Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 85.2% → 97.2%

Time: 26.6s

Alternatives: 4

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2.2 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x\_m}{z}, y, x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, \frac{y}{z}, x\_m\right)\\ \end{array} \end{array} \]

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 2.2e-131) (fma (/ x_m z) y x_m) (fma x_m (/ y z) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 2.2e-131) {
		tmp = fma((x_m / z), y, x_m);
	} else {
		tmp = fma(x_m, (y / z), x_m);
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 2.2e-131)
		tmp = fma(Float64(x_m / z), y, x_m);
	else
		tmp = fma(x_m, Float64(y / z), x_m);
	end
	return Float64(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, 2.2e-131], N[(N[(x$95$m / z), $MachinePrecision] * y + x$95$m), $MachinePrecision], N[(x$95$m * N[(y / z), $MachinePrecision] + x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.2e-131

   1. Initial program 81.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lift-+.f64 N/A

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

      7. unpow1 N/A

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

      8. remove-double-neg N/A

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

      9. neg-mul-1 N/A

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

      10. unpow-prod-down N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

          \[\leadsto \frac{x}{z} \cdot \left(y + -1 \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{\color{blue}{\left(\frac{2}{2}\right)}}\right) \]

      13. sqrt-pow1 N/A

          \[\leadsto \frac{x}{z} \cdot \left(y + -1 \cdot \color{blue}{\sqrt{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}}\right) \]

      14. pow2 N/A

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

      15. sqr-neg-rev N/A

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

      16. pow2 N/A

          \[\leadsto \frac{x}{z} \cdot \left(y + -1 \cdot \sqrt{\color{blue}{{z}^{2}}}\right) \]

      17. sqrt-pow1 N/A

          \[\leadsto \frac{x}{z} \cdot \left(y + -1 \cdot \color{blue}{{z}^{\left(\frac{2}{2}\right)}}\right) \]

      18. metadata-eval N/A

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

      19. unpow1 N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower-*.f64 N/A

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

      23. lower-/.f64 N/A

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

      24. sub-neg N/A

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

      25. neg-mul-1 N/A

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

      26. metadata-eval N/A

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

      27. unpow1 N/A

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

      28. metadata-eval N/A

          \[\leadsto \frac{x}{z} \cdot \left(y + {-1}^{1} \cdot {z}^{\color{blue}{\left(\frac{2}{2}\right)}}\right) \]

      29. sqrt-pow1 N/A

          \[\leadsto \frac{x}{z} \cdot \left(y + {-1}^{1} \cdot \color{blue}{\sqrt{{z}^{2}}}\right) \]

      30. pow2 N/A

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

   4. Applied rewrites 84.8%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. *-inverses N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 94.8

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

   6. Applied rewrites 94.8%

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

   if 2.2e-131 < x

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

Alternative 2: 70.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x\_m \cdot \left(z + y\right)}{z}\\ t_1 := \frac{x\_m \cdot y}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+148}:\\ \;\;\;\;\frac{x\_m \cdot z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* x_m (+ z y)) z)) (t_1 (/ (* x_m y) z)))
   (* x_s (if (<= t_0 -5e-298) t_1 (if (<= t_0 1e+148) (/ (* x_m z) z) t_1)))))

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 * (z + y)) / z;
	double t_1 = (x_m * y) / z;
	double tmp;
	if (t_0 <= -5e-298) {
		tmp = t_1;
	} else if (t_0 <= 1e+148) {
		tmp = (x_m * z) / z;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x_m * (z + y)) / z
    t_1 = (x_m * y) / z
    if (t_0 <= (-5d-298)) then
        tmp = t_1
    else if (t_0 <= 1d+148) then
        tmp = (x_m * z) / z
    else
        tmp = t_1
    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 * (z + y)) / z;
	double t_1 = (x_m * y) / z;
	double tmp;
	if (t_0 <= -5e-298) {
		tmp = t_1;
	} else if (t_0 <= 1e+148) {
		tmp = (x_m * z) / z;
	} else {
		tmp = t_1;
	}
	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 * (z + y)) / z
	t_1 = (x_m * y) / z
	tmp = 0
	if t_0 <= -5e-298:
		tmp = t_1
	elif t_0 <= 1e+148:
		tmp = (x_m * z) / z
	else:
		tmp = t_1
	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(z + y)) / z)
	t_1 = Float64(Float64(x_m * y) / z)
	tmp = 0.0
	if (t_0 <= -5e-298)
		tmp = t_1;
	elseif (t_0 <= 1e+148)
		tmp = Float64(Float64(x_m * z) / z);
	else
		tmp = t_1;
	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 * (z + y)) / z;
	t_1 = (x_m * y) / z;
	tmp = 0.0;
	if (t_0 <= -5e-298)
		tmp = t_1;
	elseif (t_0 <= 1e+148)
		tmp = (x_m * z) / z;
	else
		tmp = t_1;
	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[(z + y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -5e-298], t$95$1, If[LessEqual[t$95$0, 1e+148], N[(N[(x$95$m * z), $MachinePrecision] / z), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 y z)) z) < -5.0000000000000002e-298 or 1e148 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 84.2%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 57.4

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

   5. Applied rewrites 57.4%

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

   if -5.0000000000000002e-298 < (/.f64 (*.f64 x (+.f64 y z)) z) < 1e148

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 57.3

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

   5. Applied rewrites 57.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(z + y\right)}{z} \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(z + y\right)}{z} \leq 10^{+148}:\\ \;\;\;\;\frac{x \cdot z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.0% accurate, 1.1× speedup

Math

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

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

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * fma(x_m, (y / z), 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 * fma(x_m, Float64(y / z), 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 * N[(x$95$m * N[(y / z), $MachinePrecision] + x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.5%

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

3. Taylor expanded in x around 0

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

   1. associate-/l* N/A

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

   2. div-add N/A

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

   3. *-inverses N/A

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

   4. distribute-rgt-in N/A

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

   5. *-commutative N/A

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

   6. *-lft-identity N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 95.4

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

5. Applied rewrites 95.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{z}, x\right)} \]
6. Add Preprocessing

Alternative 4: 48.5% accurate, 1.2× speedup

Math

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

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

Derivation

1. Initial program 84.5%

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

3. Taylor expanded in y around inf

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

   1. lower-*.f64 49.3

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

5. Applied rewrites 49.3%

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

Developer Target 1: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z}{y + z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ x (/ z (+ y z))))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x / (z / (y + z))

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024278 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ z (+ y z))))

  (/ (* x (+ y z)) z))