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

Percentage Accurate: 84.6% → 96.9%

Time: 5.8s

Alternatives: 6

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: 84.6% 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: 96.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -5 \cdot 10^{+49}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{y - z}{y}\\ \end{array} \end{array} \]

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 (- y z)) y) -5e+49)
    (* (- y z) (/ x_m y))
    (* x_m (/ (- y 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) <= -5e+49) {
		tmp = (y - z) * (x_m / y);
	} else {
		tmp = x_m * ((y - 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) <= (-5d+49)) then
        tmp = (y - z) * (x_m / y)
    else
        tmp = x_m * ((y - 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) <= -5e+49) {
		tmp = (y - z) * (x_m / y);
	} else {
		tmp = x_m * ((y - 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) <= -5e+49:
		tmp = (y - z) * (x_m / y)
	else:
		tmp = x_m * ((y - 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) <= -5e+49)
		tmp = Float64(Float64(y - z) * Float64(x_m / y));
	else
		tmp = Float64(x_m * Float64(Float64(y - 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) <= -5e+49)
		tmp = (y - z) * (x_m / y);
	else
		tmp = x_m * ((y - 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], -5e+49], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -5.0000000000000004e49

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-/l* 91.4%

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

   4. Applied egg-rr 91.4%

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

   if -5.0000000000000004e49 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 85.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -5 \cdot 10^{+49}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2600000000000 \lor \neg \left(z \leq 1.15 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{z}{\frac{y}{-x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2600000000000.0) (not (<= z 1.15e+43)))
    (/ 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 ((z <= -2600000000000.0) || !(z <= 1.15e+43)) {
		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 ((z <= (-2600000000000.0d0)) .or. (.not. (z <= 1.15d+43))) 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 ((z <= -2600000000000.0) || !(z <= 1.15e+43)) {
		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 (z <= -2600000000000.0) or not (z <= 1.15e+43):
		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 ((z <= -2600000000000.0) || !(z <= 1.15e+43))
		tmp = Float64(z / Float64(y / Float64(-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 ((z <= -2600000000000.0) || ~((z <= 1.15e+43)))
		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[Or[LessEqual[z, -2600000000000.0], N[Not[LessEqual[z, 1.15e+43]], $MachinePrecision]], N[(z / N[(y / (-x$95$m)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e12 or 1.1500000000000001e43 < z

