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

Percentage Accurate: 88.4% → 98.8%

Time: 5.6s

Alternatives: 10

Speedup: 1.0×

• 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: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -420000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -420000.0) (not (<= z 1.0)))
   (* x (+ (/ y z) -1.0))
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -420000.0) || !(z <= 1.0)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x * (y + 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 ((z <= (-420000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y / z) + (-1.0d0))
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -420000.0) || !(z <= 1.0)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -420000.0) or not (z <= 1.0):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -420000.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -420000.0) || ~((z <= 1.0)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -420000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e5 or 1 < z

   1. Initial program 81.2%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. associate-/l* 97.4%

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

   6. Simplified 97.4%

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

   7. Taylor expanded in x around 0 99.8%

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

   if -4.2e5 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -420000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]

Alternative 2: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -200000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -200000000.0)
     (- x)
     (if (<= z -1.65e-66)
       t_0
       (if (<= z 8.5e-195)
         (/ x z)
         (if (<= z 2.8e-180)
           t_0
           (if (<= z 2.8e-73) (/ x z) (if (<= z 4.2e+16) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -200000000.0) {
		tmp = -x;
	} else if (z <= -1.65e-66) {
		tmp = t_0;
	} else if (z <= 8.5e-195) {
		tmp = x / z;
	} else if (z <= 2.8e-180) {
		tmp = t_0;
	} else if (z <= 2.8e-73) {
		tmp = x / z;
	} else if (z <= 4.2e+16) {
		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 <= (-200000000.0d0)) then
        tmp = -x
    else if (z <= (-1.65d-66)) then
        tmp = t_0
    else if (z <= 8.5d-195) then
        tmp = x / z
    else if (z <= 2.8d-180) then
        tmp = t_0
    else if (z <= 2.8d-73) then
        tmp = x / z
    else if (z <= 4.2d+16) 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 <= -200000000.0) {
		tmp = -x;
	} else if (z <= -1.65e-66) {
		tmp = t_0;
	} else if (z <= 8.5e-195) {
		tmp = x / z;
	} else if (z <= 2.8e-180) {
		tmp = t_0;
	} else if (z <= 2.8e-73) {
		tmp = x / z;
	} else if (z <= 4.2e+16) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -200000000.0:
		tmp = -x
	elif z <= -1.65e-66:
		tmp = t_0
	elif z <= 8.5e-195:
		tmp = x / z
	elif z <= 2.8e-180:
		tmp = t_0
	elif z <= 2.8e-73:
		tmp = x / z
	elif z <= 4.2e+16:
		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 <= -200000000.0)
		tmp = Float64(-x);
	elseif (z <= -1.65e-66)
		tmp = t_0;
	elseif (z <= 8.5e-195)
		tmp = Float64(x / z);
	elseif (z <= 2.8e-180)
		tmp = t_0;
	elseif (z <= 2.8e-73)
		tmp = Float64(x / z);
	elseif (z <= 4.2e+16)
		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 <= -200000000.0)
		tmp = -x;
	elseif (z <= -1.65e-66)
		tmp = t_0;
	elseif (z <= 8.5e-195)
		tmp = x / z;
	elseif (z <= 2.8e-180)
		tmp = t_0;
	elseif (z <= 2.8e-73)
		tmp = x / z;
	elseif (z <= 4.2e+16)
		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, -200000000.0], (-x), If[LessEqual[z, -1.65e-66], t$95$0, If[LessEqual[z, 8.5e-195], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.8e-180], t$95$0, If[LessEqual[z, 2.8e-73], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.2e+16], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e8 or 4.2e16 < z

   1. Initial program 81.0%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in z around inf 74.5%

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

      1. neg-mul-1 74.5%

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

   6. Simplified 74.5%

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

   if -2e8 < z < -1.6499999999999999e-66 or 8.50000000000000023e-195 < z < 2.79999999999999997e-180 or 2.80000000000000012e-73 < z < 4.2e16

