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

Percentage Accurate: 84.4% → 97.7%

Time: 7.7s

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: 84.4% 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: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x\_m - \frac{z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= x_m 5e-8) (- x_m (/ z (/ y x_m))) (- 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 (x_m <= 5e-8) {
		tmp = x_m - (z / (y / x_m));
	} else {
		tmp = x_m - (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 (x_m <= 5d-8) then
        tmp = x_m - (z / (y / x_m))
    else
        tmp = x_m - (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 (x_m <= 5e-8) {
		tmp = x_m - (z / (y / x_m));
	} else {
		tmp = x_m - (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 x_m <= 5e-8:
		tmp = x_m - (z / (y / x_m))
	else:
		tmp = x_m - (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 (x_m <= 5e-8)
		tmp = Float64(x_m - Float64(z / Float64(y / x_m)));
	else
		tmp = Float64(x_m - 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 (x_m <= 5e-8)
		tmp = x_m - (z / (y / x_m));
	else
		tmp = x_m - (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[x$95$m, 5e-8], N[(x$95$m - N[(z / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 4.9999999999999998e-8

   1. Initial program 89.5%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 94.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right) + x \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right), \color{blue}{x}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{y}{z}}\right)\right)\right), x\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(z\right)}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(z\right)\right)\right)\right), x\right) \]

      12. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left(0 - z\right)\right)\right), x\right) \]

      13. --lowering--.f64 95.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(0, z\right)\right)\right), x\right) \]

   6. Applied egg-rr 95.1%

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

      1. +-commutative N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto x - \color{blue}{\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}} \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}\right)}\right) \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{x}{\frac{y}{0 - z}}\right)\right)\right) \]

      7. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{x}{y} \cdot \left(0 - z\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\left(0 - z\right) \cdot \frac{x}{y}\right)\right)\right) \]

      9. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\left(0 - z\right) \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      10. div-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{0 - z}{\frac{y}{x}}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\mathsf{neg}\left(\left(0 - z\right)\right)}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      12. sub0-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\frac{y}{x}}\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z}{\frac{\color{blue}{y}}{x}}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      15. /-lowering-/.f64 95.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   8. Applied egg-rr 95.8%

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

   if 4.9999999999999998e-8 < x

   1. Initial program 81.6%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.8%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right) + x \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right), \color{blue}{x}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{y}{z}}\right)\right)\right), x\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(z\right)}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(z\right)\right)\right)\right), x\right) \]

      12. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left(0 - z\right)\right)\right), x\right) \]

      13. --lowering--.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(0, z\right)\right)\right), x\right) \]

   6. Applied egg-rr 99.8%

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

      1. +-commutative N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto x - \color{blue}{\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}} \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}\right)}\right) \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{x}{\frac{y}{0 - z}}\right)\right)\right) \]

      7. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{x}{y} \cdot \left(0 - z\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\left(0 - z\right) \cdot \frac{x}{y}\right)\right)\right) \]

      9. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\left(0 - z\right) \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      10. div-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{0 - z}{\frac{y}{x}}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\mathsf{neg}\left(\left(0 - z\right)\right)}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      12. sub0-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\frac{y}{x}}\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z}{\frac{\color{blue}{y}}{x}}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      15. /-lowering-/.f64 94.1%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   8. Applied egg-rr 94.1%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z}{y} \cdot \color{blue}{x}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{y}\right), \color{blue}{x}\right)\right) \]

      3. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, y\right), x\right)\right) \]

   10. Applied egg-rr 99.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{+35}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= x_m 1e+35) x_m (/ y (/ 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 (x_m <= 1e+35) {
		tmp = x_m;
	} else {
		tmp = y / (y / x_m);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 1d+35) then
        tmp = x_m
    else
        tmp = y / (y / x_m)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 1e+35) {
		tmp = x_m;
	} else {
		tmp = y / (y / x_m);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 1e+35:
		tmp = x_m
	else:
		tmp = y / (y / x_m)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 1e+35)
		tmp = x_m;
	else
		tmp = Float64(y / Float64(y / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 1e+35)
		tmp = x_m;
	else
		tmp = y / (y / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 1e+35], x$95$m, N[(y / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999997e34

