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

Percentage Accurate: 88.0% → 99.9%

Time: 5.1s

Alternatives: 10

Speedup: 0.8×

• 20.4% 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: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x_m \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot \left(y + 1\right) - x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 8.5e-49)
    (/ (* x_m (+ (- y z) 1.0)) z)
    (- (* (/ x_m z) (+ y 1.0)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8.5e-49) {
		tmp = (x_m * ((y - z) + 1.0)) / z;
	} else {
		tmp = ((x_m / z) * (y + 1.0)) - x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 8.5d-49) then
        tmp = (x_m * ((y - z) + 1.0d0)) / z
    else
        tmp = ((x_m / z) * (y + 1.0d0)) - x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8.5e-49) {
		tmp = (x_m * ((y - z) + 1.0)) / z;
	} else {
		tmp = ((x_m / z) * (y + 1.0)) - x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 8.5e-49:
		tmp = (x_m * ((y - z) + 1.0)) / z
	else:
		tmp = ((x_m / z) * (y + 1.0)) - x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 8.5e-49)
		tmp = Float64(Float64(x_m * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(Float64(x_m / z) * Float64(y + 1.0)) - x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 8.5e-49)
		tmp = (x_m * ((y - z) + 1.0)) / z;
	else
		tmp = ((x_m / z) * (y + 1.0)) - x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 8.5e-49], N[(N[(x$95$m * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x$95$m / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 8.50000000000000069e-49

   1. Initial program 89.7%

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

   if 8.50000000000000069e-49 < x

   1. Initial program 76.6%

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

   2. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. +-commutative 85.2%

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

      3. unsub-neg 85.2%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array} \]

Alternative 2: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := y \cdot \frac{x_m}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+52}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-288}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-228}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;-x_m\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* y (/ x_m z))))
   (*
    x_s
    (if (<= z -1.06e+52)
      (- x_m)
      (if (<= z -1.35e-112)
        t_0
        (if (<= z -3.2e-171)
          (/ x_m z)
          (if (<= z -7.5e-253)
            t_0
            (if (<= z 1.05e-288)
              (/ x_m z)
              (if (<= z 2.5e-228)
                t_0
                (if (<= z 1.0) (/ x_m z) (- x_m)))))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = y * (x_m / z);
	double tmp;
	if (z <= -1.06e+52) {
		tmp = -x_m;
	} else if (z <= -1.35e-112) {
		tmp = t_0;
	} else if (z <= -3.2e-171) {
		tmp = x_m / z;
	} else if (z <= -7.5e-253) {
		tmp = t_0;
	} else if (z <= 1.05e-288) {
		tmp = x_m / z;
	} else if (z <= 2.5e-228) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x_m / z;
	} else {
		tmp = -x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x_m / z)
    if (z <= (-1.06d+52)) then
        tmp = -x_m
    else if (z <= (-1.35d-112)) then
        tmp = t_0
    else if (z <= (-3.2d-171)) then
        tmp = x_m / z
    else if (z <= (-7.5d-253)) then
        tmp = t_0
    else if (z <= 1.05d-288) then
        tmp = x_m / z
    else if (z <= 2.5d-228) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x_m / z
    else
        tmp = -x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = y * (x_m / z);
	double tmp;
	if (z <= -1.06e+52) {
		tmp = -x_m;
	} else if (z <= -1.35e-112) {
		tmp = t_0;
	} else if (z <= -3.2e-171) {
		tmp = x_m / z;
	} else if (z <= -7.5e-253) {
		tmp = t_0;
	} else if (z <= 1.05e-288) {
		tmp = x_m / z;
	} else if (z <= 2.5e-228) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x_m / z;
	} else {
		tmp = -x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = y * (x_m / z)
	tmp = 0
	if z <= -1.06e+52:
		tmp = -x_m
	elif z <= -1.35e-112:
		tmp = t_0
	elif z <= -3.2e-171:
		tmp = x_m / z
	elif z <= -7.5e-253:
		tmp = t_0
	elif z <= 1.05e-288:
		tmp = x_m / z
	elif z <= 2.5e-228:
		tmp = t_0
	elif z <= 1.0:
		tmp = x_m / z
	else:
		tmp = -x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(y * Float64(x_m / z))
	tmp = 0.0
	if (z <= -1.06e+52)
		tmp = Float64(-x_m);
	elseif (z <= -1.35e-112)
		tmp = t_0;
	elseif (z <= -3.2e-171)
		tmp = Float64(x_m / z);
	elseif (z <= -7.5e-253)
		tmp = t_0;
	elseif (z <= 1.05e-288)
		tmp = Float64(x_m / z);
	elseif (z <= 2.5e-228)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x_m / z);
	else
		tmp = Float64(-x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = y * (x_m / z);
	tmp = 0.0;
	if (z <= -1.06e+52)
		tmp = -x_m;
	elseif (z <= -1.35e-112)
		tmp = t_0;
	elseif (z <= -3.2e-171)
		tmp = x_m / z;
	elseif (z <= -7.5e-253)
		tmp = t_0;
	elseif (z <= 1.05e-288)
		tmp = x_m / z;
	elseif (z <= 2.5e-228)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x_m / z;
	else
		tmp = -x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.06e+52], (-x$95$m), If[LessEqual[z, -1.35e-112], t$95$0, If[LessEqual[z, -3.2e-171], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, -7.5e-253], t$95$0, If[LessEqual[z, 1.05e-288], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 2.5e-228], t$95$0, If[LessEqual[z, 1.0], N[(x$95$m / z), $MachinePrecision], (-x$95$m)]]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0599999999999999e52 or 1 < z

