Average Error: 1.4 → 1.0
Time: 12.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z - a}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z - a}}
double f(double x, double y, double z, double t, double a) {
        double r364595 = x;
        double r364596 = y;
        double r364597 = z;
        double r364598 = t;
        double r364599 = r364597 - r364598;
        double r364600 = a;
        double r364601 = r364597 - r364600;
        double r364602 = r364599 / r364601;
        double r364603 = r364596 * r364602;
        double r364604 = r364595 + r364603;
        return r364604;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r364605 = x;
        double r364606 = z;
        double r364607 = t;
        double r364608 = r364606 - r364607;
        double r364609 = y;
        double r364610 = cbrt(r364609);
        double r364611 = r364610 * r364610;
        double r364612 = a;
        double r364613 = r364606 - r364612;
        double r364614 = cbrt(r364613);
        double r364615 = r364614 * r364614;
        double r364616 = r364611 / r364615;
        double r364617 = r364608 * r364616;
        double r364618 = r364610 / r364614;
        double r364619 = r364617 * r364618;
        double r364620 = r364605 + r364619;
        return r364620;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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Results

Enter valid numbers for all inputs

Target

Original1.4
Target1.3
Herbie1.0
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied *-un-lft-identity1.4

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

  4. Applied associate-*l*1.4

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

  5. Simplified3.0

    \[\leadsto x + 1 \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{y}{z - a}\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt3.4

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

  8. Applied add-cube-cbrt3.6

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

  9. Applied times-frac3.6

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

  10. Applied associate-*r*1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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