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

Percentage Accurate: 84.7% → 97.0%

Time: 7.5s

Alternatives: 7

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: 84.7% 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: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x\_m \cdot \left(y - z\right)}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-189}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\_m - \frac{x\_m}{\frac{y}{z}}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* x_m (- y z)) y)))
   (* x_s (if (<= t_0 -5e-189) t_0 (- x_m (/ x_m (/ y 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 t_0 = (x_m * (y - z)) / y;
	double tmp;
	if (t_0 <= -5e-189) {
		tmp = t_0;
	} else {
		tmp = x_m - (x_m / (y / 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) :: t_0
    real(8) :: tmp
    t_0 = (x_m * (y - z)) / y
    if (t_0 <= (-5d-189)) then
        tmp = t_0
    else
        tmp = x_m - (x_m / (y / 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 t_0 = (x_m * (y - z)) / y;
	double tmp;
	if (t_0 <= -5e-189) {
		tmp = t_0;
	} else {
		tmp = x_m - (x_m / (y / 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):
	t_0 = (x_m * (y - z)) / y
	tmp = 0
	if t_0 <= -5e-189:
		tmp = t_0
	else:
		tmp = x_m - (x_m / (y / z))
	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(Float64(x_m * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= -5e-189)
		tmp = t_0;
	else
		tmp = Float64(x_m - Float64(x_m / Float64(y / 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)
	t_0 = (x_m * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= -5e-189)
		tmp = t_0;
	else
		tmp = x_m - (x_m / (y / 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_] := Block[{t$95$0 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -5e-189], t$95$0, N[(x$95$m - N[(x$95$m / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -4.9999999999999997e-189

   1. Initial program 80.0%

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

   if -4.9999999999999997e-189 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 79.8%

