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

Percentage Accurate: 88.0% → 99.5%

Time: 10.0s

Alternatives: 11

Speedup: 0.8×

• 20.8% 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: 88.0% 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: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-19}:\\ \;\;\;\;\frac{1 + y}{z} \cdot x - x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{1 + \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} + \left(\frac{x}{z} - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e-19)
   (- (* (/ (+ 1.0 y) z) x) x)
   (if (<= z 3.5e-94)
     (/ (/ x z) (/ 1.0 (+ 1.0 (- y z))))
     (+ (* x (/ y z)) (- (/ x z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-19) {
		tmp = (((1.0 + y) / z) * x) - x;
	} else if (z <= 3.5e-94) {
		tmp = (x / z) / (1.0 / (1.0 + (y - z)));
	} else {
		tmp = (x * (y / z)) + ((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 (z <= (-5d-19)) then
        tmp = (((1.0d0 + y) / z) * x) - x
    else if (z <= 3.5d-94) then
        tmp = (x / z) / (1.0d0 / (1.0d0 + (y - z)))
    else
        tmp = (x * (y / z)) + ((x / z) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-19) {
		tmp = (((1.0 + y) / z) * x) - x;
	} else if (z <= 3.5e-94) {
		tmp = (x / z) / (1.0 / (1.0 + (y - z)));
	} else {
		tmp = (x * (y / z)) + ((x / z) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e-19:
		tmp = (((1.0 + y) / z) * x) - x
	elif z <= 3.5e-94:
		tmp = (x / z) / (1.0 / (1.0 + (y - z)))
	else:
		tmp = (x * (y / z)) + ((x / z) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e-19)
		tmp = Float64(Float64(Float64(Float64(1.0 + y) / z) * x) - x);
	elseif (z <= 3.5e-94)
		tmp = Float64(Float64(x / z) / Float64(1.0 / Float64(1.0 + Float64(y - z))));
	else
		tmp = Float64(Float64(x * Float64(y / z)) + Float64(Float64(x / z) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e-19)
		tmp = (((1.0 + y) / z) * x) - x;
	elseif (z <= 3.5e-94)
		tmp = (x / z) / (1.0 / (1.0 + (y - z)));
	else
		tmp = (x * (y / z)) + ((x / z) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e-19], N[(N[(N[(N[(1.0 + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 3.5e-94], N[(N[(x / z), $MachinePrecision] / N[(1.0 / N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000004e-19

   1. Initial program 72.6%

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

      1. associate-/l* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. un-div-inv 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 88.7%

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

      1. neg-mul-1 88.7%

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

      2. +-commutative 88.7%

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

      3. unsub-neg 88.7%

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

      4. associate-/l* 93.7%

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

      5. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   if -5.0000000000000004e-19 < z < 3.49999999999999998e-94

   1. Initial program 99.9%

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

      1. associate-/l* 89.7%

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

      2. div-inv 89.6%

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

   3. Applied egg-rr 89.6%

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

      1. un-div-inv 89.7%

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

      2. div-inv 89.7%

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

      3. associate-/r* 100.0%

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

      4. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   if 3.49999999999999998e-94 < z

   1. Initial program 72.9%

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

      1. distribute-lft-in 72.9%

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

      2. fma-def 72.9%

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

      3. *-rgt-identity 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in y around 0 92.9%

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

      1. associate-/l* 96.3%

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

      2. associate-/r/ 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-mul-1 99.9%

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

      5. unsub-neg 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-19}:\\ \;\;\;\;\frac{1 + y}{z} \cdot x - x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{1 + \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} + \left(\frac{x}{z} - x\right)\\ \end{array} \]

