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

Average Error: 0.02% → 0.02%

Time: 5.7s

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 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	28.16%
Cost	1180

\[\begin{array}{l} t_0 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -62000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.45:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6800:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	15.49%
Cost	1112

\[\begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -30000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	14.86%
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{y + -1}\\ t_1 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	15.5%
Cost	1048

\[\begin{array}{l} t_0 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	1.75%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]

Alternative 6
Error	26.85%
Cost	524

\[\begin{array}{l} \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6800:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	26.07%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	60.98%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023101 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))