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 74.6%

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

      1. associate-/l* 76.8%

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

      2. div-inv 76.8%

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

      3. clear-num 76.9%

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

   4. Applied egg-rr 76.9%

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

   if -1.6499999999999999e-66 < z < 8.50000000000000023e-195 or 2.79999999999999997e-180 < z < 2.80000000000000012e-73

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 76.8%

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

   5. Taylor expanded in z around 0 76.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -200000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 94.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+25} \lor \neg \left(y \leq 4.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+25) (not (<= y 4.7e-7)))
   (* x (+ (/ y z) -1.0))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+25) || !(y <= 4.7e-7)) {
		tmp = x * ((y / z) + -1.0);
	} 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 <= (-4d+25)) .or. (.not. (y <= 4.7d-7))) then
        tmp = x * ((y / z) + (-1.0d0))
    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 <= -4e+25) || !(y <= 4.7e-7)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+25) or not (y <= 4.7e-7):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+25) || !(y <= 4.7e-7))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+25) || ~((y <= 4.7e-7)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+25], N[Not[LessEqual[y, 4.7e-7]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000036e25 or 4.7e-7 < y

   1. Initial program 90.8%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 92.9%

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

      1. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

   7. Taylor expanded in x around 0 93.8%

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

   if -4.00000000000000036e25 < y < 4.7e-7

   1. Initial program 92.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.2%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+25} \lor \neg \left(y \leq 4.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 4: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+25} \lor \neg \left(y \leq 4.7 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{y}{\frac{z}{x}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+25) (not (<= y 4.7e-7))) (- (/ y (/ z x)) x) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+25) || !(y <= 4.7e-7)) {
		tmp = (y / (z / x)) - 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 <= (-4d+25)) .or. (.not. (y <= 4.7d-7))) then
        tmp = (y / (z / x)) - 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 <= -4e+25) || !(y <= 4.7e-7)) {
		tmp = (y / (z / x)) - x;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+25) or not (y <= 4.7e-7):
		tmp = (y / (z / x)) - x
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+25) || !(y <= 4.7e-7))
		tmp = Float64(Float64(y / Float64(z / x)) - 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 <= -4e+25) || ~((y <= 4.7e-7)))
		tmp = (y / (z / x)) - x;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+25], N[Not[LessEqual[y, 4.7e-7]], $MachinePrecision]], N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000036e25 or 4.7e-7 < y

   1. Initial program 90.8%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 92.9%

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

      1. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

   if -4.00000000000000036e25 < y < 4.7e-7

   1. Initial program 92.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+25} \lor \neg \left(y \leq 4.7 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{y}{\frac{z}{x}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 5: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+25} \lor \neg \left(y \leq 1.32 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e+25) (not (<= y 1.32e+95))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+25) || !(y <= 1.32e+95)) {
		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 <= (-4.3d+25)) .or. (.not. (y <= 1.32d+95))) 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 <= -4.3e+25) || !(y <= 1.32e+95)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e+25) or not (y <= 1.32e+95):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e+25) || !(y <= 1.32e+95))
		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 <= -4.3e+25) || ~((y <= 1.32e+95)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e+25], N[Not[LessEqual[y, 1.32e+95]], $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 < -4.29999999999999998e25 or 1.32e95 < y

   1. Initial program 91.4%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. associate-/l* 80.5%

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

      2. div-inv 80.5%

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

      3. clear-num 80.5%

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

   4. Applied egg-rr 80.5%

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

   if -4.29999999999999998e25 < y < 1.32e95

   1. Initial program 91.4%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 96.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+25} \lor \neg \left(y \leq 1.32 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 6: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+27)
   (* y (/ x z))
   (if (<= y 7.5e+92) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+27) {
		tmp = y * (x / z);
	} else if (y <= 7.5e+92) {
		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 <= (-1.05d+27)) then
        tmp = y * (x / z)
    else if (y <= 7.5d+92) 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 <= -1.05e+27) {
		tmp = y * (x / z);
	} else if (y <= 7.5e+92) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+27:
		tmp = y * (x / z)
	elif y <= 7.5e+92:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+27)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 7.5e+92)
		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 <= -1.05e+27)
		tmp = y * (x / z);
	elseif (y <= 7.5e+92)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+27], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+92], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999997e27