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

      1. remove-double-neg 79.8%

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

      2. distribute-frac-neg2 79.8%

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

      3. distribute-frac-neg 79.8%

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

      4. distribute-rgt-neg-in 79.8%

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

      5. associate-/l* 94.5%

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

      6. distribute-frac-neg 94.5%

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

      7. distribute-frac-neg2 94.5%

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

      8. remove-double-neg 94.5%

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

      9. div-sub 94.5%

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

      10. *-inverses 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 92.4%

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

      1. associate-*r/ 92.4%

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

      2. mul-1-neg 92.4%

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

      3. distribute-rgt-neg-out 92.4%

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

   7. Simplified 92.4%

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

      1. associate-*l/ 95.8%

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

      2. add-sqr-sqrt 38.1%

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

      3. sqrt-unprod 61.5%

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

      4. sqr-neg 61.5%

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

      5. sqrt-unprod 28.8%

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

      6. add-sqr-sqrt 49.5%

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

      7. *-commutative 49.5%

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

      8. cancel-sign-sub 49.5%

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

      9. associate-*r/ 48.8%

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

      10. *-commutative 48.8%

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

      11. associate-/l* 49.5%

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

      12. add-sqr-sqrt 20.7%

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

      13. sqrt-unprod 70.5%

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

      14. sqr-neg 70.5%

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

      15. sqrt-unprod 58.3%

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

      16. add-sqr-sqrt 94.5%

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

   9. Applied egg-rr 94.5%

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

   10. Taylor expanded in x around 0 92.4%

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

       1. associate-*l/ 95.8%

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

       2. associate-/r/ 95.1%

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

   12. Simplified 95.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -5 \cdot 10^{-189}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 70.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-110} \lor \neg \left(y \leq 8 \cdot 10^{-80}\right) \land y \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;x\_m \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -6.4e+19)
    x_m
    (if (or (<= y 2e-110) (and (not (<= y 8e-80)) (<= y 9.5e+36)))
      (* 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 <= -6.4e+19) {
		tmp = x_m;
	} else if ((y <= 2e-110) || (!(y <= 8e-80) && (y <= 9.5e+36))) {
		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 <= (-6.4d+19)) then
        tmp = x_m
    else if ((y <= 2d-110) .or. (.not. (y <= 8d-80)) .and. (y <= 9.5d+36)) 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 <= -6.4e+19) {
		tmp = x_m;
	} else if ((y <= 2e-110) || (!(y <= 8e-80) && (y <= 9.5e+36))) {
		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 <= -6.4e+19:
		tmp = x_m
	elif (y <= 2e-110) or (not (y <= 8e-80) and (y <= 9.5e+36)):
		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 <= -6.4e+19)
		tmp = x_m;
	elseif ((y <= 2e-110) || (!(y <= 8e-80) && (y <= 9.5e+36)))
		tmp = Float64(x_m * Float64(z / Float64(-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 <= -6.4e+19)
		tmp = x_m;
	elseif ((y <= 2e-110) || (~((y <= 8e-80)) && (y <= 9.5e+36)))
		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, -6.4e+19], x$95$m, If[Or[LessEqual[y, 2e-110], And[N[Not[LessEqual[y, 8e-80]], $MachinePrecision], LessEqual[y, 9.5e+36]]], N[(x$95$m * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e19 or 2.0000000000000001e-110 < y < 7.99999999999999969e-80 or 9.49999999999999974e36 < y

   1. Initial program 64.4%

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

      1. remove-double-neg 64.4%

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

      2. distribute-frac-neg2 64.4%

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

      3. distribute-frac-neg 64.4%

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

      4. distribute-rgt-neg-in 64.4%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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 84.5%

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

   if -6.4e19 < y < 2.0000000000000001e-110 or 7.99999999999999969e-80 < y < 9.49999999999999974e36

   1. Initial program 93.1%

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

      1. associate-/l* 90.9%

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

      2. add-sqr-sqrt 43.2%

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

      3. associate-*l* 43.2%

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

   4. Applied egg-rr 43.2%

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

   5. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-frac-neg2 76.6%

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

      3. associate-/l* 71.9%

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

   7. Simplified 71.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-110} \lor \neg \left(y \leq 8 \cdot 10^{-80}\right) \land y \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-110} \lor \neg \left(y \leq 1.3 \cdot 10^{-79}\right) \land y \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{x\_m}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -3.5e+14)
    x_m
    (if (or (<= y 9.2e-110) (and (not (<= y 1.3e-79)) (<= y 9.5e+36)))
      (* 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 <= -3.5e+14) {
		tmp = x_m;
	} else if ((y <= 9.2e-110) || (!(y <= 1.3e-79) && (y <= 9.5e+36))) {
		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 <= (-3.5d+14)) then
        tmp = x_m
    else if ((y <= 9.2d-110) .or. (.not. (y <= 1.3d-79)) .and. (y <= 9.5d+36)) 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 <= -3.5e+14) {
		tmp = x_m;
	} else if ((y <= 9.2e-110) || (!(y <= 1.3e-79) && (y <= 9.5e+36))) {
		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 <= -3.5e+14:
		tmp = x_m
	elif (y <= 9.2e-110) or (not (y <= 1.3e-79) and (y <= 9.5e+36)):
		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 <= -3.5e+14)
		tmp = x_m;
	elseif ((y <= 9.2e-110) || (!(y <= 1.3e-79) && (y <= 9.5e+36)))
		tmp = Float64(z * Float64(x_m / Float64(-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 <= -3.5e+14)
		tmp = x_m;
	elseif ((y <= 9.2e-110) || (~((y <= 1.3e-79)) && (y <= 9.5e+36)))
		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, -3.5e+14], x$95$m, If[Or[LessEqual[y, 9.2e-110], And[N[Not[LessEqual[y, 1.3e-79]], $MachinePrecision], LessEqual[y, 9.5e+36]]], N[(z * N[(x$95$m / (-y)), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e14 or 9.2000000000000006e-110 < y < 1.29999999999999997e-79 or 9.49999999999999974e36 < y

   1. Initial program 64.4%

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

      1. remove-double-neg 64.4%

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

      2. distribute-frac-neg2 64.4%

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

      3. distribute-frac-neg 64.4%

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

      4. distribute-rgt-neg-in 64.4%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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 84.5%

