Average Error: 10.8 → 0.6
Time: 8.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}
double f(double x, double y, double z, double t, double a) {
        double r683687 = x;
        double r683688 = y;
        double r683689 = z;
        double r683690 = t;
        double r683691 = r683689 - r683690;
        double r683692 = r683688 * r683691;
        double r683693 = a;
        double r683694 = r683693 - r683690;
        double r683695 = r683692 / r683694;
        double r683696 = r683687 + r683695;
        return r683696;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r683697 = x;
        double r683698 = y;
        double r683699 = z;
        double r683700 = t;
        double r683701 = r683699 - r683700;
        double r683702 = cbrt(r683701);
        double r683703 = r683702 * r683702;
        double r683704 = a;
        double r683705 = r683704 - r683700;
        double r683706 = cbrt(r683705);
        double r683707 = r683706 * r683706;
        double r683708 = r683703 / r683707;
        double r683709 = r683698 * r683708;
        double r683710 = r683702 / r683706;
        double r683711 = r683709 * r683710;
        double r683712 = r683697 + r683711;
        return r683712;
}

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

Original10.8
Target1.4
Herbie0.6
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied *-un-lft-identity10.8

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

  4. Applied times-frac1.6

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

  5. Simplified1.6

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

  7. Applied add-cube-cbrt2.1

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

  8. Applied add-cube-cbrt1.9

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

  9. Applied times-frac1.9

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

  10. Applied associate-*r*0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2020045 
(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))))