program 82.8%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. associate-/l* 66.5%

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

   6. Simplified 66.5%

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

      1. clear-num 66.4%

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

      2. associate-/r/ 66.5%

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

      3. clear-num 67.0%

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

   8. Applied egg-rr 67.0%

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

   if -900 < y < 9.99999999999999949e60

   1. Initial program 85.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 95.4%

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

   if 9.99999999999999949e60 < y

   1. Initial program 98.0%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

      1. div-inv 84.5%

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

      2. clear-num 84.6%

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

      3. div-inv 84.4%

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

      4. associate-*r* 87.5%

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

   8. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \]

Alternative 9: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{1 + y}{z} \cdot x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e-8)
   (* (/ (+ 1.0 y) z) x)
   (if (<= y 2.6e+63) (- (/ x z) x) (* (* y x) (/ 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e-8) {
		tmp = ((1.0 + y) / z) * x;
	} else if (y <= 2.6e+63) {
		tmp = (x / z) - x;
	} else {
		tmp = (y * x) * (1.0 / 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 (y <= (-3.6d-8)) then
        tmp = ((1.0d0 + y) / z) * x
    else if (y <= 2.6d+63) then
        tmp = (x / z) - x
    else
        tmp = (y * x) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e-8) {
		tmp = ((1.0 + y) / z) * x;
	} else if (y <= 2.6e+63) {
		tmp = (x / z) - x;
	} else {
		tmp = (y * x) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e-8:
		tmp = ((1.0 + y) / z) * x
	elif y <= 2.6e+63:
		tmp = (x / z) - x
	else:
		tmp = (y * x) * (1.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e-8)
		tmp = Float64(Float64(Float64(1.0 + y) / z) * x);
	elseif (y <= 2.6e+63)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(y * x) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e-8)
		tmp = ((1.0 + y) / z) * x;
	elseif (y <= 2.6e+63)
		tmp = (x / z) - x;
	else
		tmp = (y * x) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e-8], N[(N[(N[(1.0 + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.6e+63], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999981e-8

   1. Initial program 84.0%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 68.7%

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

      1. associate-/l* 70.1%

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

      2. associate-/r/ 67.4%

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

   6. Simplified 67.4%

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

   if -3.59999999999999981e-8 < y < 2.6000000000000001e63

   1. Initial program 85.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 97.2%

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

   if 2.6000000000000001e63 < y

   1. Initial program 98.0%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

      1. div-inv 84.5%

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

      2. clear-num 84.6%

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

      3. div-inv 84.4%

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

      4. associate-*r* 87.5%

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

   8. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{1 + y}{z} \cdot x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \]

Alternative 10: 95.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (- (/ x (/ z y)) x)
   (if (<= y 0.15) (- (/ x z) x) (- (/ (* y x) z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = (x / (z / y)) - x;
	} else if (y <= 0.15) {
		tmp = (x / z) - x;
	} else {
		tmp = ((y * x) / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = (x / (z / y)) - x
    else if (y <= 0.15d0) then
        tmp = (x / z) - x
    else
        tmp = ((y * x) / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = (x / (z / y)) - x;
	} else if (y <= 0.15) {
		tmp = (x / z) - x;
	} else {
		tmp = ((y * x) / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = (x / (z / y)) - x
	elif y <= 0.15:
		tmp = (x / z) - x
	else:
		tmp = ((y * x) / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	elseif (y <= 0.15)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(Float64(y * x) / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = (x / (z / y)) - x;
	elseif (y <= 0.15)
		tmp = (x / z) - x;
	else
		tmp = ((y * x) / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 0.15], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 82.8%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 88.4%

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

      1. neg-mul-1 88.4%

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

      2. +-commutative 88.4%

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

      3. unsub-neg 88.4%

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

      4. associate-/l* 94.5%

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

      5. associate-/r/ 92.8%

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

   6. Simplified 92.8%

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

      1. *-commutative 92.8%

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

      2. clear-num 92.7%

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

      3. un-div-inv 94.2%

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

   8. Applied egg-rr 94.2%

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

   9. Taylor expanded in y around inf 92.7%

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

   if -1 < y < 0.149999999999999994

   1. Initial program 84.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 97.9%

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

   if 0.149999999999999994 < y

   1. Initial program 98.2%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in z around 0 98.3%

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

      1. neg-mul-1 98.3%

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

      2. +-commutative 98.3%

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

      3. unsub-neg 98.3%

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

      4. associate-/l* 97.1%

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

      5. associate-/r/ 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in y around inf 96.8%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} - x\\ \end{array} \]

