Average Error: 6.8 → 2.7
Time: 21.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\frac{\frac{y}{\sqrt[3]{t}}}{\sqrt[3]{t}}}{\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}} \cdot \frac{z - x}{\sqrt[3]{\sqrt[3]{t}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\frac{\frac{y}{\sqrt[3]{t}}}{\sqrt[3]{t}}}{\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}} \cdot \frac{z - x}{\sqrt[3]{\sqrt[3]{t}}}
double f(double x, double y, double z, double t) {
        double r25269106 = x;
        double r25269107 = y;
        double r25269108 = z;
        double r25269109 = r25269108 - r25269106;
        double r25269110 = r25269107 * r25269109;
        double r25269111 = t;
        double r25269112 = r25269110 / r25269111;
        double r25269113 = r25269106 + r25269112;
        return r25269113;
}
↓
double f(double x, double y, double z, double t) {
        double r25269114 = x;
        double r25269115 = y;
        double r25269116 = t;
        double r25269117 = cbrt(r25269116);
        double r25269118 = r25269115 / r25269117;
        double r25269119 = r25269118 / r25269117;
        double r25269120 = cbrt(r25269117);
        double r25269121 = r25269120 * r25269120;
        double r25269122 = r25269119 / r25269121;
        double r25269123 = z;
        double r25269124 = r25269123 - r25269114;
        double r25269125 = r25269124 / r25269120;
        double r25269126 = r25269122 * r25269125;
        double r25269127 = r25269114 + r25269126;
        return r25269127;
}

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

Original6.8
Target1.9
Herbie2.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  3. Applied add-cube-cbrt7.3

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

  4. Applied times-frac2.9

    \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity2.9

    \[\leadsto x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{\color{blue}{1 \cdot t}}}\]

  7. Applied cbrt-prod2.9

    \[\leadsto x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{t}}}\]

  8. Applied *-un-lft-identity2.9

    \[\leadsto x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{1 \cdot \left(z - x\right)}}{\sqrt[3]{1} \cdot \sqrt[3]{t}}\]

  9. Applied times-frac2.9

    \[\leadsto x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{1}} \cdot \frac{z - x}{\sqrt[3]{t}}\right)}\]

  10. Applied associate-*r*2.9

    \[\leadsto x + \color{blue}{\left(\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{1}{\sqrt[3]{1}}\right) \cdot \frac{z - x}{\sqrt[3]{t}}}\]

  11. Simplified2.9

    \[\leadsto x + \color{blue}{\frac{\frac{y}{\sqrt[3]{t}}}{\sqrt[3]{t}}} \cdot \frac{z - x}{\sqrt[3]{t}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt3.1

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

  14. Applied *-un-lft-identity3.1

    \[\leadsto x + \frac{\frac{y}{\sqrt[3]{t}}}{\sqrt[3]{t}} \cdot \frac{\color{blue}{1 \cdot \left(z - x\right)}}{\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}}\]

  15. Applied times-frac3.1

    \[\leadsto x + \frac{\frac{y}{\sqrt[3]{t}}}{\sqrt[3]{t}} \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}} \cdot \frac{z - x}{\sqrt[3]{\sqrt[3]{t}}}\right)}\]

  16. Applied associate-*r*2.7

    \[\leadsto x + \color{blue}{\left(\frac{\frac{y}{\sqrt[3]{t}}}{\sqrt[3]{t}} \cdot \frac{1}{\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}}\right) \cdot \frac{z - x}{\sqrt[3]{\sqrt[3]{t}}}}\]

  17. Simplified2.7

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

  18. Final simplification2.7

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

Reproduce

herbie shell --seed 2019174 
(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)))