Average Error: 9.8 → 0.2
Time: 2.5min
Precision: binary64
Cost: 320
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{x}{y}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{x}{y}}{y}
(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y) :precision binary64 (/ (/ x y) y))
double code(double x, double y) {
	return x / (y * y);
}
↓
double code(double x, double y) {
	return (x / y) / y;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.8
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Alternatives

Alternative 1
Error9.8
Cost320
\[\frac{x}{y \cdot y}\]
Alternative 2
Error41.1
Cost64
\[0\]
Alternative 3
Error61.9
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 9.8

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

  3. Applied associate-/r*_binary64_119570.2

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}}\]
  4. Using strategy rm

  5. Applied frac-2neg_binary64_120240.2

    \[\leadsto \color{blue}{\frac{-\frac{x}{y}}{-y}}\]
  6. Using strategy rm

  7. Applied pow1_binary64_120740.2

    \[\leadsto \color{blue}{{\left(\frac{-\frac{x}{y}}{-y}\right)}^{1}}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity_binary64_120130.2

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

  10. Applied *-un-lft-identity_binary64_120130.2

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

  11. Applied times-frac_binary64_120190.2

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

  12. Simplified0.2

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

  13. Simplified0.2

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

  14. Simplified0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}}\]

  15. Final simplification0.2

    \[\leadsto \frac{\frac{x}{y}}{y}\]

Reproduce

herbie shell --seed 2021040 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))