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

Average Error: 0.02% → 0.02%

Time: 5.4s

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 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	25.85%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	25.75%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.75:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	12.21%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -140000 \lor \neg \left(y \leq 6800000\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]

Alternative 4
Error	12.47%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1250000 \lor \neg \left(y \leq 61000000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]

Alternative 5
Error	25.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	26.01%
Cost	520

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	25.26%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	61.17%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023102 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))