Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 97.5%

Time: 6.9s

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: 84.5% 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: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2.1 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x\_m}{z}, y, x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, \frac{y}{z}, x\_m\right)\\ \end{array} \end{array} \]

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 2.1e-64) (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 <= 2.1e-64) {
		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 <= 2.1e-64)
		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, 2.1e-64], 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 < 2.10000000000000011e-64

   1. Initial program 83.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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. lower-*.f64 N/A

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

      7. lower-/.f64 81.6

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

   4. Applied rewrites 81.6%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]
   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. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*l* N/A

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

      8. lift-/.f64 N/A

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

      9. lft-mult-inverse N/A

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

      10. *-rgt-identity N/A

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

      11. lower-fma.f64 95.0

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

   6. Applied rewrites 95.0%

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

   if 2.10000000000000011e-64 < x

   1. Initial program 82.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

      5. cancel-sign-sub-inv N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-out-- N/A

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

      10. *-lft-identity N/A

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

      11. mul-1-neg N/A

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

      12. cancel-sign-sub N/A

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

      13. distribute-rgt1-in N/A

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

      14. distribute-lft1-in N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. 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: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x\_m \cdot y}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;\frac{x\_m}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \end{array} \]

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 y) z)))
   (* x_s (if (<= y -1.65e+86) t_0 (if (<= y 1.65e-19) (/ x_m 1.0) t_0)))))

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;
	double tmp;
	if (y <= -1.65e+86) {
		tmp = t_0;
	} else if (y <= 1.65e-19) {
		tmp = x_m / 1.0;
	} else {
		tmp = t_0;
	}
	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
    if (y <= (-1.65d+86)) then
        tmp = t_0
    else if (y <= 1.65d-19) then
        tmp = x_m / 1.0d0
    else
        tmp = t_0
    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;
	double tmp;
	if (y <= -1.65e+86) {
		tmp = t_0;
	} else if (y <= 1.65e-19) {
		tmp = x_m / 1.0;
	} else {
		tmp = t_0;
	}
	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
	tmp = 0
	if y <= -1.65e+86:
		tmp = t_0
	elif y <= 1.65e-19:
		tmp = x_m / 1.0
	else:
		tmp = t_0
	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 * y) / z)
	tmp = 0.0
	if (y <= -1.65e+86)
		tmp = t_0;
	elseif (y <= 1.65e-19)
		tmp = Float64(x_m / 1.0);
	else
		tmp = t_0;
	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;
	tmp = 0.0;
	if (y <= -1.65e+86)
		tmp = t_0;
	elseif (y <= 1.65e-19)
		tmp = x_m / 1.0;
	else
		tmp = t_0;
	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 * y), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.65e+86], t$95$0, If[LessEqual[y, 1.65e-19], N[(x$95$m / 1.0), $MachinePrecision], t$95$0]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e86 or 1.6499999999999999e-19 < y

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.65e86 < y < 1.6499999999999999e-19

   1. Initial program 81.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 79.8%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.9% 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 83.3%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
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. +-commutative N/A

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

   3. *-lft-identity N/A

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

   4. metadata-eval N/A

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

   5. cancel-sign-sub-inv N/A

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

   6. div-sub N/A

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

   7. *-inverses N/A

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

   8. associate-*r/ N/A

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

   9. distribute-rgt-out-- N/A

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

   10. *-lft-identity N/A

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

   11. mul-1-neg N/A

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

   12. cancel-sign-sub N/A

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

   13. distribute-rgt1-in N/A

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

   14. distribute-lft1-in N/A

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

   15. *-commutative N/A

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

   16. lower-fma.f64 N/A

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

   17. lower-/.f64 95.5

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

5. Applied rewrites 95.5%

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

Alternative 4: 50.3% accurate, 1.7× speedup

Math

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

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)))

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);
}

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)
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);
}

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)

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 / 1.0))
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);
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 / 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.3%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
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. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 95.4

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

4. Applied rewrites 95.4%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 54.9%

   \[\leadsto \frac{x}{\color{blue}{1}} \]
8. 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 2024220 
(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))