Average Error: 1.2 → 0.5
Time: 12.9s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\]
x + y \cdot \frac{z - t}{a - t}
↓
x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}
double f(double x, double y, double z, double t, double a) {
        double r405022 = x;
        double r405023 = y;
        double r405024 = z;
        double r405025 = t;
        double r405026 = r405024 - r405025;
        double r405027 = a;
        double r405028 = r405027 - r405025;
        double r405029 = r405026 / r405028;
        double r405030 = r405023 * r405029;
        double r405031 = r405022 + r405030;
        return r405031;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r405032 = x;
        double r405033 = y;
        double r405034 = z;
        double r405035 = t;
        double r405036 = r405034 - r405035;
        double r405037 = cbrt(r405036);
        double r405038 = r405037 * r405037;
        double r405039 = a;
        double r405040 = r405039 - r405035;
        double r405041 = cbrt(r405040);
        double r405042 = r405041 * r405041;
        double r405043 = r405038 / r405042;
        double r405044 = r405033 * r405043;
        double r405045 = r405037 / r405041;
        double r405046 = r405044 * r405045;
        double r405047 = r405032 + r405046;
        return r405047;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.2

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

  3. Applied add-cube-cbrt1.8

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

  4. Applied add-cube-cbrt1.6

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

  5. Applied times-frac1.6

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

  6. Applied associate-*r*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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