Average Error: 10.9 → 1.4
Time: 9.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{1}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \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}}
double f(double x, double y, double z, double t, double a) {
        double r357560 = x;
        double r357561 = y;
        double r357562 = z;
        double r357563 = r357561 - r357562;
        double r357564 = t;
        double r357565 = r357563 * r357564;
        double r357566 = a;
        double r357567 = r357566 - r357562;
        double r357568 = r357565 / r357567;
        double r357569 = r357560 + r357568;
        return r357569;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r357570 = x;
        double r357571 = y;
        double r357572 = z;
        double r357573 = r357571 - r357572;
        double r357574 = a;
        double r357575 = r357574 - r357572;
        double r357576 = cbrt(r357575);
        double r357577 = r357576 * r357576;
        double r357578 = r357573 / r357577;
        double r357579 = t;
        double r357580 = cbrt(r357579);
        double r357581 = r357580 * r357580;
        double r357582 = 1.0;
        double r357583 = cbrt(r357582);
        double r357584 = r357581 / r357583;
        double r357585 = r357578 * r357584;
        double r357586 = r357580 / r357576;
        double r357587 = r357585 * r357586;
        double r357588 = r357570 + r357587;
        return r357588;
}

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. Final simplification1.4

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

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))))