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. associate-/l* 85.4%

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

      2. div-inv 85.5%

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

      3. clear-num 85.6%

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

   4. Applied egg-rr 85.6%

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

   if -1.04999999999999997e27 < y < 7.49999999999999946e92

   1. Initial program 91.4%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 96.3%

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

   if 7.49999999999999946e92 < y

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 72.7%

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

      1. associate-/l* 75.0%

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

      2. div-inv 74.9%

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

      3. clear-num 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in y around 0 72.7%

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

      1. associate-/l* 75.0%

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

   7. Simplified 75.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.4%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 8: 64.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -420000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -420000.0) (- x) (if (<= z 1.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -420000.0) {
		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 <= (-420000.0d0)) 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 <= -420000.0) {
		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 <= -420000.0:
		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 <= -420000.0)
		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 <= -420000.0)
		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, -420000.0], (-x), If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e5 or 1 < z

   1. Initial program 81.2%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in z around inf 73.9%

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

      1. neg-mul-1 73.9%

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

   6. Simplified 73.9%

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

   if -4.2e5 < z < 1

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 64.4%

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

   5. Taylor expanded in z around 0 63.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -420000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 9: 38.5% 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 91.4%

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

3. Simplified 96.6%

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

4. Taylor expanded in z around inf 35.2%

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

   1. neg-mul-1 35.2%

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

6. Simplified 35.2%

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

7. Final simplification 35.2%

   \[\leadsto -x \]

Alternative 10: 3.0% accurate, 9.0× 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 x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 91.4%

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

2. Taylor expanded in z around inf 29.3%

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

   1. associate-*r* 29.3%

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

   2. neg-mul-1 29.3%

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

4. Simplified 29.3%

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

   1. add-log-exp 15.2%

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

   2. *-un-lft-identity 15.2%

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

   3. log-prod 15.2%

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

   4. metadata-eval 15.2%

      \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\left(-z\right) \cdot x}{z}}\right) \]

   5. add-log-exp 29.3%

      \[\leadsto 0 + \color{blue}{\frac{\left(-z\right) \cdot x}{z}} \]

   6. associate-/l* 36.2%

      \[\leadsto 0 + \color{blue}{\frac{-z}{\frac{z}{x}}} \]

   7. div-inv 36.6%

      \[\leadsto 0 + \color{blue}{\left(-z\right) \cdot \frac{1}{\frac{z}{x}}} \]

   8. add-sqr-sqrt 21.9%

      \[\leadsto 0 + \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot \frac{1}{\frac{z}{x}} \]

   9. sqrt-unprod 14.9%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot \frac{1}{\frac{z}{x}} \]

   10. sqr-neg 14.9%

       \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \cdot \frac{1}{\frac{z}{x}} \]

   11. sqrt-unprod 8.6%

       \[\leadsto 0 + \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \frac{1}{\frac{z}{x}} \]

   12. add-sqr-sqrt 10.5%

       \[\leadsto 0 + \color{blue}{z} \cdot \frac{1}{\frac{z}{x}} \]

   13. clear-num 10.5%

       \[\leadsto 0 + z \cdot \color{blue}{\frac{x}{z}} \]

6. Applied egg-rr 10.5%

   \[\leadsto \color{blue}{0 + z \cdot \frac{x}{z}} \]
7. Step-by-step derivation

   1. +-lft-identity 10.5%

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

   2. associate-*r/ 4.3%

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

   3. associate-*l/ 3.3%

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

   4. *-inverses 3.3%

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

   5. *-lft-identity 3.3%

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

8. Simplified 3.3%

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

9. Final simplification 3.3%

   \[\leadsto x \]

Developer target: 99.4% 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 2023200 
(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))