Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D

Average Error: 0.2 → 0.2

Time: 1.8min

Precision: binary64

Cost: 7296

Math

\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

↓

\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{-3}}{-\sqrt{x}} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))

↓

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ (/ y -3.0) (- (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}

↓

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - ((y / -3.0) / -sqrt(x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - ((y / (-3.0d0)) / -sqrt(x))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}

↓

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - ((y / -3.0) / -Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))

↓

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - ((y / -3.0) / -math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end

↓

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(Float64(y / -3.0) / Float64(-sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end

↓

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - ((y / -3.0) / -sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / -3.0), $MachinePrecision] / (-N[Sqrt[x], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Target

Original	0.2
Target	0.2
Herbie	0.2

\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

Derivation

1. Initial program 0.2

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

2. Applied egg-rr 0.2

   \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \color{blue}{\frac{\frac{y}{-3}}{-\sqrt{x}}} \]

Alternatives

Alternative 1
Error	0.2
Cost	7232

\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

Alternative 2
Error	0.2
Cost	7232

\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{\sqrt{x}}}{3} \]

Alternative 3
Error	3.3
Cost	7112

\[\begin{array}{l} t_0 := 1 - \frac{y}{3 \cdot \sqrt{x}}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;1 - \frac{1}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.2
Cost	7104

\[\frac{y}{\sqrt{x} \cdot -3} - \left(\frac{0.1111111111111111}{x} + -1\right) \]

Alternative 5
Error	5.6
Cost	6984

\[\begin{array}{l} t_0 := -0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+60}:\\ \;\;\;\;1 - \frac{1}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	5.6
Cost	6984

\[\begin{array}{l} t_0 := \frac{-0.3333333333333333}{\sqrt{x}} \cdot y\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;1 - \frac{1}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	5.6
Cost	6984

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{-0.3333333333333333}{\sqrt{x}} \cdot y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;1 - \frac{1}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-3 \cdot \sqrt{x}}\\ \end{array} \]

Alternative 8
Error	5.5
Cost	6984

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{-0.3333333333333333}{\sqrt{x}} \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;1 - \frac{1}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{-3}}{\sqrt{x}}\\ \end{array} \]

Alternative 9
Error	5.6
Cost	6984

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{y}{\sqrt{x}}}{-3}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+60}:\\ \;\;\;\;1 - \frac{1}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{-3}}{\sqrt{x}}\\ \end{array} \]

Alternative 10
Error	21.2
Cost	448

\[1 - \frac{1}{x \cdot 9} \]

Alternative 11
Error	22.0
Cost	324

\[\begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12
Error	21.2
Cost	320

\[1 - \frac{0.1111111111111111}{x} \]

Alternative 13
Error	42.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))