Average Error: 33.4 → 1.1
Time: 4.4s
Precision: binary64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}
(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))
  (*
   (/ z (* (cbrt t) (cbrt t)))
   (/ (/ z (* (cbrt t) (cbrt t))) (* (cbrt t) (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)) + ((z / (cbrt(t) * cbrt(t))) * ((z / (cbrt(t) * cbrt(t))) / (cbrt(t) * 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

Original33.4
Target0.4
Herbie1.1
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.4

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

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

  8. Applied add-sqr-sqrt_binary6432.9

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

  9. Applied times-frac_binary6432.9

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

  10. Applied add-cube-cbrt_binary6433.0

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

  11. Applied add-sqr-sqrt_binary6433.0

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

  12. Applied times-frac_binary6433.0

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

  13. Applied swap-sqr_binary6433.0

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

  14. Simplified33.0

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

  15. Simplified1.1

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

  16. Final simplification1.1

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\]

Reproduce

herbie shell --seed 2020220 
(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))))