Average Error: 9.9 → 0.5
Time: 13.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r11626661 = x;
        double r11626662 = y;
        double r11626663 = z;
        double r11626664 = t;
        double r11626665 = r11626663 - r11626664;
        double r11626666 = r11626662 * r11626665;
        double r11626667 = a;
        double r11626668 = r11626663 - r11626667;
        double r11626669 = r11626666 / r11626668;
        double r11626670 = r11626661 + r11626669;
        return r11626670;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r11626671 = 1.0;
        double r11626672 = z;
        double r11626673 = a;
        double r11626674 = r11626672 - r11626673;
        double r11626675 = cbrt(r11626674);
        double r11626676 = t;
        double r11626677 = r11626672 - r11626676;
        double r11626678 = cbrt(r11626677);
        double r11626679 = r11626675 / r11626678;
        double r11626680 = r11626679 * r11626679;
        double r11626681 = r11626671 / r11626680;
        double r11626682 = y;
        double r11626683 = r11626682 / r11626679;
        double r11626684 = r11626681 * r11626683;
        double r11626685 = x;
        double r11626686 = r11626684 + r11626685;
        return r11626686;
}

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

Original9.9
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 9.9

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

  3. Applied associate-/l*1.2

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

  5. Applied add-cube-cbrt1.7

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

  6. Applied add-cube-cbrt1.6

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

  7. Applied times-frac1.6

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

  8. Applied *-un-lft-identity1.6

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

  9. Applied times-frac0.5

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

  10. Simplified0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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