Average Error: 11.0 → 0.5
Time: 17.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot t\right)\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot t\right)
double f(double x, double y, double z, double t, double a) {
        double r40147318 = x;
        double r40147319 = y;
        double r40147320 = z;
        double r40147321 = r40147319 - r40147320;
        double r40147322 = t;
        double r40147323 = r40147321 * r40147322;
        double r40147324 = a;
        double r40147325 = r40147324 - r40147320;
        double r40147326 = r40147323 / r40147325;
        double r40147327 = r40147318 + r40147326;
        return r40147327;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r40147328 = x;
        double r40147329 = y;
        double r40147330 = z;
        double r40147331 = r40147329 - r40147330;
        double r40147332 = cbrt(r40147331);
        double r40147333 = r40147332 * r40147332;
        double r40147334 = a;
        double r40147335 = r40147334 - r40147330;
        double r40147336 = cbrt(r40147335);
        double r40147337 = r40147336 * r40147336;
        double r40147338 = r40147333 / r40147337;
        double r40147339 = r40147332 / r40147336;
        double r40147340 = t;
        double r40147341 = r40147339 * r40147340;
        double r40147342 = r40147338 * r40147341;
        double r40147343 = r40147328 + r40147342;
        return r40147343;
}

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

Original11.0
Target0.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*3.1

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

  5. Applied associate-/r/1.4

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

  7. Applied add-cube-cbrt1.9

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

  8. Applied add-cube-cbrt1.7

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

  9. Applied times-frac1.7

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

  10. Applied associate-*l*0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(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))))