Alternative 2: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -51000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -51000000.0)
     (- x)
     (if (<= z 1.45e-232)
       t_0
       (if (<= z 1.22e-80) (/ x z) (if (<= z 4.4e+79) t_0 (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -51000000.0) {
		tmp = -x;
	} else if (z <= 1.45e-232) {
		tmp = t_0;
	} else if (z <= 1.22e-80) {
		tmp = x / z;
	} else if (z <= 4.4e+79) {
		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 <= (-51000000.0d0)) then
        tmp = -x
    else if (z <= 1.45d-232) then
        tmp = t_0
    else if (z <= 1.22d-80) then
        tmp = x / z
    else if (z <= 4.4d+79) 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 <= -51000000.0) {
		tmp = -x;
	} else if (z <= 1.45e-232) {
		tmp = t_0;
	} else if (z <= 1.22e-80) {
		tmp = x / z;
	} else if (z <= 4.4e+79) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -51000000.0:
		tmp = -x
	elif z <= 1.45e-232:
		tmp = t_0
	elif z <= 1.22e-80:
		tmp = x / z
	elif z <= 4.4e+79:
		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 <= -51000000.0)
		tmp = Float64(-x);
	elseif (z <= 1.45e-232)
		tmp = t_0;
	elseif (z <= 1.22e-80)
		tmp = Float64(x / z);
	elseif (z <= 4.4e+79)
		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 <= -51000000.0)
		tmp = -x;
	elseif (z <= 1.45e-232)
		tmp = t_0;
	elseif (z <= 1.22e-80)
		tmp = x / z;
	elseif (z <= 4.4e+79)
		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, -51000000.0], (-x), If[LessEqual[z, 1.45e-232], t$95$0, If[LessEqual[z, 1.22e-80], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.4e+79], t$95$0, (-x)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1e7 or 4.3999999999999998e79 < z

   1. Initial program 65.9%

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

   2. Taylor expanded in z around inf 81.6%

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

      1. neg-mul-1 81.6%

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

   4. Simplified 81.6%

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

   if -5.1e7 < z < 1.45e-232 or 1.22e-80 < z < 4.3999999999999998e79

   1. Initial program 99.0%

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

      1. associate-/l* 91.4%

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

      2. div-inv 91.3%

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

   3. Applied egg-rr 91.3%

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

   4. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 59.6%

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

   6. Simplified 59.6%

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

   if 1.45e-232 < z < 1.22e-80

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around 0 75.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -51000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -70000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -70000000.0)
   (- x)
   (if (<= z 1.3e-232)
     (* y (/ x z))
     (if (<= z 1.28e-80) (/ x z) (if (<= z 1.5e+80) (* x (/ y z)) (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -70000000.0) {
		tmp = -x;
	} else if (z <= 1.3e-232) {
		tmp = y * (x / z);
	} else if (z <= 1.28e-80) {
		tmp = x / z;
	} else if (z <= 1.5e+80) {
		tmp = x * (y / 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 <= (-70000000.0d0)) then
        tmp = -x
    else if (z <= 1.3d-232) then
        tmp = y * (x / z)
    else if (z <= 1.28d-80) then
        tmp = x / z
    else if (z <= 1.5d+80) then
        tmp = x * (y / 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 <= -70000000.0) {
		tmp = -x;
	} else if (z <= 1.3e-232) {
		tmp = y * (x / z);
	} else if (z <= 1.28e-80) {
		tmp = x / z;
	} else if (z <= 1.5e+80) {
		tmp = x * (y / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -70000000.0:
		tmp = -x
	elif z <= 1.3e-232:
		tmp = y * (x / z)
	elif z <= 1.28e-80:
		tmp = x / z
	elif z <= 1.5e+80:
		tmp = x * (y / z)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -70000000.0)
		tmp = Float64(-x);
	elseif (z <= 1.3e-232)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.28e-80)
		tmp = Float64(x / z);
	elseif (z <= 1.5e+80)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -70000000.0)
		tmp = -x;
	elseif (z <= 1.3e-232)
		tmp = y * (x / z);
	elseif (z <= 1.28e-80)
		tmp = x / z;
	elseif (z <= 1.5e+80)
		tmp = x * (y / z);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -70000000.0], (-x), If[LessEqual[z, 1.3e-232], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.28e-80], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.5e+80], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], (-x)]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7e7 or 1.49999999999999993e80 < z

   1. Initial program 65.9%

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

   2. Taylor expanded in z around inf 81.6%

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

      1. neg-mul-1 81.6%

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

   4. Simplified 81.6%

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

   if -7e7 < z < 1.29999999999999998e-232

   1. Initial program 99.9%

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

      1. associate-/l* 88.7%

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

      2. div-inv 88.6%

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

   3. Applied egg-rr 88.6%

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

   4. Taylor expanded in y around inf 54.7%

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

      1. associate-*r/ 57.3%

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

   6. Simplified 57.3%

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

   if 1.29999999999999998e-232 < z < 1.28e-80

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around 0 75.8%

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

   if 1.28e-80 < z < 1.49999999999999993e80

   1. Initial program 96.4%

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

   2. Taylor expanded in y around inf 67.3%

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

      1. associate-/l* 66.9%

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

      2. associate-/r/ 66.9%

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

   4. Simplified 66.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+16} \lor \neg \left(z \leq 3.3 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+16) (not (<= z 3.3e+15)))
   (- (* x (/ y z)) x)
   (* (/ x z) (+ 1.0 (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+16) || !(z <= 3.3e+15)) {
		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 <= (-1.35d+16)) .or. (.not. (z <= 3.3d+15))) 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 <= -1.35e+16) || !(z <= 3.3e+15)) {
		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 <= -1.35e+16) or not (z <= 3.3e+15):
		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 <= -1.35e+16) || !(z <= 3.3e+15))
		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 <= -1.35e+16) || ~((z <= 3.3e+15)))
		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, -1.35e+16], N[Not[LessEqual[z, 3.3e+15]], $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 < -1.35e16 or 3.3e15 < z

