Linear.Projection:inversePerspective from linear-1.19.1.3, B

Percentage Accurate: 77.0% → 100.0%

Time: 1.2s

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

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

FPCore

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

C

double code(double x, double y) {
	return (0.5 / y) - (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 / y) - (0.5d0 / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

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

Alternative 2: 74.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.1004388755873057 \cdot 10^{+78}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;x \leq 8.249630193851516 \cdot 10^{+85}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{y}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= x -3.1004388755873057e+78)
  (/ 0.5 y)
  (if (<= x 8.249630193851516e+85) (/ -0.5 x) (/ 0.5 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.1004388755873057e+78) {
		tmp = 0.5 / y;
	} else if (x <= 8.249630193851516e+85) {
		tmp = -0.5 / x;
	} else {
		tmp = 0.5 / 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 (x <= (-3.1004388755873057d+78)) then
        tmp = 0.5d0 / y
    else if (x <= 8.249630193851516d+85) then
        tmp = (-0.5d0) / x
    else
        tmp = 0.5d0 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.1004388755873057e+78) {
		tmp = 0.5 / y;
	} else if (x <= 8.249630193851516e+85) {
		tmp = -0.5 / x;
	} else {
		tmp = 0.5 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.1004388755873057e+78:
		tmp = 0.5 / y
	elif x <= 8.249630193851516e+85:
		tmp = -0.5 / x
	else:
		tmp = 0.5 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.1004388755873057e+78)
		tmp = Float64(0.5 / y);
	elseif (x <= 8.249630193851516e+85)
		tmp = Float64(-0.5 / x);
	else
		tmp = Float64(0.5 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.1004388755873057e+78)
		tmp = 0.5 / y;
	elseif (x <= 8.249630193851516e+85)
		tmp = -0.5 / x;
	else
		tmp = 0.5 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.1004388755873057e+78], N[(0.5 / y), $MachinePrecision], If[LessEqual[x, 8.249630193851516e+85], N[(-0.5 / x), $MachinePrecision], N[(0.5 / y), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (x <= (82496301938515155595674366554481906850508119056615024982644090771514546196319800655872)) THEN ((-5e-1) / x) ELSE ((5e-1) / y) ENDIF IN
	LET tmp = IF (x <= (-3100438875587305715332076491679402000941895339773951932515938630303066099810304)) THEN ((5e-1) / y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -3.1004388755873057e78 or 8.2496301938515156e85 < x

   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 50.1%

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

   if -3.1004388755873057e78 < x < 8.2496301938515156e85

   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, B"
  :precision binary64
  (/ (- x y) (* (* x 2.0) y)))