Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, B

Average Error: 7.9 → 0.0

Time: 21.7s

Precision: binary64

Cost: 448

Math

\[\frac{x \cdot y}{y + 1} \]

↓

\[\frac{y}{1 + y} \cdot x \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	7.9
Target	0.0
Herbie	0.0

\[\begin{array}{l} \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array} \]

Derivation

1. Initial program 7.9

   \[\frac{x \cdot y}{y + 1} \]

2. Simplified 7.9

   \[\leadsto \color{blue}{\frac{y \cdot x}{1 + y}} \]
   Proof

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{y}{1 + y} \cdot x} \]

Alternatives

Alternative 1
Error	1.1
Cost	584

\[\begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.32:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	31.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1.0)))