Average Error: 34.0 → 0.9
Time: 5.9s
Precision: binary64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \left(\frac{z}{t} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right)\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \left(\frac{z}{t} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right)\right)
(FPCore (x y z t)
 :precision binary64
 (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  (* (/ x y) (/ x y))
  (*
   (/ (cbrt z) (cbrt t))
   (* (/ z t) (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t)))))))
double code(double x, double y, double z, double t) {
	return ((double) ((((double) (x * x)) / ((double) (y * y))) + (((double) (z * z)) / ((double) (t * t)))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) ((x / y) * (x / y))) + ((double) ((((double) cbrt(z)) / ((double) cbrt(t))) * ((double) ((z / t) * ((double) ((((double) cbrt(z)) / ((double) cbrt(t))) * (((double) cbrt(z)) / ((double) cbrt(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

Original34.0
Target0.4
Herbie0.9
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.0

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

  2. Simplified25.0

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

  4. Applied add-sqr-sqrt44.4

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

  5. Applied times-frac40.6

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

  6. Applied add-sqr-sqrt40.7

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

  7. Applied unswap-sqr38.9

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

  8. Simplified38.8

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

  9. Simplified13.3

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

  11. Applied add-sqr-sqrt38.7

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

  12. Applied times-frac34.1

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

  13. Applied add-sqr-sqrt34.1

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

  14. Applied unswap-sqr32.2

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

  15. Simplified32.1

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

  16. Simplified0.4

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

  18. Applied add-cube-cbrt0.8

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

  19. Applied add-cube-cbrt0.9

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

  20. Applied times-frac0.9

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

  21. Applied associate-*r*0.9

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

  22. Simplified0.9

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

  23. Final simplification0.9

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

Reproduce

herbie shell --seed 2020198 
(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))))