Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.8% → 96.9%

Time: 1.7s

Alternatives: 5

Speedup: 1.1×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (y + z)) / z
END code

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (y + z)) / z
END code

Alternative 1: 96.9% accurate, 0.4× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 2.604772325003076 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left|x\right|, \frac{1}{z}, \left|x\right|\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left|x\right|, \frac{y}{z}, \left|x\right|\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 x)
 (if (<= (fabs x) 2.604772325003076e-139)
   (fma (* y (fabs x)) (/ 1.0 z) (fabs x))
   (fma (fabs x) (/ y z) (fabs x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fabs(x) <= 2.604772325003076e-139) {
		tmp = fma((y * fabs(x)), (1.0 / z), fabs(x));
	} else {
		tmp = fma(fabs(x), (y / z), fabs(x));
	}
	return copysign(1.0, x) * tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (abs(x) <= 2.604772325003076e-139)
		tmp = fma(Float64(y * abs(x)), Float64(1.0 / z), abs(x));
	else
		tmp = fma(abs(x), Float64(y / z), abs(x));
	end
	return Float64(copysign(1.0, x) * tmp)
end

Wolfram

code[x_, y_, z_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 2.604772325003076e-139], N[(N[(y * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision] + N[Abs[x], $MachinePrecision]), $MachinePrecision], N[(N[Abs[x], $MachinePrecision] * N[(y / z), $MachinePrecision] + N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.6047723250030761e-139

   1. Initial program 84.8%

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

   3. Applied rewrites 94.0%

      \[\leadsto \mathsf{fma}\left(y \cdot x, \frac{1}{z}, x\right) \]

   if 2.6047723250030761e-139 < x

   1. Initial program 84.8%

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

   3. Applied rewrites 95.5%

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

Alternative 2: 95.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (y / z)) + x
END code

Derivation

1. Initial program 84.8%

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

3. Applied rewrites 95.5%

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

Alternative 3: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ \mathbf{if}\;y \leq -4.4496981415615434 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.727054120548146 \cdot 10^{+47}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (* x y) z)))
  (if (<= y -4.4496981415615434e-17)
    t_0
    (if (<= y 3.727054120548146e+47) (* x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (y <= -4.4496981415615434e-17) {
		tmp = t_0;
	} else if (y <= 3.727054120548146e+47) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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 * y) / z
    if (y <= (-4.4496981415615434d-17)) then
        tmp = t_0
    else if (y <= 3.727054120548146d+47) then
        tmp = x * 1.0d0
    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 * y) / z;
	double tmp;
	if (y <= -4.4496981415615434e-17) {
		tmp = t_0;
	} else if (y <= 3.727054120548146e+47) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) / z
	tmp = 0
	if y <= -4.4496981415615434e-17:
		tmp = t_0
	elif y <= 3.727054120548146e+47:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (y <= -4.4496981415615434e-17)
		tmp = t_0;
	elseif (y <= 3.727054120548146e+47)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) / z;
	tmp = 0.0;
	if (y <= -4.4496981415615434e-17)
		tmp = t_0;
	elseif (y <= 3.727054120548146e+47)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -4.4496981415615434e-17], t$95$0, If[LessEqual[y, 3.727054120548146e+47], N[(x * 1.0), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = ((x * y) / z) IN
		LET tmp_1 = IF (y <= (372705412054814616519807377301979582364609675264)) THEN (x * (1)) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-4449698141561543378010010345383822612506954265860180386393807339118211530148983001708984375e-107)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -4.4496981415615434e-17 or 3.7270541205481462e47 < y

   1. Initial program 84.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 46.9%

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

   if -4.4496981415615434e-17 < y < 3.7270541205481462e47

   1. Initial program 84.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.7%

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

   6. Applied rewrites 51.4%

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

   7. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 \]
   8. Step-by-step derivation

   9. Applied rewrites 51.4%

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

Alternative 4: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -4.4496981415615434 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.727054120548146 \cdot 10^{+47}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (/ y z))))
  (if (<= y -4.4496981415615434e-17)
    t_0
    (if (<= y 3.727054120548146e+47) (* x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (y <= -4.4496981415615434e-17) {
		tmp = t_0;
	} else if (y <= 3.727054120548146e+47) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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 * (y / z)
    if (y <= (-4.4496981415615434d-17)) then
        tmp = t_0
    else if (y <= 3.727054120548146d+47) then
        tmp = x * 1.0d0
    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 * (y / z);
	double tmp;
	if (y <= -4.4496981415615434e-17) {
		tmp = t_0;
	} else if (y <= 3.727054120548146e+47) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if y <= -4.4496981415615434e-17:
		tmp = t_0
	elif y <= 3.727054120548146e+47:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -4.4496981415615434e-17)
		tmp = t_0;
	elseif (y <= 3.727054120548146e+47)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (y <= -4.4496981415615434e-17)
		tmp = t_0;
	elseif (y <= 3.727054120548146e+47)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4496981415615434e-17], t$95$0, If[LessEqual[y, 3.727054120548146e+47], N[(x * 1.0), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * (y / z)) IN
		LET tmp_1 = IF (y <= (372705412054814616519807377301979582364609675264)) THEN (x * (1)) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-4449698141561543378010010345383822612506954265860180386393807339118211530148983001708984375e-107)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -4.4496981415615434e-17 or 3.7270541205481462e47 < y

   1. Initial program 84.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.7%

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

   6. Applied rewrites 51.4%

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

   7. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 \]
   8. Step-by-step derivation

   9. Applied rewrites 51.4%

      \[\leadsto x \cdot 1 \]

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 46.0%

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

   if -4.4496981415615434e-17 < y < 3.7270541205481462e47

   1. Initial program 84.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.7%

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

   6. Applied rewrites 51.4%

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

   7. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 \]
   8. Step-by-step derivation

   9. Applied rewrites 51.4%

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

Alternative 5: 51.4% accurate, 2.6× speedup

Math

\[x \cdot 1 \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * (1)
END code

Derivation

1. Initial program 84.8%

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

2. Taylor expanded in y around 0

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

4. Applied rewrites 40.7%

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

6. Applied rewrites 51.4%

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

7. Taylor expanded in y around 0

   \[\leadsto x \cdot 1 \]
8. Step-by-step derivation

9. Applied rewrites 51.4%

   \[\leadsto x \cdot 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (+ y z)) z))