Average Error: 0.2 → 0.2
Time: 26.2s
Precision: binary64
Cost: 7360
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{-1}{\sqrt{x}} \cdot \frac{y}{-3} \]
(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))) (* (/ -1.0 (sqrt x)) (/ y -3.0))))
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))) - ((-1.0 / sqrt(x)) * (y / -3.0));
}

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))) - (((-1.0d0) / sqrt(x)) * (y / (-3.0d0)))
end function

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))) - ((-1.0 / Math.sqrt(x)) * (y / -3.0));
}

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))) - ((-1.0 / math.sqrt(x)) * (y / -3.0))

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(-1.0 / sqrt(x)) * Float64(y / -3.0)))
end

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))) - ((-1.0 / sqrt(x)) * (y / -3.0));
end

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[(-1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(y / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

Derivation

  1. Initial program 0.2

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

  2. Applied egg-rr0.2

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

Alternatives

Alternative 1
Error0.3
Cost7232
\[\left(1 - \frac{0.3333333333333333}{x \cdot 3}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
Alternative 2
Error0.2
Cost7232
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{0.3333333333333333}{\sqrt{x}} \cdot y \]
Alternative 3
Error0.2
Cost7232
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
Alternative 4
Error3.9
Cost7112
\[\begin{array}{l} t_0 := 1 - 0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+38}:\\ \;\;\;\;1 - \frac{1}{\left(x \cdot 3\right) \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error0.4
Cost7104
\[1 - 0.3333333333333333 \cdot \left(\frac{y}{\sqrt{x}} + \frac{0.3333333333333333}{x}\right) \]
Alternative 6
Error0.2
Cost7104
\[\frac{y}{-3 \cdot \sqrt{x}} - \left(\frac{0.1111111111111111}{x} + -1\right) \]
Alternative 7
Error5.3
Cost6984
\[\begin{array}{l} t_0 := -0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+61}:\\ \;\;\;\;1 - \frac{1}{\left(x \cdot 3\right) \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error5.3
Cost6984
\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{-3 \cdot \sqrt{x}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;1 - \frac{1}{\left(x \cdot 3\right) \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\\ \end{array} \]
Alternative 9
Error5.3
Cost6984
\[\begin{array}{l} t_0 := \frac{\frac{y}{\sqrt{x}}}{-3}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;1 - \frac{1}{\left(x \cdot 3\right) \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 10
Error21.2
Cost576
\[1 - \frac{1}{\left(x \cdot 3\right) \cdot 3} \]
Alternative 11
Error21.9
Cost452
\[\begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\frac{1}{x} \cdot -0.1111111111111111\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 12
Error21.2
Cost448
\[1 - 0.1111111111111111 \cdot \frac{1}{x} \]
Alternative 13
Error21.2
Cost448
\[1 - \frac{1}{\frac{x}{0.1111111111111111}} \]
Alternative 14
Error21.9
Cost324
\[\begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 15
Error21.2
Cost320
\[1 - \frac{0.1111111111111111}{x} \]
Alternative 16
Error41.8
Cost64
\[1 \]

Error

Reproduce

herbie shell --seed 2023010 
(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)))))