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. mul-1-neg 79.4%

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

   4. Simplified 79.4%

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

   if -1.0599999999999999e52 < z < -1.35e-112 or -3.2000000000000001e-171 < z < -7.49999999999999987e-253 or 1.04999999999999998e-288 < z < 2.49999999999999986e-228

   1. Initial program 98.2%

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

   2. Taylor expanded in y around inf 73.7%

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

      1. associate-/l* 62.0%

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

      2. associate-/r/ 78.8%

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

   4. Simplified 78.8%

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

   if -1.35e-112 < z < -3.2000000000000001e-171 or -7.49999999999999987e-253 < z < 1.04999999999999998e-288 or 2.49999999999999986e-228 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.4%

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

   3. Taylor expanded in y around 0 69.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+52}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-288}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-11} \lor \neg \left(z \leq 5.2 \cdot 10^{-39}\right):\\ \;\;\;\;x_m \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.2e-11) (not (<= z 5.2e-39)))
    (* x_m (/ (+ y (- 1.0 z)) z))
    (/ (* x_m (+ y 1.0)) z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -2.2e-11) || !(z <= 5.2e-39)) {
		tmp = x_m * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x_m * (y + 1.0)) / z;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.2d-11)) .or. (.not. (z <= 5.2d-39))) then
        tmp = x_m * ((y + (1.0d0 - z)) / z)
    else
        tmp = (x_m * (y + 1.0d0)) / z
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -2.2e-11) || !(z <= 5.2e-39)) {
		tmp = x_m * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x_m * (y + 1.0)) / z;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -2.2e-11) or not (z <= 5.2e-39):
		tmp = x_m * ((y + (1.0 - z)) / z)
	else:
		tmp = (x_m * (y + 1.0)) / z
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -2.2e-11) || !(z <= 5.2e-39))
		tmp = Float64(x_m * Float64(Float64(y + Float64(1.0 - z)) / z));
	else
		tmp = Float64(Float64(x_m * Float64(y + 1.0)) / z);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -2.2e-11) || ~((z <= 5.2e-39)))
		tmp = x_m * ((y + (1.0 - z)) / z);
	else
		tmp = (x_m * (y + 1.0)) / z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -2.2e-11], N[Not[LessEqual[z, 5.2e-39]], $MachinePrecision]], N[(x$95$m * N[(N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000002e-11 or 5.2e-39 < z

   1. Initial program 75.1%

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

   2. Taylor expanded in x around 0 75.1%

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

      1. associate--l+ 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-*r/ 99.9%

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

      4. associate-+l- 99.9%

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

   4. Simplified 99.9%

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

   if -2.2000000000000002e-11 < z < 5.2e-39

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-11} \lor \neg \left(z \leq 5.2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]

Alternative 4: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1750000000 \lor \neg \left(y \leq 2.15 \cdot 10^{-13}\right):\\ \;\;\;\;x_m \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -1750000000.0) (not (<= y 2.15e-13)))
    (* x_m (+ (/ y z) -1.0))
    (- (/ x_m z) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1750000000.0) || !(y <= 2.15e-13)) {
		tmp = x_m * ((y / z) + -1.0);
	} else {
		tmp = (x_m / z) - x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1750000000.0d0)) .or. (.not. (y <= 2.15d-13))) then
        tmp = x_m * ((y / z) + (-1.0d0))
    else
        tmp = (x_m / z) - x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1750000000.0) || !(y <= 2.15e-13)) {
		tmp = x_m * ((y / z) + -1.0);
	} else {
		tmp = (x_m / z) - x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -1750000000.0) or not (y <= 2.15e-13):
		tmp = x_m * ((y / z) + -1.0)
	else:
		tmp = (x_m / z) - x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -1750000000.0) || !(y <= 2.15e-13))
		tmp = Float64(x_m * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x_m / z) - x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -1750000000.0) || ~((y <= 2.15e-13)))
		tmp = x_m * ((y / z) + -1.0);
	else
		tmp = (x_m / z) - x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -1750000000.0], N[Not[LessEqual[y, 2.15e-13]], $MachinePrecision]], N[(x$95$m * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e9 or 2.1499999999999999e-13 < y

