Average Error: 2.2 → 1.5
Time: 44.8s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\left(\left(\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot \sqrt[3]{z - t} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\left(\left(\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot \sqrt[3]{z - t} + t
double f(double x, double y, double z, double t) {
        double r410461 = x;
        double r410462 = y;
        double r410463 = r410461 / r410462;
        double r410464 = z;
        double r410465 = t;
        double r410466 = r410464 - r410465;
        double r410467 = r410463 * r410466;
        double r410468 = r410467 + r410465;
        return r410468;
}
↓
double f(double x, double y, double z, double t) {
        double r410469 = z;
        double r410470 = t;
        double r410471 = r410469 - r410470;
        double r410472 = cbrt(r410471);
        double r410473 = r410472 * r410472;
        double r410474 = cbrt(r410473);
        double r410475 = cbrt(r410472);
        double r410476 = r410474 * r410475;
        double r410477 = r410472 * r410476;
        double r410478 = x;
        double r410479 = cbrt(r410478);
        double r410480 = r410479 * r410479;
        double r410481 = y;
        double r410482 = cbrt(r410481);
        double r410483 = r410482 * r410482;
        double r410484 = r410480 / r410483;
        double r410485 = r410477 * r410484;
        double r410486 = r410479 / r410482;
        double r410487 = r410485 * r410486;
        double r410488 = r410487 * r410472;
        double r410489 = r410488 + r410470;
        return r410489;
}

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

Original2.2
Target2.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.2

    \[\frac{x}{y} \cdot \left(z - t\right) + t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.8

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

  4. Applied associate-*r*2.8

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

  5. Simplified2.8

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

  7. Applied add-cube-cbrt2.8

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

  8. Applied cbrt-prod2.8

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

  10. Applied add-cube-cbrt2.9

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

  11. Applied add-cube-cbrt3.0

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

  12. Applied times-frac3.0

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

  13. Applied associate-*r*1.5

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

  14. Final simplification1.5

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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