Average Error: 5.6 → 1.6
Time: 19.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\left(\frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} \cdot y\right) \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\left(\frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} \cdot y\right) \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} + x
double f(double x, double y, double z, double t) {
        double r13623822 = x;
        double r13623823 = y;
        double r13623824 = z;
        double r13623825 = r13623824 - r13623822;
        double r13623826 = r13623823 * r13623825;
        double r13623827 = t;
        double r13623828 = r13623826 / r13623827;
        double r13623829 = r13623822 + r13623828;
        return r13623829;
}
↓
double f(double x, double y, double z, double t) {
        double r13623830 = z;
        double r13623831 = x;
        double r13623832 = r13623830 - r13623831;
        double r13623833 = cbrt(r13623832);
        double r13623834 = t;
        double r13623835 = cbrt(r13623834);
        double r13623836 = r13623833 / r13623835;
        double r13623837 = y;
        double r13623838 = r13623836 * r13623837;
        double r13623839 = r13623833 * r13623833;
        double r13623840 = r13623835 * r13623835;
        double r13623841 = r13623839 / r13623840;
        double r13623842 = r13623838 * r13623841;
        double r13623843 = r13623842 + r13623831;
        return r13623843;
}

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

Original5.6
Target2.1
Herbie1.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 5.6

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

  2. Simplified6.4

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

  4. Applied fma-udef6.4

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

  6. Applied add-cube-cbrt6.9

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

  7. Applied add-cube-cbrt7.0

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

  8. Applied times-frac7.0

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

  9. Applied associate-*l*1.6

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

  10. Final simplification1.6

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

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

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