Average Error: 1.2 → 0.5
Time: 16.9s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} + x\]
x + y \cdot \frac{z - t}{a - t}
↓
\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r29356666 = x;
        double r29356667 = y;
        double r29356668 = z;
        double r29356669 = t;
        double r29356670 = r29356668 - r29356669;
        double r29356671 = a;
        double r29356672 = r29356671 - r29356669;
        double r29356673 = r29356670 / r29356672;
        double r29356674 = r29356667 * r29356673;
        double r29356675 = r29356666 + r29356674;
        return r29356675;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29356676 = y;
        double r29356677 = a;
        double r29356678 = t;
        double r29356679 = r29356677 - r29356678;
        double r29356680 = cbrt(r29356679);
        double r29356681 = z;
        double r29356682 = r29356681 - r29356678;
        double r29356683 = cbrt(r29356682);
        double r29356684 = r29356680 / r29356683;
        double r29356685 = r29356684 * r29356684;
        double r29356686 = r29356676 / r29356685;
        double r29356687 = r29356683 / r29356680;
        double r29356688 = r29356686 * r29356687;
        double r29356689 = x;
        double r29356690 = r29356688 + r29356689;
        return r29356690;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.2
Target0.5
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.2

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

  3. Applied add-cube-cbrt1.7

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

  4. Applied *-un-lft-identity1.7

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

  5. Applied times-frac1.7

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

  6. Applied associate-*r*2.3

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

  7. Simplified2.3

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

  9. Applied *-un-lft-identity2.3

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

  10. Applied cbrt-prod2.3

    \[\leadsto x + \frac{y}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{a - t}}}\]

  11. Applied add-cube-cbrt2.2

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

  12. Applied times-frac2.2

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

  13. Applied associate-*r*2.0

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

  14. Simplified0.5

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

  15. Final simplification0.5

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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