Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B

Average Error: 0.4 → 0.4

Time: 30.1s

Precision: binary64

Cost: 7232

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.4
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 0.4

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

2. Applied egg-rr 0.4

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

Alternatives

Alternative 1
Error	27.6
Cost	7380

\[\begin{array}{l} t_0 := -3 \cdot \sqrt{x}\\ t_1 := \left(y \cdot 3\right) \cdot \sqrt{x}\\ t_2 := 0.3333333333333333 \cdot \frac{\sqrt{x}}{x}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.08 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	27.6
Cost	7380

\[\begin{array}{l} t_0 := -3 \cdot \sqrt{x}\\ t_1 := 0.3333333333333333 \cdot \frac{\sqrt{x}}{x}\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+90}:\\ \;\;\;\;\left(y \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 3
Error	27.6
Cost	7380

\[\begin{array}{l} t_0 := -3 \cdot \sqrt{x}\\ t_1 := \frac{0.3333333333333333}{x} \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -4.15 \cdot 10^{+92}:\\ \;\;\;\;\left(y \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 4
Error	27.6
Cost	7380

\[\begin{array}{l} t_0 := -3 \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;\left(y \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{0.3333333333333333}{x} \cdot \sqrt{x}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-273}:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 5
Error	27.5
Cost	7380

\[\begin{array}{l} t_0 := -3 \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+91}:\\ \;\;\;\;\left(y \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{\sqrt{x}}{3}}{x}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-271}:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 6
Error	27.6
Cost	7380

\[\begin{array}{l} t_0 := -3 \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -1.58 \cdot 10^{+90}:\\ \;\;\;\;\left(y \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{\sqrt{x}}{x}}{3}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-273}:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 7
Error	1.2
Cost	7240

\[\begin{array}{l} t_0 := 3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{0.1111111111111111}{x}\right)\right)\\ \mathbf{if}\;y \leq -15.2:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\left(\frac{0.3333333333333333}{x} - 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	1.2
Cost	7240

\[\begin{array}{l} t_0 := y + \frac{0.1111111111111111}{x}\\ \mathbf{if}\;y \leq -15.2:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot t_0\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\left(\frac{0.3333333333333333}{x} - 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 9
Error	0.4
Cost	7232

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

Alternative 10
Error	11.3
Cost	7112

\[\begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+90}:\\ \;\;\;\;\left(y \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-36}:\\ \;\;\;\;\left(\frac{0.3333333333333333}{x} - 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + -1\right) \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]

Alternative 11
Error	0.4
Cost	7104

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

Alternative 12
Error	0.4
Cost	7104

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

Alternative 13
Error	0.4
Cost	7104

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

Alternative 14
Error	10.4
Cost	6980

\[\begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{\sqrt{x}}{x}}{3}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 15
Error	22.3
Cost	6852

\[\begin{array}{l} \mathbf{if}\;x \leq 120:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\sqrt{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \]

Alternative 16
Error	47.0
Cost	6592

\[-3 \cdot \sqrt{x} \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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