Average Error: 33.6 → 0.5
Time: 4.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}
double code(double x, double y, double z, double t) {
	return (((x * x) / (y * y)) + ((z * z) / (t * t)));
}
↓
double code(double x, double y, double z, double t) {
	return ((pow(fabs((x / y)), 1.5) * sqrt(fabs((x / y)))) + ((z / t) * (z / t)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.6
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.6

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

  3. Applied add-sqr-sqrt33.6

    \[\leadsto \color{blue}{\sqrt{\frac{x \cdot x}{y \cdot y}} \cdot \sqrt{\frac{x \cdot x}{y \cdot y}}} + \frac{z \cdot z}{t \cdot t}\]

  4. Simplified33.6

    \[\leadsto \color{blue}{\left|\frac{x}{y}\right|} \cdot \sqrt{\frac{x \cdot x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t}\]

  5. Simplified19.0

    \[\leadsto \left|\frac{x}{y}\right| \cdot \color{blue}{\left|\frac{x}{y}\right|} + \frac{z \cdot z}{t \cdot t}\]
  6. Using strategy rm

  7. Applied times-frac0.4

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \color{blue}{\frac{z}{t} \cdot \frac{z}{t}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.6

    \[\leadsto \color{blue}{{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
  12. Using strategy rm

  13. Applied pow1/20.6

    \[\leadsto {\color{blue}{\left({\left(\left|\frac{x}{y}\right|\right)}^{\frac{1}{2}}\right)}}^{3} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

  14. Applied pow-pow0.5

    \[\leadsto \color{blue}{{\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{1}{2} \cdot 3\right)}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

  15. Simplified0.5

    \[\leadsto {\left(\left|\frac{x}{y}\right|\right)}^{\color{blue}{\frac{3}{2}}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

  16. Final simplification0.5

    \[\leadsto {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))