Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Percentage Accurate: 95.0% → 100.0%

Time: 1.0s

Alternatives: 3

Speedup: 1.4×

• 72.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[2 \cdot \left(x \cdot x - x \cdot y\right) \]

FPCore

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

C

double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 * ((x * x) - (x * y))
end function

Java

public static double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}

Python

def code(x, y):
	return 2.0 * ((x * x) - (x * y))

Julia

function code(x, y)
	return Float64(2.0 * Float64(Float64(x * x) - Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = 2.0 * ((x * x) - (x * y));
end

Wolfram

code[x_, y_] := N[(2.0 * N[(N[(x * x), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

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

Initial Program: 95.0% accurate, 1.0× speedup

Math

\[2 \cdot \left(x \cdot x - x \cdot y\right) \]

FPCore

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

C

double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 * ((x * x) - (x * y))
end function

Java

public static double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}

Python

def code(x, y):
	return 2.0 * ((x * x) - (x * y))

Julia

function code(x, y)
	return Float64(2.0 * Float64(Float64(x * x) - Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = 2.0 * ((x * x) - (x * y));
end

Wolfram

code[x_, y_] := N[(2.0 * N[(N[(x * x), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + x) * (x - y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 95.0%

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

3. Applied rewrites 100.0%

   \[\leadsto \left(x + x\right) \cdot \left(x - y\right) \]
4. Add Preprocessing

Alternative 2: 57.0% accurate, 1.8× speedup

Math

\[\left(-2 \cdot x\right) \cdot y \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* (* -2.0 x) y))

C

double code(double x, double y) {
	return (-2.0 * x) * y;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((-2.0d0) * x) * y
end function

Java

public static double code(double x, double y) {
	return (-2.0 * x) * y;
}

Python

def code(x, y):
	return (-2.0 * x) * y

Julia

function code(x, y)
	return Float64(Float64(-2.0 * x) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (-2.0 * x) * y;
end

Wolfram

code[x_, y_] := N[(N[(-2.0 * x), $MachinePrecision] * y), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((-2) * x) * y
END code

Derivation

1. Initial program 95.0%

   \[2 \cdot \left(x \cdot x - x \cdot y\right) \]

2. Taylor expanded in x around 0

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

4. Applied rewrites 56.9%

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

6. Applied rewrites 57.0%

   \[\leadsto \left(-2 \cdot x\right) \cdot y \]
7. Add Preprocessing

Alternative 3: 56.9% accurate, 1.8× speedup

Math

\[-2 \cdot \left(x \cdot y\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* -2.0 (* x y)))

C

double code(double x, double y) {
	return -2.0 * (x * y);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-2.0d0) * (x * y)
end function

Java

public static double code(double x, double y) {
	return -2.0 * (x * y);
}

Python

def code(x, y):
	return -2.0 * (x * y)

Julia

function code(x, y)
	return Float64(-2.0 * Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = -2.0 * (x * y);
end

Wolfram

code[x_, y_] := N[(-2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(-2) * (x * y)
END code

Derivation

1. Initial program 95.0%

   \[2 \cdot \left(x \cdot x - x \cdot y\right) \]

2. Taylor expanded in x around 0

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

4. Applied rewrites 56.9%

   \[\leadsto -2 \cdot \left(x \cdot y\right) \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64
  (* 2.0 (- (* x x) (* x y))))