   1. Initial program 85.2%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 85.2%

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

      2. clear-num 85.1%

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

      3. associate-/r* 89.9%

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

   6. Applied egg-rr 89.9%

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

   7. Taylor expanded in y around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-neg-frac2 71.6%

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

      3. neg-mul-1 71.6%

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

      4. *-commutative 71.6%

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

      5. *-commutative 71.6%

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

      6. associate-/l* 75.1%

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

      7. *-commutative 75.1%

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

      8. neg-mul-1 75.1%

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

   9. Simplified 75.1%

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

       1. associate-*r/ 71.6%

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

       2. distribute-frac-neg2 71.6%

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

       3. add-sqr-sqrt 39.5%

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

       4. sqrt-unprod 35.3%

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

       5. sqr-neg 35.3%

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

       6. sqrt-unprod 0.8%

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

       7. add-sqr-sqrt 1.6%

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

       8. associate-*r/ 1.8%

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

       9. clear-num 1.8%

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

       10. un-div-inv 1.8%

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

       11. add-sqr-sqrt 0.8%

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

       12. sqrt-unprod 35.5%

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

       13. sqr-neg 35.5%

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

       14. sqrt-unprod 41.1%

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

       15. add-sqr-sqrt 75.0%

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

   11. Applied egg-rr 75.0%

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

   if -2.6e12 < z < 1.1500000000000001e43

   1. Initial program 79.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2600000000000 \lor \neg \left(z \leq 1.15 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8000000000000 \lor \neg \left(z \leq 1.6 \cdot 10^{+43}\right):\\ \;\;\;\;z \cdot \frac{x\_m}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8000000000000.0) (not (<= z 1.6e+43)))
    (* 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 ((z <= -8000000000000.0) || !(z <= 1.6e+43)) {
		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 ((z <= (-8000000000000.0d0)) .or. (.not. (z <= 1.6d+43))) 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 ((z <= -8000000000000.0) || !(z <= 1.6e+43)) {
		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 (z <= -8000000000000.0) or not (z <= 1.6e+43):
		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 ((z <= -8000000000000.0) || !(z <= 1.6e+43))
		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 ((z <= -8000000000000.0) || ~((z <= 1.6e+43)))
		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[Or[LessEqual[z, -8000000000000.0], N[Not[LessEqual[z, 1.6e+43]], $MachinePrecision]], N[(z * N[(x$95$m / (-y)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8e12 or 1.60000000000000007e43 < z

   1. Initial program 85.2%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 85.2%

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

      2. clear-num 85.1%

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

      3. associate-/r* 89.9%

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

   6. Applied egg-rr 89.9%

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

   7. Taylor expanded in y around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-neg-frac2 71.6%

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

      3. neg-mul-1 71.6%

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

      4. *-commutative 71.6%

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

      5. *-commutative 71.6%

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

      6. associate-/l* 75.1%

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

      7. *-commutative 75.1%

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

      8. neg-mul-1 75.1%

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

   9. Simplified 75.1%

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

   if -8e12 < z < 1.60000000000000007e43

   1. Initial program 79.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8000000000000 \lor \neg \left(z \leq 1.6 \cdot 10^{+43}\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -470000000000:\\ \;\;\;\;z \cdot \frac{x\_m}{-y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+43}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -470000000000.0)
    (* z (/ x_m (- y)))
    (if (<= z 2.7e+43) x_m (/ (* x_m (- 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 (z <= -470000000000.0) {
		tmp = z * (x_m / -y);
	} else if (z <= 2.7e+43) {
		tmp = x_m;
	} else {
		tmp = (x_m * -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 (z <= (-470000000000.0d0)) then
        tmp = z * (x_m / -y)
    else if (z <= 2.7d+43) then
        tmp = x_m
    else
        tmp = (x_m * -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 (z <= -470000000000.0) {
		tmp = z * (x_m / -y);
	} else if (z <= 2.7e+43) {
		tmp = x_m;
	} else {
		tmp = (x_m * -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 z <= -470000000000.0:
		tmp = z * (x_m / -y)
	elif z <= 2.7e+43:
		tmp = x_m
	else:
		tmp = (x_m * -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 (z <= -470000000000.0)
		tmp = Float64(z * Float64(x_m / Float64(-y)));
	elseif (z <= 2.7e+43)
		tmp = x_m;
	else
		tmp = Float64(Float64(x_m * 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 (z <= -470000000000.0)
		tmp = z * (x_m / -y);
	elseif (z <= 2.7e+43)
		tmp = x_m;
	else
		tmp = (x_m * -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[z, -470000000000.0], N[(z * N[(x$95$m / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+43], x$95$m, N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -4.7e11

   1. Initial program 83.2%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

      1. associate-*r/ 83.2%

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

      2. clear-num 83.2%

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

      3. associate-/r* 87.8%

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

   6. Applied egg-rr 87.8%

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

   7. Taylor expanded in y around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-neg-frac2 66.4%

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

      3. neg-mul-1 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

      6. associate-/l* 72.9%

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

      7. *-commutative 72.9%

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

      8. neg-mul-1 72.9%

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

   9. Simplified 72.9%

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

   if -4.7e11 < z < 2.7000000000000002e43

   1. Initial program 79.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.8%

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

   if 2.7000000000000002e43 < z

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-rgt-neg-out 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -470000000000:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.1% accurate, 1.0× speedup

Math

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

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 (/ (- y 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 * ((y - 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 * ((y - 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 * ((y - 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 * ((y - 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(Float64(y - 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 * ((y - 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[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Final simplification 96.2%

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

Alternative 6: 51.0% 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 81.8%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in y around inf 54.9%

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

6. Final simplification 54.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.3% 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 2024044 
(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))