Average Error: 0.3 → 0.5
Time: 2.0s
Precision: binary64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\left(x \cdot \left(\sqrt{100} \cdot \left|\sqrt[3]{100}\right|\right)\right) \cdot \frac{\sqrt{\sqrt[3]{100}}}{x + y}\]
\frac{x \cdot 100}{x + y}
↓
\left(x \cdot \left(\sqrt{100} \cdot \left|\sqrt[3]{100}\right|\right)\right) \cdot \frac{\sqrt{\sqrt[3]{100}}}{x + y}
double code(double x, double y) {
	return (((double) (x * 100.0)) / ((double) (x + y)));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * ((double) (((double) sqrt(100.0)) * ((double) fabs(((double) cbrt(100.0)))))))) * (((double) sqrt(((double) cbrt(100.0)))) / ((double) (x + 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

Original0.3
Target0.2
Herbie0.5
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program Error: 0.3 bits

    \[\frac{x \cdot 100}{x + y}\]

  2. SimplifiedError: 0.2 bits

    \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identityError: 0.2 bits

    \[\leadsto x \cdot \frac{100}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  5. Applied add-sqr-sqrtError: 0.2 bits

    \[\leadsto x \cdot \frac{\color{blue}{\sqrt{100} \cdot \sqrt{100}}}{1 \cdot \left(x + y\right)}\]

  6. Applied times-fracError: 0.3 bits

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt{100}}{1} \cdot \frac{\sqrt{100}}{x + y}\right)}\]

  7. Applied associate-*r*Error: 0.4 bits

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt{100}}{1}\right) \cdot \frac{\sqrt{100}}{x + y}}\]

  8. SimplifiedError: 0.4 bits

    \[\leadsto \color{blue}{\left(x \cdot \sqrt{100}\right)} \cdot \frac{\sqrt{100}}{x + y}\]
  9. Using strategy rm

  10. Applied *-un-lft-identityError: 0.4 bits

    \[\leadsto \left(x \cdot \sqrt{100}\right) \cdot \frac{\sqrt{100}}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  11. Applied add-cube-cbrtError: 1.0 bits

    \[\leadsto \left(x \cdot \sqrt{100}\right) \cdot \frac{\sqrt{\color{blue}{\left(\sqrt[3]{100} \cdot \sqrt[3]{100}\right) \cdot \sqrt[3]{100}}}}{1 \cdot \left(x + y\right)}\]

  12. Applied sqrt-prodError: 0.4 bits

    \[\leadsto \left(x \cdot \sqrt{100}\right) \cdot \frac{\color{blue}{\sqrt{\sqrt[3]{100} \cdot \sqrt[3]{100}} \cdot \sqrt{\sqrt[3]{100}}}}{1 \cdot \left(x + y\right)}\]

  13. Applied times-fracError: 0.6 bits

    \[\leadsto \left(x \cdot \sqrt{100}\right) \cdot \color{blue}{\left(\frac{\sqrt{\sqrt[3]{100} \cdot \sqrt[3]{100}}}{1} \cdot \frac{\sqrt{\sqrt[3]{100}}}{x + y}\right)}\]

  14. Applied associate-*r*Error: 0.6 bits

    \[\leadsto \color{blue}{\left(\left(x \cdot \sqrt{100}\right) \cdot \frac{\sqrt{\sqrt[3]{100} \cdot \sqrt[3]{100}}}{1}\right) \cdot \frac{\sqrt{\sqrt[3]{100}}}{x + y}}\]

  15. SimplifiedError: 0.5 bits

    \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt{100} \cdot \left|\sqrt[3]{100}\right|\right)\right)} \cdot \frac{\sqrt{\sqrt[3]{100}}}{x + y}\]

  16. Final simplificationError: 0.5 bits

    \[\leadsto \left(x \cdot \left(\sqrt{100} \cdot \left|\sqrt[3]{100}\right|\right)\right) \cdot \frac{\sqrt{\sqrt[3]{100}}}{x + y}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))