Average Error: 1.2 → 1.0
Time: 9.8s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\frac{\sqrt[3]{z - t}}{\frac{\sqrt[3]{a - t}}{y}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\right) + x\]
x + y \cdot \frac{z - t}{a - t}
↓
\frac{\sqrt[3]{z - t}}{\frac{\sqrt[3]{a - t}}{y}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\right) + x
double f(double x, double y, double z, double t, double a) {
        double r9813668 = x;
        double r9813669 = y;
        double r9813670 = z;
        double r9813671 = t;
        double r9813672 = r9813670 - r9813671;
        double r9813673 = a;
        double r9813674 = r9813673 - r9813671;
        double r9813675 = r9813672 / r9813674;
        double r9813676 = r9813669 * r9813675;
        double r9813677 = r9813668 + r9813676;
        return r9813677;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r9813678 = z;
        double r9813679 = t;
        double r9813680 = r9813678 - r9813679;
        double r9813681 = cbrt(r9813680);
        double r9813682 = a;
        double r9813683 = r9813682 - r9813679;
        double r9813684 = cbrt(r9813683);
        double r9813685 = y;
        double r9813686 = r9813684 / r9813685;
        double r9813687 = r9813681 / r9813686;
        double r9813688 = r9813681 / r9813684;
        double r9813689 = r9813688 * r9813688;
        double r9813690 = r9813687 * r9813689;
        double r9813691 = x;
        double r9813692 = r9813690 + r9813691;
        return r9813692;
}

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
Target0.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.2

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

  2. Simplified1.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y, x\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity1.2

    \[\leadsto \mathsf{fma}\left(\frac{z - t}{\color{blue}{1 \cdot \left(a - t\right)}}, y, x\right)\]

  5. Applied add-cube-cbrt1.8

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

  6. Applied times-frac1.7

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

  7. Simplified1.7

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

  9. Applied fma-udef1.7

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

  10. Simplified2.9

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

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

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

  13. Applied add-cube-cbrt3.3

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

  14. Applied times-frac3.3

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

  15. Applied add-cube-cbrt3.3

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

  16. Applied times-frac1.0

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

  17. Simplified1.0

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

  18. Final simplification1.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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)))))