Average Error: 6.4 → 1.0
Time: 23.8s
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 r295804 = x;
        double r295805 = y;
        double r295806 = z;
        double r295807 = r295806 - r295804;
        double r295808 = r295805 * r295807;
        double r295809 = t;
        double r295810 = r295808 / r295809;
        double r295811 = r295804 + r295810;
        return r295811;
}
↓
double f(double x, double y, double z, double t) {
        double r295812 = z;
        double r295813 = x;
        double r295814 = r295812 - r295813;
        double r295815 = y;
        double r295816 = cbrt(r295815);
        double r295817 = r295816 * r295816;
        double r295818 = t;
        double r295819 = cbrt(r295818);
        double r295820 = r295819 * r295819;
        double r295821 = r295817 / r295820;
        double r295822 = r295814 * r295821;
        double r295823 = r295816 / r295819;
        double r295824 = r295822 * r295823;
        double r295825 = r295824 + r295813;
        return r295825;
}

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)))