Average Error: 11.2 → 0.5
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r568496 = x;
        double r568497 = y;
        double r568498 = z;
        double r568499 = t;
        double r568500 = r568498 - r568499;
        double r568501 = r568497 * r568500;
        double r568502 = a;
        double r568503 = r568502 - r568499;
        double r568504 = r568501 / r568503;
        double r568505 = r568496 + r568504;
        return r568505;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r568506 = x;
        double r568507 = z;
        double r568508 = t;
        double r568509 = r568507 - r568508;
        double r568510 = cbrt(r568509);
        double r568511 = r568510 * r568510;
        double r568512 = a;
        double r568513 = r568512 - r568508;
        double r568514 = cbrt(r568513);
        double r568515 = r568514 * r568514;
        double r568516 = r568511 / r568515;
        double r568517 = y;
        double r568518 = r568514 / r568510;
        double r568519 = r568517 / r568518;
        double r568520 = r568516 * r568519;
        double r568521 = r568506 + r568520;
        return r568521;
}

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

Original11.2
Target1.3
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.2

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

  3. Applied associate-/l*1.3

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

  5. Applied add-cube-cbrt1.8

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

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

  8. Applied *-un-lft-identity1.7

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

  9. Applied times-frac0.5

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

  10. Simplified0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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