Average Error: 10.2 → 0.5
Time: 18.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r24316619 = x;
        double r24316620 = y;
        double r24316621 = z;
        double r24316622 = t;
        double r24316623 = r24316621 - r24316622;
        double r24316624 = r24316620 * r24316623;
        double r24316625 = a;
        double r24316626 = r24316625 - r24316622;
        double r24316627 = r24316624 / r24316626;
        double r24316628 = r24316619 + r24316627;
        return r24316628;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24316629 = y;
        double r24316630 = a;
        double r24316631 = t;
        double r24316632 = r24316630 - r24316631;
        double r24316633 = cbrt(r24316632);
        double r24316634 = z;
        double r24316635 = r24316634 - r24316631;
        double r24316636 = cbrt(r24316635);
        double r24316637 = r24316633 / r24316636;
        double r24316638 = r24316637 * r24316637;
        double r24316639 = r24316629 / r24316638;
        double r24316640 = r24316639 / r24316637;
        double r24316641 = x;
        double r24316642 = r24316640 + r24316641;
        return r24316642;
}

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

Original10.2
Target1.1
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.2

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

  3. Applied associate-/l*1.1

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

  5. Applied add-cube-cbrt1.6

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

  6. Applied add-cube-cbrt1.5

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

  7. Applied times-frac1.5

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

  8. Applied associate-/r*0.5

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

  9. Simplified0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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