Average Error: 6.4 → 1.0
Time: 23.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\left(\left(z - x\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{t}} + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\left(\left(z - x\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{t}} + x
double f(double x, double y, double z, double t) {
        double r246348 = x;
        double r246349 = y;
        double r246350 = z;
        double r246351 = r246350 - r246348;
        double r246352 = r246349 * r246351;
        double r246353 = t;
        double r246354 = r246352 / r246353;
        double r246355 = r246348 + r246354;
        return r246355;
}
↓
double f(double x, double y, double z, double t) {
        double r246356 = z;
        double r246357 = x;
        double r246358 = r246356 - r246357;
        double r246359 = y;
        double r246360 = cbrt(r246359);
        double r246361 = r246360 * r246360;
        double r246362 = t;
        double r246363 = cbrt(r246362);
        double r246364 = r246363 * r246363;
        double r246365 = r246361 / r246364;
        double r246366 = r246358 * r246365;
        double r246367 = r246360 / r246363;
        double r246368 = r246366 * r246367;
        double r246369 = r246368 + r246357;
        return r246369;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target2.2
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.4

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

  2. Simplified2.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.2

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

  5. Simplified2.2

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

  7. Applied add-cube-cbrt2.7

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

  8. Applied add-cube-cbrt2.8

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

  9. Applied times-frac2.8

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

  10. Applied associate-*r*1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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