Average Error: 1.4 → 0.8
Time: 14.2s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r381582 = x;
        double r381583 = y;
        double r381584 = z;
        double r381585 = t;
        double r381586 = r381584 - r381585;
        double r381587 = a;
        double r381588 = r381584 - r381587;
        double r381589 = r381586 / r381588;
        double r381590 = r381583 * r381589;
        double r381591 = r381582 + r381590;
        return r381591;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r381592 = y;
        double r381593 = cbrt(r381592);
        double r381594 = r381593 * r381593;
        double r381595 = z;
        double r381596 = a;
        double r381597 = r381595 - r381596;
        double r381598 = cbrt(r381597);
        double r381599 = r381598 * r381598;
        double r381600 = t;
        double r381601 = r381595 - r381600;
        double r381602 = cbrt(r381601);
        double r381603 = r381602 * r381602;
        double r381604 = r381599 / r381603;
        double r381605 = r381594 / r381604;
        double r381606 = r381598 / r381602;
        double r381607 = r381593 / r381606;
        double r381608 = r381605 * r381607;
        double r381609 = x;
        double r381610 = r381608 + r381609;
        return r381610;
}

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

Original1.4
Target1.3
Herbie0.8
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied clear-num1.4

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied pow11.4

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

  6. Applied pow11.4

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

  7. Applied pow-prod-down1.4

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

  8. Simplified1.3

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

  10. Applied add-cube-cbrt1.8

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

  11. Applied add-cube-cbrt1.6

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

  12. Applied times-frac1.6

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

  13. Applied add-cube-cbrt1.9

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

  14. Applied times-frac0.8

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

  15. Final simplification0.8

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

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)))))