   1. Initial program 86.0%

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

   2. Taylor expanded in z around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. +-commutative 88.0%

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

      3. unsub-neg 88.0%

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

      4. associate-/l* 91.8%

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

      5. associate-/r/ 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in y around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-/l* 94.2%

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

   7. Simplified 94.2%

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

   8. Taylor expanded in x around 0 91.0%

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

   if -1.75e9 < y < 2.1499999999999999e-13

   1. Initial program 86.9%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1750000000 \lor \neg \left(y \leq 2.15 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x_m \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.05) (not (<= z 1.0)))
    (* x_m (+ (/ y z) -1.0))
    (/ (* x_m (+ y 1.0)) z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = x_m * ((y / z) + -1.0);
	} else {
		tmp = (x_m * (y + 1.0)) / z;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.05d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x_m * ((y / z) + (-1.0d0))
    else
        tmp = (x_m * (y + 1.0d0)) / z
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = x_m * ((y / z) + -1.0);
	} else {
		tmp = (x_m * (y + 1.0)) / z;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -1.05) or not (z <= 1.0):
		tmp = x_m * ((y / z) + -1.0)
	else:
		tmp = (x_m * (y + 1.0)) / z
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 1.0))
		tmp = Float64(x_m * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x_m * Float64(y + 1.0)) / z);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -1.05) || ~((z <= 1.0)))
		tmp = x_m * ((y / z) + -1.0);
	else
		tmp = (x_m * (y + 1.0)) / z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x$95$m * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 1 < z

   1. Initial program 72.9%

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

   2. Taylor expanded in z around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. +-commutative 88.1%

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

      3. unsub-neg 88.1%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in x around 0 99.4%

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

   if -1.05000000000000004 < 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 98.4%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]

Alternative 6: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1750000000:\\ \;\;\;\;x_m \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-13}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x_m}} - x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -1750000000.0)
    (* x_m (+ (/ y z) -1.0))
    (if (<= y 2.15e-13) (- (/ x_m z) x_m) (- (/ y (/ z x_m)) x_m)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1750000000.0) {
		tmp = x_m * ((y / z) + -1.0);
	} else if (y <= 2.15e-13) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = (y / (z / x_m)) - x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1750000000.0d0)) then
        tmp = x_m * ((y / z) + (-1.0d0))
    else if (y <= 2.15d-13) then
        tmp = (x_m / z) - x_m
    else
        tmp = (y / (z / x_m)) - x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1750000000.0) {
		tmp = x_m * ((y / z) + -1.0);
	} else if (y <= 2.15e-13) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = (y / (z / x_m)) - x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -1750000000.0:
		tmp = x_m * ((y / z) + -1.0)
	elif y <= 2.15e-13:
		tmp = (x_m / z) - x_m
	else:
		tmp = (y / (z / x_m)) - x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -1750000000.0)
		tmp = Float64(x_m * Float64(Float64(y / z) + -1.0));
	elseif (y <= 2.15e-13)
		tmp = Float64(Float64(x_m / z) - x_m);
	else
		tmp = Float64(Float64(y / Float64(z / x_m)) - x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -1750000000.0)
		tmp = x_m * ((y / z) + -1.0);
	elseif (y <= 2.15e-13)
		tmp = (x_m / z) - x_m;
	else
		tmp = (y / (z / x_m)) - x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -1750000000.0], N[(x$95$m * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-13], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(N[(y / N[(z / x$95$m), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.75e9

   1. Initial program 83.1%

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

   2. Taylor expanded in z around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. +-commutative 84.2%

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

      3. unsub-neg 84.2%

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

      4. associate-/l* 93.2%

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

      5. associate-/r/ 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in y around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-/l* 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in x around 0 92.8%

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

   if -1.75e9 < y < 2.1499999999999999e-13

   1. Initial program 86.9%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

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

   if 2.1499999999999999e-13 < y

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. mul-1-neg 92.9%

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

      2. +-commutative 92.9%

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

      3. unsub-neg 92.9%

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

      4. associate-/l* 90.0%

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

      5. associate-/r/ 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in y around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/l* 97.2%

