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

Average Error: 0.0 → 0.0

Time: 2.7s

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	10.1
Cost	1240

\[\begin{array}{l} t_0 := \frac{y}{y + -1}\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-103}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 220000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]

Alternative 2
Error	17.8
Cost	1113

\[\begin{array}{l} t_0 := \frac{y}{y + -1}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-73} \lor \neg \left(y \leq 1.2 \cdot 10^{+60}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]

Alternative 3
Error	10.1
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{y + -1}\\ t_1 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-103}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2500:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	1.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -0.82:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]

Alternative 5
Error	16.7
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1600000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+60}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	16.6
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1600000:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	16.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	16.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9
Error	39.3
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023041 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))