   1. Initial program 89.7%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 95.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 53.7%

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

   if 9.9999999999999997e34 < x

   1. Initial program 79.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 28.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), y\right) \]

   5. Simplified 28.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      6. /-lowering-/.f64 53.3%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 53.3%

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

Alternative 3: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.4 \cdot 10^{+76}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= x_m 1.4e+76) 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 <= 1.4e+76) {
		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 <= 1.4d+76) 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 <= 1.4e+76) {
		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 <= 1.4e+76:
		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 <= 1.4e+76)
		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 <= 1.4e+76)
		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, 1.4e+76], x$95$m, N[(y * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.3999999999999999e76

   1. Initial program 89.8%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 95.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 53.6%

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

   if 1.3999999999999999e76 < x

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 21.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), y\right) \]

   5. Simplified 21.9%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-/r/ N/A

         \[\leadsto \frac{1}{\frac{y}{x}} \cdot y \]

      5. clear-num N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{y}\right) \]

      7. /-lowering-/.f64 52.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right) \]

   7. Applied egg-rr 52.8%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.7% accurate, 1.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (- 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) {
	return x_s * (x_m - (x_m * (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 - (x_m * (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 - (x_m * (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 - (x_m * (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(x_m * 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 - (x_m * (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[(x$95$m * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.5%

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

   1. associate-/l* N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

   3. div-sub N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 96.2%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

3. Simplified 96.2%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. distribute-lft-in N/A

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

   4. *-rgt-identity N/A

      \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right) + x \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right), \color{blue}{x}\right) \]

   6. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{y}{z}}\right)\right)\right), x\right) \]

   7. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

   8. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

   10. distribute-neg-frac2 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(z\right)}\right)\right), x\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(z\right)\right)\right)\right), x\right) \]

   12. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left(0 - z\right)\right)\right), x\right) \]

   13. --lowering--.f64 96.3%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(0, z\right)\right)\right), x\right) \]

6. Applied egg-rr 96.3%

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

   1. +-commutative N/A

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

   2. frac-2neg N/A

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

   3. distribute-frac-neg N/A

      \[\leadsto x + \left(\mathsf{neg}\left(\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}\right)\right) \]

   4. unsub-neg N/A

      \[\leadsto x - \color{blue}{\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}} \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{x}{\mathsf{neg}\left(\frac{y}{0 - z}\right)}\right)}\right) \]

   6. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{x}{\frac{y}{0 - z}}\right)\right)\right) \]

   7. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{x}{y} \cdot \left(0 - z\right)\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\left(0 - z\right) \cdot \frac{x}{y}\right)\right)\right) \]

   9. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\left(0 - z\right) \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

   10. div-inv N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{0 - z}{\frac{y}{x}}\right)\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\mathsf{neg}\left(\left(0 - z\right)\right)}{\color{blue}{\frac{y}{x}}}\right)\right) \]

   12. sub0-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\frac{y}{x}}\right)\right) \]

   13. remove-double-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z}{\frac{\color{blue}{y}}{x}}\right)\right) \]

   14. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

   15. /-lowering-/.f64 95.3%

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

8. Applied egg-rr 95.3%

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

   1. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z}{y} \cdot \color{blue}{x}\right)\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{y}\right), \color{blue}{x}\right)\right) \]

   3. /-lowering-/.f64 96.2%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, y\right), x\right)\right) \]

10. Applied egg-rr 96.2%

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

11. Final simplification 96.2%

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

Alternative 5: 95.7% 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 #s(literal 1 binary64) 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 87.5%

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

   1. associate-/l* N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

   3. div-sub N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 96.2%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

3. Simplified 96.2%

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

Alternative 6: 50.2% 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 #s(literal 1 binary64) 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 87.5%

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

   1. associate-/l* N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

   3. div-sub N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 96.2%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

3. Simplified 96.2%

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

5. Taylor expanded in z around 0

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

7. Simplified 52.1%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 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 2024138 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

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