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

Average Error: 0.0 → 0.0

Time: 4.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (x - y) / (1.0d0 - y)
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 (x - y) / (1.0 - y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	18.5
Cost	1176

\[\begin{array}{l} t_0 := \frac{x}{1 - y}\\ t_1 := -\frac{y}{1 - y}\\ \mathbf{if}\;x \leq -1.82 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-164}:\\ \;\;\;\;y \cdot x + x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.8
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+115}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+91}:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq -0.0012:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	16.7
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	8.8
Cost	712

\[\begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -245000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 105000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	17.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+115}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq -245000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	16.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -245000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))