Average Error: 33.8 → 1.0
Time: 5.2s
Precision: binary64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right)\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{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))
  (*
   (pow (cbrt (/ z t)) 4.0)
   (*
    (cbrt (/ z t))
    (* (cbrt (/ 1.0 (* (cbrt t) (cbrt t)))) (cbrt (/ z (cbrt 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 ((x / y) * (x / y)) + (pow(cbrt(z / t), 4.0) * (cbrt(z / t) * (cbrt(1.0 / (cbrt(t) * cbrt(t))) * cbrt(z / 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

Original33.8
Target0.4
Herbie1.0
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

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

  3. Applied times-frac_binary6418.9

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

  5. Applied times-frac_binary640.4

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

  7. Applied add-cube-cbrt_binary640.8

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

  8. Applied add-cube-cbrt_binary641.1

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

  9. Applied swap-sqr_binary641.1

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

  10. Simplified1.1

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{{\left(\sqrt[3]{\frac{z}{t}}\right)}^{4}} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right)\]
  11. Using strategy rm

  12. Applied add-cube-cbrt_binary641.0

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}}\right)\]

  13. Applied *-un-lft-identity_binary641.0

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{\color{blue}{1 \cdot z}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\right)\]

  14. Applied times-frac_binary641.0

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\color{blue}{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}}\right)\]

  15. Applied cbrt-prod_binary641.0

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \color{blue}{\left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right)}\right)\]

  16. Final simplification1.0

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt[3]{\frac{z}{t}}\right)}^{4} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right)\right)\]

Reproduce

herbie shell --seed 2020224 
(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))))