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

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

↓

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

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	9.3
Cost	1044

\[\begin{array}{l} t_0 := \frac{-x}{y + -1}\\ t_1 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -56000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-88}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3900000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	9.5
Cost	980

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -31000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-89}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	9.0
Cost	912

\[\begin{array}{l} t_0 := \frac{-x}{y + -1}\\ \mathbf{if}\;y \leq -1800:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-89}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 15000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 4
Error	17.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -0.45:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	17.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-60} \lor \neg \left(y \leq 5.6 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	17.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -0.092:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023027 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))