Linear.Quaternion:$c/ from linear-1.19.1.3, C

Percentage Accurate: 63.5% → 100.0%

Time: 1.2s

Alternatives: 3

Speedup: 3.2×

• 80.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y \]

FPCore

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

C

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

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) + (y * y)) - (y * z)) - (y * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 63.5% accurate, 1.0× speedup

Math

\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y \]

FPCore

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

C

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

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) + (y * y)) - (y * z)) - (y * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 3.2× speedup

Math

\[y \cdot \left(x - z\right) \]

FPCore

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

C

double code(double x, double y, double z) {
	return y * (x - 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 = y * (x - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.5%

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

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(y, x - z, 0\right) \]
4. Step-by-step derivation

5. Applied rewrites 100.0%

   \[\leadsto y \cdot \left(x - z\right) \]
6. Add Preprocessing

Alternative 2: 76.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := -z \cdot y\\ \mathbf{if}\;z \leq -1.5998878487717716 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.4132947115915006 \cdot 10^{-40}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (* z y))))
  (if (<= z -1.5998878487717716e-87)
    t_0
    (if (<= z 1.4132947115915006e-40) (* x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(z * y);
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * y;
	} 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 = -(z * y)
    if (z <= (-1.5998878487717716d-87)) then
        tmp = t_0
    else if (z <= 1.4132947115915006d-40) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -(z * y);
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(z * y)
	tmp = 0
	if z <= -1.5998878487717716e-87:
		tmp = t_0
	elif z <= 1.4132947115915006e-40:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(z * y))
	tmp = 0.0
	if (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.4132947115915006e-40)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(z * y);
	tmp = 0.0;
	if (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.4132947115915006e-40)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(z * y), $MachinePrecision])}, If[LessEqual[z, -1.5998878487717716e-87], t$95$0, If[LessEqual[z, 1.4132947115915006e-40], N[(x * y), $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 = (- (z * y)) IN
		LET tmp_1 = IF (z <= (14132947115915006468182910235642061199906833362565967651395812855413318177857125598375794078304482317867511731446228395725484006106853485107421875e-185)) THEN (x * y) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-159988784877177164685523371169830722870522374072384409119026858684832480050318864005140114871679013601761552483193181404403016128515199488354968070059220853336754264519220820635743157089849151568897638446024723319315030689580225953250192105770111083984375e-341)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.5998878487717716e-87 or 1.4132947115915006e-40 < z

   1. Initial program 63.5%

      \[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y \]

   2. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \left(y \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 54.2%

      \[\leadsto -1 \cdot \left(y \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 54.2%

      \[\leadsto -z \cdot y \]

   if -1.5998878487717716e-87 < z < 1.4132947115915006e-40

   1. Initial program 63.5%

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

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(y, x - z, 0\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

      \[\leadsto y \cdot \left(x - z\right) \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 53.8%

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

Alternative 3: 53.8% accurate, 5.2× speedup

Math

\[x \cdot y \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * y), $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
END code

Derivation

1. Initial program 63.5%

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

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(y, x - z, 0\right) \]
4. Step-by-step derivation

5. Applied rewrites 100.0%

   \[\leadsto y \cdot \left(x - z\right) \]

6. Taylor expanded in x around inf

   \[\leadsto x \cdot y \]
7. Step-by-step derivation

8. Applied rewrites 53.8%

   \[\leadsto x \cdot y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64
  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))