Average Error: 0.2 → 0.2
Time: 3.7s
Precision: binary64
Cost: 7232
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\sqrt{x} \cdot 3}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\sqrt{x} \cdot 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)) (/ y (* (sqrt x) 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)) - (y / (sqrt(x) * 3.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Alternatives

Alternative 1
Error0.2
Cost7104
\[\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{y}{\sqrt{x} \cdot 3}\]
Alternative 2
Error0.2
Cost7104
\[\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
Alternative 3
Error0.3
Cost7104
\[\left(1 - \frac{0.1111111111111111}{x}\right) - 0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\]
Alternative 4
Error1.0
Cost7297
\[\begin{array}{l} \mathbf{if}\;x \leq 0.1094437204698468:\\ \;\;\;\;\frac{-0.1111111111111111}{x} - \frac{y}{\sqrt{x} \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{3}}{\sqrt{x}}\\ \end{array}\]
Alternative 5
Error1.0
Cost7297
\[\begin{array}{l} \mathbf{if}\;x \leq 0.1094437204698468:\\ \;\;\;\;\frac{-0.1111111111111111}{x} - \frac{\frac{y}{3}}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{3}}{\sqrt{x}}\\ \end{array}\]
Alternative 6
Error21.4
Cost6848
\[1 - \frac{y}{\sqrt{x} \cdot 3}\]
Alternative 7
Error21.4
Cost6848
\[1 - \frac{\frac{y}{3}}{\sqrt{x}}\]
Alternative 8
Error42.5
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*_binary64_116160.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2021044 
(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)))))