Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 96.1%

Time: 6.0s

Alternatives: 5

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: 96.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{z}, x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

3. Taylor expanded in z around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 48.8

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

5. Applied rewrites 48.8%

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

6. Taylor expanded in z around 0

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

   1. distribute-lft-in N/A

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

   2. associate-/l* N/A

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

   3. +-commutative N/A

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

   4. remove-double-neg N/A

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

   5. mul-1-neg N/A

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

   6. unsub-neg N/A

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

   7. div-sub N/A

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

   8. *-inverses N/A

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

   9. associate-*r/ N/A

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

   10. distribute-lft-out-- N/A

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

   11. *-rgt-identity N/A

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

   12. mul-1-neg N/A

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

   13. distribute-rgt-neg-in N/A

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

   14. associate-/l* N/A

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

   15. mul-1-neg N/A

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

   16. sub-neg N/A

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

   17. *-lft-identity N/A

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

   18. distribute-lft-neg-in N/A

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

   19. metadata-eval N/A

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

   20. distribute-lft-out N/A

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

   21. *-lft-identity N/A

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

   22. +-commutative N/A

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

   23. *-commutative N/A

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

   24. associate-*l/ N/A

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

   25. lower-fma.f64 N/A

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

8. Applied rewrites 97.3%

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

Alternative 2: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+40}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+49}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.6e+40) (* 1.0 x) (if (<= z 3.3e+49) (/ (* y x) z) (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.6e+40) {
		tmp = 1.0 * x;
	} else if (z <= 3.3e+49) {
		tmp = (y * x) / z;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-8.6d+40)) then
        tmp = 1.0d0 * x
    else if (z <= 3.3d+49) then
        tmp = (y * x) / z
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.6e+40) {
		tmp = 1.0 * x;
	} else if (z <= 3.3e+49) {
		tmp = (y * x) / z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.6e+40:
		tmp = 1.0 * x
	elif z <= 3.3e+49:
		tmp = (y * x) / z
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.6e+40)
		tmp = Float64(1.0 * x);
	elseif (z <= 3.3e+49)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.6e+40)
		tmp = 1.0 * x;
	elseif (z <= 3.3e+49)
		tmp = (y * x) / z;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.6e+40], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 3.3e+49], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000005e40 or 3.2999999999999998e49 < z

   1. Initial program 77.6%

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

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 82.7%

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

   if -8.6000000000000005e40 < z < 3.2999999999999998e49

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

Alternative 3: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)))
   (if (<= y -1.9e-58) t_0 (if (<= y 1.15e+23) (* 1.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -1.9e-58) {
		tmp = t_0;
	} else if (y <= 1.15e+23) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (x / z) * y
    if (y <= (-1.9d-58)) then
        tmp = t_0
    else if (y <= 1.15d+23) then
        tmp = 1.0d0 * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -1.9e-58) {
		tmp = t_0;
	} else if (y <= 1.15e+23) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	tmp = 0
	if y <= -1.9e-58:
		tmp = t_0
	elif y <= 1.15e+23:
		tmp = 1.0 * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * y)
	tmp = 0.0
	if (y <= -1.9e-58)
		tmp = t_0;
	elseif (y <= 1.15e+23)
		tmp = Float64(1.0 * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * y;
	tmp = 0.0;
	if (y <= -1.9e-58)
		tmp = t_0;
	elseif (y <= 1.15e+23)
		tmp = 1.0 * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.9e-58], t$95$0, If[LessEqual[y, 1.15e+23], N[(1.0 * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999999e-58 or 1.15e23 < y

   1. Initial program 91.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 95.2

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 95.2

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

   4. Applied rewrites 95.2%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 70.7

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

   7. Applied rewrites 70.7%

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

   9. Applied rewrites 70.7%

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

   10. Taylor expanded in z around 0

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

       1. associate-*l/ N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 72.1

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

   12. Applied rewrites 72.1%

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

   if -1.8999999999999999e-58 < y < 1.15e23

   1. Initial program 81.6%

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

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 83.2%

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

Alternative 4: 94.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{z}, y, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

3. Taylor expanded in z around 0

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

   1. distribute-lft-in N/A

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

   2. associate-/l* N/A

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

   3. +-commutative N/A

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

   4. *-lft-identity N/A

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

   5. metadata-eval N/A

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

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

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

   7. div-sub N/A

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

   8. *-inverses N/A

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

   9. associate-*r/ N/A

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

   10. unsub-neg N/A

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

   11. mul-1-neg N/A

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

   12. remove-double-neg N/A

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

   13. +-commutative N/A

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

   14. metadata-eval N/A

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

   15. sub-neg N/A

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

   16. sub-neg N/A

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

   17. metadata-eval N/A

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

   18. distribute-lft-out N/A

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

   19. associate-/l* N/A

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

   20. associate-*l/ N/A

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

   21. *-rgt-identity N/A

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

   22. lower-fma.f64 N/A

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

   23. lower-/.f64 93.1

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

5. Applied rewrites 93.1%

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

Alternative 5: 50.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z) {
	return 1.0 * x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 * x;
}

Python

def code(x, y, z):
	return 1.0 * x

Julia

function code(x, y, z)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 87.0%

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

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 97.3

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

   7. lift-+.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 97.3

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

4. Applied rewrites 97.3%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 51.8%

   \[\leadsto \color{blue}{1} \cdot x \]
8. Add Preprocessing

Developer Target 1: 96.4% 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 2024243 
(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))