Average Error: 10.9 → 1.4
Time: 14.5s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \frac{y - z}{\left(\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right) \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \frac{y - z}{\left(\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right) \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}
double f(double x, double y, double z, double t, double a) {
        double r386043 = x;
        double r386044 = y;
        double r386045 = z;
        double r386046 = r386044 - r386045;
        double r386047 = t;
        double r386048 = r386046 * r386047;
        double r386049 = a;
        double r386050 = r386049 - r386045;
        double r386051 = r386048 / r386050;
        double r386052 = r386043 + r386051;
        return r386052;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r386053 = x;
        double r386054 = t;
        double r386055 = cbrt(r386054);
        double r386056 = r386055 * r386055;
        double r386057 = y;
        double r386058 = z;
        double r386059 = r386057 - r386058;
        double r386060 = a;
        double r386061 = r386060 - r386058;
        double r386062 = cbrt(r386061);
        double r386063 = r386062 * r386062;
        double r386064 = cbrt(r386063);
        double r386065 = cbrt(r386062);
        double r386066 = r386064 * r386065;
        double r386067 = r386066 * r386062;
        double r386068 = r386059 / r386067;
        double r386069 = r386056 * r386068;
        double r386070 = r386055 / r386062;
        double r386071 = r386069 * r386070;
        double r386072 = r386053 + r386071;
        return r386072;
}

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

Original10.9
Target0.5
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.9

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

  3. Applied add-cube-cbrt11.3

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

  4. Applied times-frac1.7

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

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

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

  7. Applied cbrt-prod1.7

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

  8. Applied add-cube-cbrt1.8

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

  9. Applied times-frac1.8

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

  10. Applied associate-*r*1.4

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

  11. Simplified1.4

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

  13. Applied add-cube-cbrt1.4

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

  14. Applied cbrt-prod1.4

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

  15. Final simplification1.4

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :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))))