   1. Initial program 67.1%

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

      1. associate-/l* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. un-div-inv 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 89.0%

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

      1. neg-mul-1 89.0%

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

      2. +-commutative 89.0%

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

      3. unsub-neg 89.0%

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

      4. associate-/l* 94.8%

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

      5. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 100.0%

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

   if -1.35e16 < z < 3.3e15

   1. Initial program 99.9%

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

      1. associate-/l* 91.9%

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

      2. associate-/r/ 99.9%

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

   3. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+16} \lor \neg \left(z \leq 3.3 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \]

Alternative 5: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-14} \lor \neg \left(z \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{1 + y}{z} \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e-14) (not (<= z 2e-12)))
   (- (* (/ (+ 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 <= -2e-14) || !(z <= 2e-12)) {
		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 <= (-2d-14)) .or. (.not. (z <= 2d-12))) 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 <= -2e-14) || !(z <= 2e-12)) {
		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 <= -2e-14) or not (z <= 2e-12):
		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 <= -2e-14) || !(z <= 2e-12))
		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 <= -2e-14) || ~((z <= 2e-12)))
		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, -2e-14], N[Not[LessEqual[z, 2e-12]], $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 < -2e-14 or 1.99999999999999996e-12 < z

   1. Initial program 70.1%

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

      1. associate-/l* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. un-div-inv 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 90.0%

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

      1. neg-mul-1 90.0%

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

      2. +-commutative 90.0%

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

      3. unsub-neg 90.0%

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

      4. associate-/l* 95.3%

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

      5. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   if -2e-14 < z < 1.99999999999999996e-12

   1. Initial program 99.9%

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

      1. associate-/l* 91.0%

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

      2. associate-/r/ 99.9%

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

   3. 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 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-14} \lor \neg \left(z \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{1 + y}{z} \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \]

Alternative 6: 95.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 82.3%

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

      1. associate-/l* 92.2%

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

      2. div-inv 92.2%

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

   3. Applied egg-rr 92.2%

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

      1. un-div-inv 92.2%

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

      2. +-commutative 92.2%

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

   5. Applied egg-rr 92.2%

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

   6. Taylor expanded in z around 0 89.3%

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

      1. neg-mul-1 89.3%

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

      2. +-commutative 89.3%

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

      3. unsub-neg 89.3%

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

      4. associate-/l* 94.9%

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

      5. associate-/r/ 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in y around inf 91.6%

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

   if -1 < y < 1

   1. Initial program 84.6%

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

      1. associate-/l* 100.0%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 84.2%

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

      1. sub-neg 84.2%

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

      2. +-commutative 84.2%

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

      3. distribute-rgt1-in 84.2%

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

      4. cancel-sign-sub-inv 84.2%

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

      5. *-commutative 84.2%

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

      6. div-sub 84.2%

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

      7. associate-*l/ 86.4%

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

      8. associate-/r/ 99.6%

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

      9. *-inverses 99.6%

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

      10. /-rgt-identity 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 95.4%

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

Alternative 7: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 7.5 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 7.5e-31)))
   (- (* x (/ y z)) x)
   (/ (* (+ 1.0 y) x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 7.5e-31)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = ((1.0 + 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 <= (-1.0d0)) .or. (.not. (z <= 7.5d-31))) then
        tmp = (x * (y / z)) - x
    else
        tmp = ((1.0d0 + y) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 7.5e-31)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = ((1.0 + y) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 7.5e-31):
		tmp = (x * (y / z)) - x
	else:
		tmp = ((1.0 + y) * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 7.5e-31))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(Float64(1.0 + y) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 7.5e-31)))
		tmp = (x * (y / z)) - x;
	else
		tmp = ((1.0 + y) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 7.5e-31]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(1.0 + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 7.49999999999999975e-31 < z

   1. Initial program 69.9%

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

      1. associate-/l* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. un-div-inv 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 89.9%

