Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 85.2% → 97.2%

Time: 6.9s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{+58}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

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 (- y z)) y) -2e+58)
    (/ (- y z) (/ y x_m))
    (* x_m (- 1.0 (/ z y))))))

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 * (y - z)) / y) <= -2e+58) {
		tmp = (y - z) / (y / x_m);
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	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 * (y - z)) / y) <= (-2d+58)) then
        tmp = (y - z) / (y / x_m)
    else
        tmp = x_m * (1.0d0 - (z / y))
    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 * (y - z)) / y) <= -2e+58) {
		tmp = (y - z) / (y / x_m);
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	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 * (y - z)) / y) <= -2e+58:
		tmp = (y - z) / (y / x_m)
	else:
		tmp = x_m * (1.0 - (z / y))
	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 (Float64(Float64(x_m * Float64(y - z)) / y) <= -2e+58)
		tmp = Float64(Float64(y - z) / Float64(y / x_m));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	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 * (y - z)) / y) <= -2e+58)
		tmp = (y - z) / (y / x_m);
	else
		tmp = x_m * (1.0 - (z / y));
	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[N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], -2e+58], N[(N[(y - z), $MachinePrecision] / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.99999999999999989e58

   1. Initial program 74.3%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

      1. *-commutative 95.9%

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

      2. clear-num 95.7%

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

      3. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   if -1.99999999999999989e58 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

      4. div-sub 94.6%

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

      5. *-inverses 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{+58}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{+58}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

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 (- y z)) y) -2e+58)
    (* (- y z) (/ x_m y))
    (* x_m (- 1.0 (/ z y))))))

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 * (y - z)) / y) <= -2e+58) {
		tmp = (y - z) * (x_m / y);
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	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 * (y - z)) / y) <= (-2d+58)) then
        tmp = (y - z) * (x_m / y)
    else
        tmp = x_m * (1.0d0 - (z / y))
    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 * (y - z)) / y) <= -2e+58) {
		tmp = (y - z) * (x_m / y);
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	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 * (y - z)) / y) <= -2e+58:
		tmp = (y - z) * (x_m / y)
	else:
		tmp = x_m * (1.0 - (z / y))
	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 (Float64(Float64(x_m * Float64(y - z)) / y) <= -2e+58)
		tmp = Float64(Float64(y - z) * Float64(x_m / y));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	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 * (y - z)) / y) <= -2e+58)
		tmp = (y - z) * (x_m / y);
	else
		tmp = x_m * (1.0 - (z / y));
	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[N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], -2e+58], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.99999999999999989e58

   1. Initial program 74.3%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   if -1.99999999999999989e58 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

      4. div-sub 94.6%

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

      5. *-inverses 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{+58}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+103}:\\ \;\;\;\;x\_m \cdot \left(-\frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.65e-16) x_m (if (<= y 4.3e+103) (* x_m (- (/ z y))) 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 <= -1.65e-16) {
		tmp = x_m;
	} else if (y <= 4.3e+103) {
		tmp = x_m * -(z / y);
	} 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) :: tmp
    if (y <= (-1.65d-16)) then
        tmp = x_m
    else if (y <= 4.3d+103) then
        tmp = x_m * -(z / y)
    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 tmp;
	if (y <= -1.65e-16) {
		tmp = x_m;
	} else if (y <= 4.3e+103) {
		tmp = x_m * -(z / y);
	} 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):
	tmp = 0
	if y <= -1.65e-16:
		tmp = x_m
	elif y <= 4.3e+103:
		tmp = x_m * -(z / y)
	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)
	tmp = 0.0
	if (y <= -1.65e-16)
		tmp = x_m;
	elseif (y <= 4.3e+103)
		tmp = Float64(x_m * Float64(-Float64(z / y)));
	else
		tmp = 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 <= -1.65e-16)
		tmp = x_m;
	elseif (y <= 4.3e+103)
		tmp = x_m * -(z / y);
	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_] := N[(x$95$s * If[LessEqual[y, -1.65e-16], x$95$m, If[LessEqual[y, 4.3e+103], N[(x$95$m * (-N[(z / y), $MachinePrecision])), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999994e-16 or 4.29999999999999969e103 < y

