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

Average Error: 0.0 → 0.0

Time: 4.9s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

def code(x, y):
	return (y - 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 - 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 - 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 - x), $MachinePrecision] / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{y - x}{y + -1}} \]
   Proof
   (/.f64 (-.f64 y x) (+.f64 y -1)): 0 points increase in error, 0 points decrease in error
   (/.f64 (-.f64 y x) (+.f64 y (Rewrite<= metadata-eval (neg.f64 1)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (-.f64 y x) (Rewrite<= sub-neg_binary64 (-.f64 y 1))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (-.f64 y x) (-.f64 y 1)))): 0 points increase in error, 0 points decrease in error
   (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (-.f64 y x) (-.f64 y 1))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 y x)) (*.f64 -1 (-.f64 y 1)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (*.f64 -1 (-.f64 y x)) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 y 1)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (*.f64 -1 (-.f64 y x)) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 y 1)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (*.f64 -1 (-.f64 y x)) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 y) 1))): 0 points increase in error, 0 points decrease in error
   (/.f64 (*.f64 -1 (-.f64 y x)) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 y)) 1)): 0 points increase in error, 0 points decrease in error
   (/.f64 (*.f64 -1 (-.f64 y x)) (Rewrite<= +-commutative_binary64 (+.f64 1 (neg.f64 y)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (*.f64 -1 (-.f64 y x)) (Rewrite<= sub-neg_binary64 (-.f64 1 y))): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 y x))) (-.f64 1 y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 y x))) (-.f64 1 y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 y) x)) (-.f64 1 y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 y)) x) (-.f64 1 y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 x (neg.f64 y))) (-.f64 1 y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x y)) (-.f64 1 y)): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	9.4
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -218.53919179681262:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.751493842131984 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2574566598129833 \cdot 10^{-139}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.193297866889741 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	9.2
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := x + y \cdot x\\ \mathbf{if}\;y \leq -218.53919179681262:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.751493842131984 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2574566598129833 \cdot 10^{-139}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.193297866889741 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -218.53919179681262:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.193297866889741 \cdot 10^{-8}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	17.2
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -127503433539.99725:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.751493842131984 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2574566598129833 \cdot 10^{-139}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.193297866889741 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	1.3
Cost	584

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -218.53919179681262:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.193297866889741 \cdot 10^{-8}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	16.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -127503433539.99725:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.193297866889741 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))