Alternative 11: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500 \lor \neg \left(y \leq 8.3 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1500.0) (not (<= y 8.3e+65))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1500.0) || !(y <= 8.3e+65)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	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 <= (-1500.0d0)) .or. (.not. (y <= 8.3d+65))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1500.0) || !(y <= 8.3e+65)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1500.0) or not (y <= 8.3e+65):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1500.0) || !(y <= 8.3e+65))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1500.0) || ~((y <= 8.3e+65)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1500.0], N[Not[LessEqual[y, 8.3e+65]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1500 or 8.3000000000000004e65 < y

   1. Initial program 89.8%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in y around inf 75.3%

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

      1. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

      1. clear-num 74.7%

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

      2. associate-/r/ 74.8%

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

      3. clear-num 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -1500 < y < 8.3000000000000004e65

   1. Initial program 85.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 95.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500 \lor \neg \left(y \leq 8.3 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 12: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1500.0)
   (* y (/ x z))
   (if (<= y 1.92e+59) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * (x / z);
	} else if (y <= 1.92e+59) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	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 <= (-1500.0d0)) then
        tmp = y * (x / z)
    else if (y <= 1.92d+59) then
        tmp = (x / z) - x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * (x / z);
	} else if (y <= 1.92e+59) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1500.0:
		tmp = y * (x / z)
	elif y <= 1.92e+59:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1500.0)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.92e+59)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1500.0)
		tmp = y * (x / z);
	elseif (y <= 1.92e+59)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1500.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.92e+59], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1500

   1. Initial program 82.8%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. associate-/l* 66.5%

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

   6. Simplified 66.5%

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

      1. clear-num 66.4%

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

      2. associate-/r/ 66.5%

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

      3. clear-num 67.0%

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

   8. Applied egg-rr 67.0%

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

   if -1500 < y < 1.92e59

   1. Initial program 85.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 95.4%

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

   if 1.92e59 < y

   1. Initial program 98.0%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 13: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1500.0)
   (* y (/ x z))
   (if (<= y 3.8e+57) (- (/ x z) x) (/ (* y x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * (x / z);
	} else if (y <= 3.8e+57) {
		tmp = (x / z) - x;
	} else {
		tmp = (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 (y <= (-1500.0d0)) then
        tmp = y * (x / z)
    else if (y <= 3.8d+57) then
        tmp = (x / z) - x
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * (x / z);
	} else if (y <= 3.8e+57) {
		tmp = (x / z) - x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1500.0:
		tmp = y * (x / z)
	elif y <= 3.8e+57:
		tmp = (x / z) - x
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1500.0)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3.8e+57)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1500.0)
		tmp = y * (x / z);
	elseif (y <= 3.8e+57)
		tmp = (x / z) - x;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1500.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+57], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1500

   1. Initial program 82.8%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. associate-/l* 66.5%

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

   6. Simplified 66.5%

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

      1. clear-num 66.4%

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

      2. associate-/r/ 66.5%

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

      3. clear-num 67.0%

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

   8. Applied egg-rr 67.0%

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

   if -1500 < y < 3.7999999999999999e57

   1. Initial program 85.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 95.4%

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

   if 3.7999999999999999e57 < y

   1. Initial program 98.0%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around inf 87.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 14: 64.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.35) (- x) (if (<= z 1.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.35) {
		tmp = -x;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	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 <= (-1.35d0)) then
        tmp = -x
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.35) {
		tmp = -x;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.35:
		tmp = -x
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.35)
		tmp = Float64(-x);
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.35)
		tmp = -x;
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.35], (-x), If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001 or 1 < z

   1. Initial program 75.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 72.1%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   5. Step-by-step derivation

      1. neg-mul-1 72.1%

         \[\leadsto \color{blue}{-x} \]

   6. Simplified 72.1%

      \[\leadsto \color{blue}{-x} \]

   if -1.3500000000000001 < z < 1

   1. Initial program 99.8%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around 0 99.5%

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

      1. associate-/l* 99.3%

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

      2. associate-/r/ 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in y around 0 53.2%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 15: 37.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 87.7%

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

   1. associate-/l* 95.0%

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

3. Simplified 95.0%

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

4. Taylor expanded in z around inf 37.1%

   \[\leadsto \color{blue}{-1 \cdot x} \]
5. Step-by-step derivation

   1. neg-mul-1 37.1%

      \[\leadsto \color{blue}{-x} \]

6. Simplified 37.1%

   \[\leadsto \color{blue}{-x} \]

7. Final simplification 37.1%

   \[\leadsto -x \]

Developer target: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} 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) :: tmp
    t_0 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023213 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))