Average Error: 33.0 → 0.8
Time: 3.9s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \left(\sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}} \cdot \sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}}\right) + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \left(\sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}} \cdot \sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}}\right) + \frac{z}{t} \cdot \frac{z}{t}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x * x)) / ((double) (y * y)))) + ((double) (((double) (z * z)) / ((double) (t * t))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) cbrt(((double) (((double) (x / y)) * ((double) (x / y)))))) * ((double) cbrt(((double) (((double) (x / y)) * ((double) (x / y)))))))) * ((double) (((double) sqrt(((double) cbrt(((double) (((double) (x / y)) * ((double) (x / y)))))))) * ((double) sqrt(((double) cbrt(((double) (((double) (x / y)) * ((double) (x / y)))))))))))) + ((double) (((double) (z / t)) * ((double) (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

Original33.0
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.0

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

  3. Applied times-frac18.8

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  9. Applied add-sqr-sqrt0.8

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

  10. Final simplification0.8

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

Reproduce

herbie shell --seed 2020124 
(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) 2.0) (pow (/ z t) 2.0))

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