Average Error: 33.6 → 0.5
Time: 18.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}
double f(double x, double y, double z, double t) {
        double r489655 = x;
        double r489656 = r489655 * r489655;
        double r489657 = y;
        double r489658 = r489657 * r489657;
        double r489659 = r489656 / r489658;
        double r489660 = z;
        double r489661 = r489660 * r489660;
        double r489662 = t;
        double r489663 = r489662 * r489662;
        double r489664 = r489661 / r489663;
        double r489665 = r489659 + r489664;
        return r489665;
}
↓
double f(double x, double y, double z, double t) {
        double r489666 = x;
        double r489667 = y;
        double r489668 = r489666 / r489667;
        double r489669 = fabs(r489668);
        double r489670 = sqrt(r489669);
        double r489671 = 1.5;
        double r489672 = pow(r489669, r489671);
        double r489673 = r489670 * r489672;
        double r489674 = z;
        double r489675 = t;
        double r489676 = r489674 / r489675;
        double r489677 = fabs(r489676);
        double r489678 = sqrt(r489677);
        double r489679 = pow(r489677, r489671);
        double r489680 = r489678 * r489679;
        double r489681 = r489673 + r489680;
        return r489681;
}

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. Simplified18.7

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

  7. Applied add-sqr-sqrt18.8

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

  8. Simplified18.7

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*l*0.5

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

  13. Simplified0.5

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

  15. Applied add-sqr-sqrt0.5

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

  16. Applied associate-*l*0.5

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

  17. Simplified0.5

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

  18. Final simplification0.5

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

Reproduce

herbie shell --seed 2019323 
(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))))