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

Average Error: 0.0 → 0.0

Time: 3.3s

Precision: binary64

Cost: 448

Math

\[\frac{x - y}{1 - y} \]

↓

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

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[\frac{x - y}{1 - y} \]

2. Simplified 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.9
Cost	988

\[\begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -963087761.6241825:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.226740379858147 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2834374157684195 \cdot 10^{-102}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.0725131574691057 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.705181824743841 \cdot 10^{-30}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 0.18645086324144028:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	17.7
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1599504212554834 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.226740379858147 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2834374157684195 \cdot 10^{-102}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.0725131574691057 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.705181824743841 \cdot 10^{-30}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 0.18645086324144028:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	9.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -963087761.6241825:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq 0.18645086324144028:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 4
Error	9.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -963087761.6241825:\\ \;\;\;\;\frac{-x}{y + -1}\\ \mathbf{elif}\;y \leq 0.18645086324144028:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 5
Error	9.7
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -963087761.6241825:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq 0.18645086324144028:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	17.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1599504212554834 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.18645086324144028:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022217 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))