Average Error: 16.2 → 7.8
Time: 8.5s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{z - t}}}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\right)\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{z - t}}}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r600631 = x;
        double r600632 = y;
        double r600633 = r600631 + r600632;
        double r600634 = z;
        double r600635 = t;
        double r600636 = r600634 - r600635;
        double r600637 = r600636 * r600632;
        double r600638 = a;
        double r600639 = r600638 - r600635;
        double r600640 = r600637 / r600639;
        double r600641 = r600633 - r600640;
        return r600641;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r600642 = x;
        double r600643 = y;
        double r600644 = z;
        double r600645 = t;
        double r600646 = r600644 - r600645;
        double r600647 = cbrt(r600646);
        double r600648 = r600647 * r600647;
        double r600649 = a;
        double r600650 = r600649 - r600645;
        double r600651 = cbrt(r600650);
        double r600652 = r600648 / r600651;
        double r600653 = cbrt(r600647);
        double r600654 = r600653 * r600653;
        double r600655 = cbrt(r600651);
        double r600656 = r600655 * r600655;
        double r600657 = r600654 / r600656;
        double r600658 = r600653 / r600655;
        double r600659 = r600643 / r600651;
        double r600660 = r600658 * r600659;
        double r600661 = r600657 * r600660;
        double r600662 = r600652 * r600661;
        double r600663 = r600643 - r600662;
        double r600664 = r600642 + r600663;
        return r600664;
}

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

Original16.2
Target8.7
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Initial program 16.2

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

  3. Applied add-cube-cbrt16.3

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

  4. Applied times-frac11.7

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

  6. Applied add-cube-cbrt11.7

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

  7. Applied times-frac11.7

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

  8. Applied associate-*l*11.0

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

  10. Applied associate--l+7.7

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

  12. Applied add-cube-cbrt10.4

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

  13. Applied add-cube-cbrt7.8

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

  14. Applied times-frac7.8

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

  15. Applied associate-*l*7.8

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

  16. Final simplification7.8

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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