Linear.Projection:inversePerspective from linear-1.19.1.3, B

Average Error: 15.8 → 0.0

Time: 3.6s

Precision: binary64

Cost: 576

Math

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

↓

\[\left(\frac{-1}{x} + \frac{1}{y}\right) \cdot 0.5 \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (* (* x 2.0) y)))

↓

(FPCore (x y) :precision binary64 (* (+ (/ -1.0 x) (/ 1.0 y)) 0.5))

C

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

↓

double code(double x, double y) {
	return ((-1.0 / x) + (1.0 / y)) * 0.5;
}

Fortran

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (((-1.0d0) / x) + (1.0d0 / y)) * 0.5d0
end function

Java

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

↓

public static double code(double x, double y) {
	return ((-1.0 / x) + (1.0 / y)) * 0.5;
}

Python

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

↓

def code(x, y):
	return ((-1.0 / x) + (1.0 / y)) * 0.5

Julia

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

↓

function code(x, y)
	return Float64(Float64(Float64(-1.0 / x) + Float64(1.0 / y)) * 0.5)
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = ((-1.0 / x) + (1.0 / y)) * 0.5;
end

Wolfram

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

↓

code[x_, y_] := N[(N[(N[(-1.0 / x), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]

Target

Original	15.8
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 15.8

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

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\left(\frac{-1}{x} + \frac{1}{y}\right) \cdot 0.5} \]

3. Final simplification 0.0

   \[\leadsto \left(\frac{-1}{x} + \frac{1}{y}\right) \cdot 0.5 \]

Alternatives

Alternative 1
Error	17.0
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-132}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{y}\\ \end{array} \]

Alternative 2
Error	31.4
Cost	192

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

Reproduce

herbie shell --seed 2023068 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

  (/ (- x y) (* (* x 2.0) y)))