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

Average Error: 0.03% → 0.02%

Time: 4.8s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.03

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

2. Simplified 0.03

   \[\leadsto \color{blue}{\frac{y - x}{y + -1}} \]
   Proof

   [Start] 0.03	\[ \frac{x - y}{1 - y} \]
   sub-neg [=>] 0.03	\[ \frac{\color{blue}{x + \left(-y\right)}}{1 - y} \]
   +-commutative [=>] 0.03	\[ \frac{\color{blue}{\left(-y\right) + x}}{1 - y} \]
   neg-sub0 [=>] 0.03	\[ \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]
   associate-+l- [=>] 0.03	\[ \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]
   sub0-neg [=>] 0.03	\[ \frac{\color{blue}{-\left(y - x\right)}}{1 - y} \]
   neg-mul-1 [=>] 0.03	\[ \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{1 - y} \]
   sub-neg [=>] 0.03	\[ \frac{-1 \cdot \left(y - x\right)}{\color{blue}{1 + \left(-y\right)}} \]
   +-commutative [=>] 0.03	\[ \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + 1}} \]
   neg-sub0 [=>] 0.03	\[ \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]
   associate-+l- [=>] 0.03	\[ \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]
   sub0-neg [=>] 0.03	\[ \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - 1\right)}} \]
   neg-mul-1 [=>] 0.03	\[ \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - 1\right)}} \]
   times-frac [=>] 0.03	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - 1}} \]
   metadata-eval [=>] 0.03	\[ \color{blue}{1} \cdot \frac{y - x}{y - 1} \]
   *-lft-identity [=>] 0.03	\[ \color{blue}{\frac{y - x}{y - 1}} \]
   sub-neg [=>] 0.03	\[ \frac{y - x}{\color{blue}{y + \left(-1\right)}} \]
   metadata-eval [=>] 0.03	\[ \frac{y - x}{y + \color{blue}{-1}} \]

3. Applied egg-rr 0.02

   \[\leadsto \color{blue}{\frac{y}{y + -1} - \frac{x}{y + -1}} \]

4. Final simplification 0.02

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

Alternatives

Alternative 1
Error	15.37%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 2
Error	2.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]

Alternative 3
Error	1.78%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -0.96 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(-1 + x\right)\\ \end{array} \]

Alternative 4
Error	16.18%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -820000000:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	15.72%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	2.36%
Cost	585

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

Alternative 7
Error	14.62%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -18:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	0.03%
Cost	448

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

Alternative 9
Error	26.78%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Error	61.98%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))