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

      1. neg-mul-1 89.9%

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

      2. +-commutative 89.9%

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

      3. unsub-neg 89.9%

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

      4. associate-/l* 95.2%

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

      5. associate-/r/ 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 97.8%

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

   if -1 < z < 7.49999999999999975e-31

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 7.5 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 + y\right) \cdot x}{z}\\ \end{array} \]

Alternative 8: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+23} \lor \neg \left(y \leq 4 \cdot 10^{+132}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+23) (not (<= y 4e+132))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+23) || !(y <= 4e+132)) {
		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 <= (-5d+23)) .or. (.not. (y <= 4d+132))) 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 <= -5e+23) || !(y <= 4e+132)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+23) or not (y <= 4e+132):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+23) || !(y <= 4e+132))
		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 <= -5e+23) || ~((y <= 4e+132)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+23], N[Not[LessEqual[y, 4e+132]], $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 < -4.9999999999999999e23 or 3.99999999999999996e132 < y

   1. Initial program 85.1%

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

      1. associate-/l* 90.0%

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

      2. div-inv 90.0%

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

   3. Applied egg-rr 90.0%

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

   4. Taylor expanded in y around inf 73.8%

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

      1. associate-*r/ 70.9%

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

   6. Simplified 70.9%

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

   if -4.9999999999999999e23 < y < 3.99999999999999996e132

   1. Initial program 82.4%

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

      1. associate-/l* 99.4%

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

      2. div-inv 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in y around 0 75.6%

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

      1. sub-neg 75.6%

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

      2. +-commutative 75.6%

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

      3. distribute-rgt1-in 75.6%

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

      4. cancel-sign-sub-inv 75.6%

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

      5. *-commutative 75.6%

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

      6. div-sub 75.7%

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

      7. associate-*l/ 75.9%

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

      8. associate-/r/ 93.2%

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

      9. *-inverses 93.2%

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

      10. /-rgt-identity 93.2%

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

   6. Simplified 93.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+23} \lor \neg \left(y \leq 4 \cdot 10^{+132}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 9: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+24} \lor \neg \left(y \leq 1.6 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e+24) (not (<= y 1.6e+138))) (/ (* y x) z) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e+24) || !(y <= 1.6e+138)) {
		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 <= (-1.65d+24)) .or. (.not. (y <= 1.6d+138))) 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 <= -1.65e+24) || !(y <= 1.6e+138)) {
		tmp = (y * x) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e+24) or not (y <= 1.6e+138):
		tmp = (y * x) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e+24) || !(y <= 1.6e+138))
		tmp = Float64(Float64(y * 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 <= -1.65e+24) || ~((y <= 1.6e+138)))
		tmp = (y * x) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e+24], N[Not[LessEqual[y, 1.6e+138]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e24 or 1.6000000000000001e138 < y

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 73.8%

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

   if -1.6499999999999999e24 < y < 1.6000000000000001e138

   1. Initial program 82.4%

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

      1. associate-/l* 99.4%

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

      2. div-inv 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in y around 0 75.6%

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

      1. sub-neg 75.6%

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

      2. +-commutative 75.6%

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

      3. distribute-rgt1-in 75.6%

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

      4. cancel-sign-sub-inv 75.6%

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

      5. *-commutative 75.6%

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

      6. div-sub 75.7%

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

      7. associate-*l/ 75.9%

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

      8. associate-/r/ 93.2%

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

      9. *-inverses 93.2%

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

      10. /-rgt-identity 93.2%

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

   6. Simplified 93.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+24} \lor \neg \left(y \leq 1.6 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 10: 64.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 3.4e-42) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3.4e-42) {
		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 <= (-1.0d0)) then
        tmp = -x
    else if (z <= 3.4d-42) 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 <= -1.0) {
		tmp = -x;
	} else if (z <= 3.4e-42) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 3.4e-42:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 3.4e-42)
		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 <= -1.0)
		tmp = -x;
	elseif (z <= 3.4e-42)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 3.4e-42], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3.40000000000000022e-42 < z

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 73.7%

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

      1. neg-mul-1 73.7%

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

   4. Simplified 73.7%

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

   if -1 < z < 3.40000000000000022e-42

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.3%

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

   3. Taylor expanded in y around 0 56.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 11: 39.4% 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 83.4%

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

2. Taylor expanded in z around inf 42.1%

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

   1. neg-mul-1 42.1%

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

4. Simplified 42.1%

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

5. Final simplification 42.1%

   \[\leadsto -x \]

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 2023274 
(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))