Average Error: 10.0 → 1.0
Time: 22.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{a - z}}{t}} + x\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{a - z}}{t}} + x
double f(double x, double y, double z, double t, double a) {
        double r28985714 = x;
        double r28985715 = y;
        double r28985716 = z;
        double r28985717 = r28985715 - r28985716;
        double r28985718 = t;
        double r28985719 = r28985717 * r28985718;
        double r28985720 = a;
        double r28985721 = r28985720 - r28985716;
        double r28985722 = r28985719 / r28985721;
        double r28985723 = r28985714 + r28985722;
        return r28985723;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28985724 = y;
        double r28985725 = z;
        double r28985726 = r28985724 - r28985725;
        double r28985727 = cbrt(r28985726);
        double r28985728 = a;
        double r28985729 = r28985728 - r28985725;
        double r28985730 = cbrt(r28985729);
        double r28985731 = r28985727 / r28985730;
        double r28985732 = r28985731 * r28985731;
        double r28985733 = t;
        double r28985734 = r28985730 / r28985733;
        double r28985735 = r28985727 / r28985734;
        double r28985736 = r28985732 * r28985735;
        double r28985737 = x;
        double r28985738 = r28985736 + r28985737;
        return r28985738;
}

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

Original10.0
Target0.6
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.0

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

  3. Applied associate-/l*2.9

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

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

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

  6. Applied add-cube-cbrt3.3

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

  7. Applied times-frac3.4

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

  8. Applied add-cube-cbrt3.3

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

  9. Applied times-frac1.0

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

  10. Simplified1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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