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

   if -3.5e14 < y < 9.2000000000000006e-110 or 1.29999999999999997e-79 < y < 9.49999999999999974e36

   1. Initial program 93.1%

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

      1. remove-double-neg 93.1%

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

      2. distribute-frac-neg2 93.1%

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

      3. distribute-frac-neg 93.1%

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

      4. distribute-rgt-neg-in 93.1%

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

      5. associate-/l* 90.9%

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

      6. distribute-frac-neg 90.9%

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

      7. distribute-frac-neg2 90.9%

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

      8. remove-double-neg 90.9%

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

      9. div-sub 90.9%

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

      10. *-inverses 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-/l* 75.9%

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

      4. distribute-lft-neg-in 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-110} \lor \neg \left(y \leq 1.3 \cdot 10^{-79}\right) \land y \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-109}:\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-79}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x\_m}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.55e+19)
    x_m
    (if (<= y 1.02e-109)
      (/ (* x_m (- z)) y)
      (if (<= y 1.5e-79) x_m (if (<= y 1.55e+38) (* 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 <= -1.55e+19) {
		tmp = x_m;
	} else if (y <= 1.02e-109) {
		tmp = (x_m * -z) / y;
	} else if (y <= 1.5e-79) {
		tmp = x_m;
	} else if (y <= 1.55e+38) {
		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 <= (-1.55d+19)) then
        tmp = x_m
    else if (y <= 1.02d-109) then
        tmp = (x_m * -z) / y
    else if (y <= 1.5d-79) then
        tmp = x_m
    else if (y <= 1.55d+38) 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 <= -1.55e+19) {
		tmp = x_m;
	} else if (y <= 1.02e-109) {
		tmp = (x_m * -z) / y;
	} else if (y <= 1.5e-79) {
		tmp = x_m;
	} else if (y <= 1.55e+38) {
		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 <= -1.55e+19:
		tmp = x_m
	elif y <= 1.02e-109:
		tmp = (x_m * -z) / y
	elif y <= 1.5e-79:
		tmp = x_m
	elif y <= 1.55e+38:
		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 <= -1.55e+19)
		tmp = x_m;
	elseif (y <= 1.02e-109)
		tmp = Float64(Float64(x_m * Float64(-z)) / y);
	elseif (y <= 1.5e-79)
		tmp = x_m;
	elseif (y <= 1.55e+38)
		tmp = Float64(z * Float64(x_m / Float64(-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 <= -1.55e+19)
		tmp = x_m;
	elseif (y <= 1.02e-109)
		tmp = (x_m * -z) / y;
	elseif (y <= 1.5e-79)
		tmp = x_m;
	elseif (y <= 1.55e+38)
		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, -1.55e+19], x$95$m, If[LessEqual[y, 1.02e-109], N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.5e-79], x$95$m, If[LessEqual[y, 1.55e+38], N[(z * N[(x$95$m / (-y)), $MachinePrecision]), $MachinePrecision], x$95$m]]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e19 or 1.02e-109 < y < 1.5e-79 or 1.55000000000000009e38 < y

   1. Initial program 64.4%

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

      1. remove-double-neg 64.4%

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

      2. distribute-frac-neg2 64.4%

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

      3. distribute-frac-neg 64.4%

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

      4. distribute-rgt-neg-in 64.4%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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 84.5%

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

   if -1.55e19 < y < 1.02e-109

   1. Initial program 91.8%

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

      1. remove-double-neg 91.8%

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

      2. distribute-frac-neg2 91.8%

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

      3. distribute-frac-neg 91.8%

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

      4. distribute-rgt-neg-in 91.8%

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

      5. associate-/l* 89.7%

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

      6. distribute-frac-neg 89.7%

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

      7. distribute-frac-neg2 89.7%

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

      8. remove-double-neg 89.7%

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

      9. div-sub 89.7%

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

      10. *-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 79.6%

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

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

      3. distribute-rgt-neg-out 79.6%

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

   7. Simplified 79.6%

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

   if 1.5e-79 < y < 1.55000000000000009e38

   1. Initial program 98.4%

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

      1. remove-double-neg 98.4%

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

      2. distribute-frac-neg2 98.4%

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

      3. distribute-frac-neg 98.4%

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

      4. distribute-rgt-neg-in 98.4%

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

      5. associate-/l* 96.0%

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

      6. distribute-frac-neg 96.0%

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

      7. distribute-frac-neg2 96.0%

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

      8. remove-double-neg 96.0%

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

      9. div-sub 96.0%

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

      10. *-inverses 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. associate-/l* 64.2%

