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

Average Error: 8.1 → 0.0

Time: 3.9s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return (y / (y + 1.0)) * 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 / (y + 1.0d0)) * 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 / (y + 1.0)) * x;
}

Python

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	8.1
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 8.1

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

2. Simplified 0.1

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

   [Start] 8.1	\[ \frac{x \cdot y}{y + 1} \]
   associate-/l* [=>] 0.1	\[ \color{blue}{\frac{x}{\frac{y + 1}{y}}} \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.35\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	1.3
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	31.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023073 
(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)))