   1. Initial program 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.8%

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

   if -1.64999999999999994e-16 < y < 4.29999999999999969e103

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*l/ 89.6%

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

      3. *-commutative 89.6%

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

      4. div-sub 89.7%

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

      5. *-inverses 89.7%

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

   3. Simplified 89.7%

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

      1. sub-neg 89.7%

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

      2. distribute-rgt-in 89.6%

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

      3. *-un-lft-identity 89.6%

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

      4. distribute-neg-frac 89.6%

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

   6. Applied egg-rr 89.6%

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

      1. *-un-lft-identity 89.6%

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

      2. *-inverses 89.6%

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

      3. associate-/r/ 79.0%

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

      4. distribute-frac-neg 79.0%

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

      5. distribute-lft-neg-out 79.0%

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

      6. associate-/r/ 89.0%

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

      7. sub-neg 89.0%

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

      8. div-sub 94.2%

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

      9. associate-/r/ 89.6%

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

      10. *-commutative 89.6%

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

      11. div-sub 89.7%

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

      12. *-inverses 89.7%

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

      13. add-sqr-sqrt 41.9%

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

      14. sqrt-unprod 49.0%

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

      15. sqr-neg 49.0%

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

      16. sqrt-unprod 11.0%

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

      17. add-sqr-sqrt 21.8%

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

      18. distribute-rgt-out-- 21.8%

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

      19. *-un-lft-identity 21.8%

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

      20. associate-*l/ 21.9%

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

   8. Applied egg-rr 95.1%

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

   9. Taylor expanded in z around inf 73.4%

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

       1. associate-*r/ 73.4%

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

       2. mul-1-neg 73.4%

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

       3. distribute-rgt-neg-out 73.4%

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

       4. associate-*r/ 67.8%

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

   11. Simplified 67.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \frac{-x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.65e-16) x_m (if (<= y 4e+103) (* z (/ (- x_m) y)) 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 <= -1.65e-16) {
		tmp = x_m;
	} else if (y <= 4e+103) {
		tmp = z * (-x_m / y);
	} 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) :: tmp
    if (y <= (-1.65d-16)) then
        tmp = x_m
    else if (y <= 4d+103) then
        tmp = z * (-x_m / y)
    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 tmp;
	if (y <= -1.65e-16) {
		tmp = x_m;
	} else if (y <= 4e+103) {
		tmp = z * (-x_m / y);
	} 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):
	tmp = 0
	if y <= -1.65e-16:
		tmp = x_m
	elif y <= 4e+103:
		tmp = z * (-x_m / y)
	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)
	tmp = 0.0
	if (y <= -1.65e-16)
		tmp = x_m;
	elseif (y <= 4e+103)
		tmp = Float64(z * Float64(Float64(-x_m) / y));
	else
		tmp = 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 <= -1.65e-16)
		tmp = x_m;
	elseif (y <= 4e+103)
		tmp = z * (-x_m / y);
	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_] := N[(x$95$s * If[LessEqual[y, -1.65e-16], x$95$m, If[LessEqual[y, 4e+103], N[(z * N[((-x$95$m) / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999994e-16 or 4e103 < y

   1. Initial program 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.8%

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

   if -1.64999999999999994e-16 < y < 4e103

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*l/ 89.6%

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

      3. *-commutative 89.6%

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

      4. div-sub 89.7%

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

      5. *-inverses 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*l/ 76.6%

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

      3. distribute-rgt-neg-out 76.6%

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

      4. *-commutative 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{z}{\frac{-y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.6e-16) x_m (if (<= y 5.5e+103) (/ z (/ (- y) 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 <= -1.6e-16) {
		tmp = x_m;
	} else if (y <= 5.5e+103) {
		tmp = z / (-y / x_m);
	} 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) :: tmp
    if (y <= (-1.6d-16)) then
        tmp = x_m
    else if (y <= 5.5d+103) then
        tmp = z / (-y / x_m)
    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 tmp;
	if (y <= -1.6e-16) {
		tmp = x_m;
	} else if (y <= 5.5e+103) {
		tmp = z / (-y / x_m);
	} 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):
	tmp = 0
	if y <= -1.6e-16:
		tmp = x_m
	elif y <= 5.5e+103:
		tmp = z / (-y / x_m)
	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)
	tmp = 0.0
	if (y <= -1.6e-16)
		tmp = x_m;
	elseif (y <= 5.5e+103)
		tmp = Float64(z / Float64(Float64(-y) / x_m));
	else
		tmp = 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 <= -1.6e-16)
		tmp = x_m;
	elseif (y <= 5.5e+103)
		tmp = z / (-y / x_m);
	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_] := N[(x$95$s * If[LessEqual[y, -1.6e-16], x$95$m, If[LessEqual[y, 5.5e+103], N[(z / N[((-y) / x$95$m), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000011e-16 or 5.50000000000000001e103 < y

