Average Error: 6.4 → 0.9
Time: 17.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\left(\left(t - z\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} + x\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\left(\left(t - z\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} + x
double f(double x, double y, double z, double t, double a) {
        double r257134 = x;
        double r257135 = y;
        double r257136 = z;
        double r257137 = t;
        double r257138 = r257136 - r257137;
        double r257139 = r257135 * r257138;
        double r257140 = a;
        double r257141 = r257139 / r257140;
        double r257142 = r257134 - r257141;
        return r257142;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r257143 = t;
        double r257144 = z;
        double r257145 = r257143 - r257144;
        double r257146 = y;
        double r257147 = cbrt(r257146);
        double r257148 = a;
        double r257149 = cbrt(r257148);
        double r257150 = r257147 / r257149;
        double r257151 = r257145 * r257150;
        double r257152 = r257147 * r257147;
        double r257153 = r257149 * r257149;
        double r257154 = r257152 / r257153;
        double r257155 = r257151 * r257154;
        double r257156 = x;
        double r257157 = r257155 + r257156;
        return r257157;
}

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

Original6.4
Target0.7
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.4

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

  2. Simplified2.6

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

  4. Applied add-cube-cbrt3.1

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

  5. Applied add-cube-cbrt3.2

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

  6. Applied times-frac3.2

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

  7. Applied associate-*l*0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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