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

      4. distribute-lft-neg-in 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-109}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 79.9%

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

   1. remove-double-neg 79.9%

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

   2. distribute-frac-neg2 79.9%

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

   3. distribute-frac-neg 79.9%

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

   4. distribute-rgt-neg-in 79.9%

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

   5. associate-/l* 95.1%

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

   6. distribute-frac-neg 95.1%

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

   7. distribute-frac-neg2 95.1%

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

   8. remove-double-neg 95.1%

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

   9. div-sub 95.1%

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

   10. *-inverses 95.1%

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

3. Simplified 95.1%

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

5. Final simplification 95.1%

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

Alternative 6: 96.1% accurate, 1.0× speedup

Math

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

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 (/ x_m (/ y z)))))

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 - (x_m / (y / z)));
}

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 - (x_m / (y / z)))
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 - (x_m / (y / z)));
}

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 - (x_m / (y / z)))

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

Derivation

1. Initial program 79.9%

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

   1. remove-double-neg 79.9%

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

   2. distribute-frac-neg2 79.9%

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

   3. distribute-frac-neg 79.9%

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

   4. distribute-rgt-neg-in 79.9%

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

   5. associate-/l* 95.1%

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

   6. distribute-frac-neg 95.1%

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

   7. distribute-frac-neg2 95.1%

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

   8. remove-double-neg 95.1%

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

   9. div-sub 95.1%

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

   10. *-inverses 95.1%

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

3. Simplified 95.1%

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

5. Taylor expanded in z around 0 92.5%

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

   1. associate-*r/ 92.5%

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

   2. mul-1-neg 92.5%

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

   3. distribute-rgt-neg-out 92.5%

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

7. Simplified 92.5%

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

   1. associate-*l/ 95.1%

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

   2. add-sqr-sqrt 42.2%

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

   3. sqrt-unprod 60.8%

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

   4. sqr-neg 60.8%

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

   5. sqrt-unprod 25.6%

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

   6. add-sqr-sqrt 47.1%

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

   7. *-commutative 47.1%

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

   8. cancel-sign-sub 47.1%

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

   9. associate-*r/ 45.8%

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

   10. *-commutative 45.8%

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

   11. associate-/l* 48.0%

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

   12. add-sqr-sqrt 22.1%

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

   13. sqrt-unprod 68.5%

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

   14. sqr-neg 68.5%

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

   15. sqrt-unprod 52.4%

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

   16. add-sqr-sqrt 95.1%

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

9. Applied egg-rr 95.1%

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

10. Taylor expanded in x around 0 92.5%

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

    1. associate-*l/ 95.1%

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

    2. associate-/r/ 95.7%

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

12. Simplified 95.7%

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

13. Final simplification 95.7%

    \[\leadsto x - \frac{x}{\frac{y}{z}} \]
14. Add Preprocessing

Alternative 7: 50.7% 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 79.9%

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

   1. remove-double-neg 79.9%

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

   2. distribute-frac-neg2 79.9%

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

   3. distribute-frac-neg 79.9%

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

   4. distribute-rgt-neg-in 79.9%

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

   5. associate-/l* 95.1%

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

   6. distribute-frac-neg 95.1%

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

   7. distribute-frac-neg2 95.1%

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

   8. remove-double-neg 95.1%

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

   9. div-sub 95.1%

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

   10. *-inverses 95.1%

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

3. Simplified 95.1%

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

5. Taylor expanded in z around 0 49.6%

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

6. Final simplification 49.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.0% 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 2024041 
(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))