   1. Initial program 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.8%

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

   if -1.60000000000000011e-16 < y < 5.50000000000000001e103

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*l/ 89.6%

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

      3. *-commutative 89.6%

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

      4. div-sub 89.7%

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

      5. *-inverses 89.7%

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

   3. Simplified 89.7%

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

      1. sub-neg 89.7%

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

      2. distribute-rgt-in 89.6%

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

      3. *-un-lft-identity 89.6%

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

      4. distribute-neg-frac 89.6%

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

   6. Applied egg-rr 89.6%

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

      1. *-un-lft-identity 89.6%

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

      2. *-inverses 89.6%

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

      3. associate-/r/ 79.0%

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

      4. distribute-frac-neg 79.0%

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

      5. distribute-lft-neg-out 79.0%

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

      6. associate-/r/ 89.0%

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

      7. sub-neg 89.0%

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

      8. div-sub 94.2%

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

      9. associate-/r/ 89.6%

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

      10. *-commutative 89.6%

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

      11. div-sub 89.7%

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

      12. *-inverses 89.7%

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

      13. add-sqr-sqrt 41.9%

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

      14. sqrt-unprod 49.0%

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

      15. sqr-neg 49.0%

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

      16. sqrt-unprod 11.0%

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

      17. add-sqr-sqrt 21.8%

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

      18. distribute-rgt-out-- 21.8%

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

      19. *-un-lft-identity 21.8%

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

      20. associate-*l/ 21.9%

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

   8. Applied egg-rr 95.1%

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

   9. Taylor expanded in z around inf 73.4%

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

       1. associate-*r/ 73.4%

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

       2. mul-1-neg 73.4%

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

       3. distribute-rgt-neg-out 73.4%

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

       4. associate-*r/ 67.8%

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

   11. Simplified 67.8%

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

       1. *-commutative 67.8%

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

       2. associate-*l/ 73.4%

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

       3. associate-/l* 76.6%

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

       4. add-sqr-sqrt 40.6%

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

       5. sqrt-unprod 35.1%

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

       6. sqr-neg 35.1%

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

       7. sqrt-unprod 0.8%

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

       8. add-sqr-sqrt 1.5%

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

       9. frac-2neg 1.5%

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

       10. add-sqr-sqrt 0.7%

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

       11. sqrt-unprod 28.7%

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

       12. sqr-neg 28.7%

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

       13. sqrt-unprod 35.9%

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

       14. add-sqr-sqrt 76.6%

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

       15. distribute-neg-frac 76.6%

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

   13. Applied egg-rr 76.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5.5 \cdot 10^{+156}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \]

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 5.5e+156) x_m (* y (/ x_m y)))))

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 <= 5.5e+156) {
		tmp = x_m;
	} else {
		tmp = y * (x_m / y);
	}
	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 <= 5.5d+156) then
        tmp = x_m
    else
        tmp = y * (x_m / y)
    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 <= 5.5e+156) {
		tmp = x_m;
	} else {
		tmp = y * (x_m / y);
	}
	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 <= 5.5e+156:
		tmp = x_m
	else:
		tmp = y * (x_m / y)
	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 <= 5.5e+156)
		tmp = x_m;
	else
		tmp = Float64(y * Float64(x_m / y));
	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 <= 5.5e+156)
		tmp = x_m;
	else
		tmp = y * (x_m / y);
	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, 5.5e+156], x$95$m, N[(y * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 5.5000000000000003e156

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l/ 93.5%

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

      3. *-commutative 93.5%

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

      4. div-sub 93.5%

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

      5. *-inverses 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 48.1%

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

   if 5.5000000000000003e156 < x

   1. Initial program 61.1%

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

   3. Taylor expanded in y around inf 20.4%

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

      1. associate-/l* 55.9%

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

      2. associate-/r/ 64.1%

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

   5. Applied egg-rr 64.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.9% accurate, 1.0× speedup

Math

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

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 (- 1.0 (/ z y)))))

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 * (1.0 - (z / y)));
}

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 * (1.0d0 - (z / y)))
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 * (1.0 - (z / y)));
}

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 * (1.0 - (z / y)))

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 * Float64(1.0 - Float64(z / y))))
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 * (1.0 - (z / y)));
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 * N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.3%

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

   1. *-commutative 81.3%

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

   2. associate-*l/ 94.4%

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

   3. *-commutative 94.4%

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

   4. div-sub 94.4%

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

   5. *-inverses 94.4%

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

3. Simplified 94.4%

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

5. Final simplification 94.4%

   \[\leadsto x \cdot \left(1 - \frac{z}{y}\right) \]
6. Add Preprocessing

Alternative 8: 50.3% accurate, 7.0× speedup

Math

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

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 * 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 81.3%

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

   1. *-commutative 81.3%

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

   2. associate-*l/ 94.4%

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

   3. *-commutative 94.4%

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

   4. div-sub 94.4%

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

   5. *-inverses 94.4%

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

3. Simplified 94.4%

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

5. Taylor expanded in z around 0 49.1%

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

6. Final simplification 49.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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