Average Error: 0.5 → 0
Time: 701.0ms
Precision: binary64
\[\frac{1}{x \cdot x}\]
↓
\[{x}^{-2}\]
\frac{1}{x \cdot x}
↓
{x}^{-2}
(FPCore (x) :precision binary64 (/ 1.0 (* x x)))
↓
(FPCore (x) :precision binary64 (pow x -2.0))
double code(double x) {
	return 1.0 / (x * x);
}
↓
double code(double x) {
	return pow(x, -2.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.2
Herbie0
\[\frac{\frac{1}{x}}{x}\]

Derivation

  1. Initial program 0.5

    \[\frac{1}{x \cdot x}\]
  2. Using strategy rm

  3. Applied pow1_binary640.5

    \[\leadsto \frac{1}{x \cdot \color{blue}{{x}^{1}}}\]

  4. Applied pow1_binary640.5

    \[\leadsto \frac{1}{\color{blue}{{x}^{1}} \cdot {x}^{1}}\]

  5. Applied pow-prod-up_binary640.5

    \[\leadsto \frac{1}{\color{blue}{{x}^{\left(1 + 1\right)}}}\]

  6. Applied pow-flip_binary640

    \[\leadsto \color{blue}{{x}^{\left(-\left(1 + 1\right)\right)}}\]

  7. Simplified0

    \[\leadsto {x}^{\color{blue}{-2}}\]

  8. Final simplification0

    \[\leadsto {x}^{-2}\]

Reproduce

herbie shell --seed 2020224 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))