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

   7. Simplified 97.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1750000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - x\\ \end{array} \]

Alternative 7: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+235}:\\ \;\;\;\;x_m \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot \left(y + 1\right) - x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -1.3e+235)
    (* x_m (+ (/ y z) -1.0))
    (- (* (/ x_m z) (+ y 1.0)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.3e+235) {
		tmp = x_m * ((y / z) + -1.0);
	} else {
		tmp = ((x_m / z) * (y + 1.0)) - x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.3d+235)) then
        tmp = x_m * ((y / z) + (-1.0d0))
    else
        tmp = ((x_m / z) * (y + 1.0d0)) - x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.3e+235) {
		tmp = x_m * ((y / z) + -1.0);
	} else {
		tmp = ((x_m / z) * (y + 1.0)) - x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -1.3e+235:
		tmp = x_m * ((y / z) + -1.0)
	else:
		tmp = ((x_m / z) * (y + 1.0)) - x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -1.3e+235)
		tmp = Float64(x_m * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(Float64(x_m / z) * Float64(y + 1.0)) - x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -1.3e+235)
		tmp = x_m * ((y / z) + -1.0);
	else
		tmp = ((x_m / z) * (y + 1.0)) - x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -1.3e+235], N[(x$95$m * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x$95$m / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e235

   1. Initial program 75.7%

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

   2. Taylor expanded in z around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. +-commutative 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/l* 95.6%

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

      5. associate-/r/ 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in y around inf 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x around 0 95.7%

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

   if -1.2999999999999999e235 < y

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 95.9%

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

      1. mul-1-neg 95.9%

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

      2. +-commutative 95.9%

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

      3. unsub-neg 95.9%

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

      4. associate-/l* 96.0%

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

      5. associate-/r/ 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+235}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array} \]

Alternative 8: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+37} \lor \neg \left(y \leq 2.05 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -5.5e+37) (not (<= y 2.05e+77)))
    (* y (/ x_m z))
    (- (/ x_m z) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -5.5e+37) || !(y <= 2.05e+77)) {
		tmp = y * (x_m / z);
	} else {
		tmp = (x_m / z) - x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5.5d+37)) .or. (.not. (y <= 2.05d+77))) then
        tmp = y * (x_m / z)
    else
        tmp = (x_m / z) - x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -5.5e+37) || !(y <= 2.05e+77)) {
		tmp = y * (x_m / z);
	} else {
		tmp = (x_m / z) - x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -5.5e+37) or not (y <= 2.05e+77):
		tmp = y * (x_m / z)
	else:
		tmp = (x_m / z) - x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -5.5e+37) || !(y <= 2.05e+77))
		tmp = Float64(y * Float64(x_m / z));
	else
		tmp = Float64(Float64(x_m / z) - x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -5.5e+37) || ~((y <= 2.05e+77)))
		tmp = y * (x_m / z);
	else
		tmp = (x_m / z) - x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -5.5e+37], N[Not[LessEqual[y, 2.05e+77]], $MachinePrecision]], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000016e37 or 2.05e77 < y

   1. Initial program 86.2%

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

   2. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 66.2%

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

      2. associate-/r/ 71.9%

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

   4. Simplified 71.9%

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

   if -5.50000000000000016e37 < y < 2.05e77

   1. Initial program 86.6%

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

   2. Taylor expanded in z around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. +-commutative 98.7%

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

      3. unsub-neg 98.7%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+37} \lor \neg \left(y \leq 2.05 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 9: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= z -1.0) (not (<= z 1.0))) (- x_m) (/ x_m z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = -x_m;
	} else {
		tmp = x_m / z;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = -x_m
    else
        tmp = x_m / z
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = -x_m;
	} else {
		tmp = x_m / z;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = -x_m
	else:
		tmp = x_m / z
	return x_s * tmp

Julia

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

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], (-x$95$m), N[(x$95$m / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 75.7%

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

      1. mul-1-neg 75.7%

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

   4. Simplified 75.7%

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

   if -1 < 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 98.4%

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

   3. Taylor expanded in y around 0 55.4%

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

4. Final simplification 65.6%

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

Alternative 10: 39.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(-x_m\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (- x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * -x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * -x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * -x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * -x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(-x_m))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * -x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * (-x$95$m)), $MachinePrecision]

Derivation

1. Initial program 86.4%

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

2. Taylor expanded in z around inf 39.3%

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

   1. mul-1-neg 39.3%

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

4. Simplified 39.3%

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

5. Final simplification 39.3%

   \[\leadsto -x \]

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 2023332 
(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))