Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 77.0% → 100.0%

Time: 887.0ms

Alternatives: 3

Speedup: 1.2×

Specification

Math

\[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / ((x * 2.0) * y)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Initial Program: 77.0% accurate, 1.0× speedup

Math

\[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / ((x * 2.0) * y)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\frac{0.5}{x} + \frac{0.5}{y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (+ (/ 0.5 x) (/ 0.5 y)))

C

double code(double x, double y) {
	return (0.5 / x) + (0.5 / y);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (0.5d0 / x) + (0.5d0 / y)
end function

Java

public static double code(double x, double y) {
	return (0.5 / x) + (0.5 / y);
}

Python

def code(x, y):
	return (0.5 / x) + (0.5 / y)

Julia

function code(x, y)
	return Float64(Float64(0.5 / x) + Float64(0.5 / y))
end

MATLAB

function tmp = code(x, y)
	tmp = (0.5 / x) + (0.5 / y);
end

Wolfram

code[x_, y_] := N[(N[(0.5 / x), $MachinePrecision] + N[(0.5 / y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((5e-1) / x) + ((5e-1) / y)
END code

Derivation

1. Initial program 77.0%

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

3. Applied rewrites 100.0%

   \[\leadsto \frac{0.5}{x} + \frac{0.5}{y} \]
4. Add Preprocessing

Alternative 2: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(x, y\right) \leq -6.880405119228122 \cdot 10^{-63}:\\ \;\;\;\;\frac{0.5}{\mathsf{max}\left(x, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\mathsf{min}\left(x, y\right)}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (fmin x y) -6.880405119228122e-63)
  (/ 0.5 (fmax x y))
  (/ 0.5 (fmin x y))))

C

double code(double x, double y) {
	double tmp;
	if (fmin(x, y) <= -6.880405119228122e-63) {
		tmp = 0.5 / fmax(x, y);
	} else {
		tmp = 0.5 / fmin(x, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (fmin(x, y) <= (-6.880405119228122d-63)) then
        tmp = 0.5d0 / fmax(x, y)
    else
        tmp = 0.5d0 / fmin(x, y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (fmin(x, y) <= -6.880405119228122e-63) {
		tmp = 0.5 / fmax(x, y);
	} else {
		tmp = 0.5 / fmin(x, y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if fmin(x, y) <= -6.880405119228122e-63:
		tmp = 0.5 / fmax(x, y)
	else:
		tmp = 0.5 / fmin(x, y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (fmin(x, y) <= -6.880405119228122e-63)
		tmp = Float64(0.5 / fmax(x, y));
	else
		tmp = Float64(0.5 / fmin(x, y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (min(x, y) <= -6.880405119228122e-63)
		tmp = 0.5 / max(x, y);
	else
		tmp = 0.5 / min(x, y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Min[x, y], $MachinePrecision], -6.880405119228122e-63], N[(0.5 / N[Max[x, y], $MachinePrecision]), $MachinePrecision], N[(0.5 / N[Min[x, y], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_4 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 <= (-68804051192281219585901139254960001215248046074855352696448477138479341380611927281996856719191995576752147176451878101687846773781836984194551142165398207976856337353410708601586520671844482421875e-259)) THEN ((5e-1) / tmp_3) ELSE ((5e-1) / tmp_4) ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 2 regimes

2. if x < -6.880405119228122e-63

   1. Initial program 77.0%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\frac{1}{2}}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.2%

      \[\leadsto \frac{0.5}{y} \]

   if -6.880405119228122e-63 < x

   1. Initial program 77.0%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{1}{2}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.1%

      \[\leadsto \frac{0.5}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.1% accurate, 2.8× speedup

Math

\[\frac{0.5}{x} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ 0.5 x))

C

double code(double x, double y) {
	return 0.5 / x;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 / x
end function

Java

public static double code(double x, double y) {
	return 0.5 / x;
}

Python

def code(x, y):
	return 0.5 / x

Julia

function code(x, y)
	return Float64(0.5 / x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 / x;
end

Wolfram

code[x_, y_] := N[(0.5 / x), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(5e-1) / x
END code

Derivation

1. Initial program 77.0%

   \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]

2. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{1}{2}}{x} \]
3. Step-by-step derivation

4. Applied rewrites 51.1%

   \[\leadsto \frac{0.5}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64
  (/ (+ x y) (* (* x 2.0) y)))