Average Error: 33.4 → 0.7
Time: 22.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\frac{\sqrt[3]{z}}{t}}\right) \cdot \frac{z}{t}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} + \frac{x}{y} \cdot \frac{x}{y}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\frac{\sqrt[3]{z}}{t}}\right) \cdot \frac{z}{t}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} + \frac{x}{y} \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r29396183 = x;
        double r29396184 = r29396183 * r29396183;
        double r29396185 = y;
        double r29396186 = r29396185 * r29396185;
        double r29396187 = r29396184 / r29396186;
        double r29396188 = z;
        double r29396189 = r29396188 * r29396188;
        double r29396190 = t;
        double r29396191 = r29396190 * r29396190;
        double r29396192 = r29396189 / r29396191;
        double r29396193 = r29396187 + r29396192;
        return r29396193;
}
↓
double f(double x, double y, double z, double t) {
        double r29396194 = z;
        double r29396195 = cbrt(r29396194);
        double r29396196 = r29396195 * r29396195;
        double r29396197 = cbrt(r29396196);
        double r29396198 = t;
        double r29396199 = r29396195 / r29396198;
        double r29396200 = cbrt(r29396199);
        double r29396201 = r29396197 * r29396200;
        double r29396202 = r29396194 / r29396198;
        double r29396203 = r29396201 * r29396202;
        double r29396204 = r29396202 * r29396202;
        double r29396205 = cbrt(r29396204);
        double r29396206 = r29396203 * r29396205;
        double r29396207 = x;
        double r29396208 = y;
        double r29396209 = r29396207 / r29396208;
        double r29396210 = r29396209 * r29396209;
        double r29396211 = r29396206 + r29396210;
        return r29396211;
}

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
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.4

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

  2. Simplified0.4

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

  4. Applied add-cube-cbrt0.8

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

  5. Applied associate-*l*0.8

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

  7. Applied cbrt-unprod0.6

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

  9. Applied *-un-lft-identity0.6

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

  10. Applied add-cube-cbrt0.7

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

  11. Applied times-frac0.7

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

  12. Applied cbrt-prod0.7

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

  13. Simplified0.7

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

  14. Final simplification0.7

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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