Average Error: 6.7 → 1.7
Time: 5.2s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}}{\frac{\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}}}{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}} \cdot \frac{\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}}{\frac{\sqrt[3]{\sqrt[3]{t}}}{\sqrt[3]{z - x}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}}{\frac{\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}}}{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}} \cdot \frac{\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}}{\frac{\sqrt[3]{\sqrt[3]{t}}}{\sqrt[3]{z - x}}}
double f(double x, double y, double z, double t) {
        double r391575 = x;
        double r391576 = y;
        double r391577 = z;
        double r391578 = r391577 - r391575;
        double r391579 = r391576 * r391578;
        double r391580 = t;
        double r391581 = r391579 / r391580;
        double r391582 = r391575 + r391581;
        return r391582;
}
↓
double f(double x, double y, double z, double t) {
        double r391583 = x;
        double r391584 = y;
        double r391585 = t;
        double r391586 = cbrt(r391585);
        double r391587 = r391586 * r391586;
        double r391588 = r391584 / r391587;
        double r391589 = cbrt(r391588);
        double r391590 = r391589 * r391589;
        double r391591 = cbrt(r391587);
        double r391592 = z;
        double r391593 = r391592 - r391583;
        double r391594 = cbrt(r391593);
        double r391595 = r391594 * r391594;
        double r391596 = r391591 / r391595;
        double r391597 = r391590 / r391596;
        double r391598 = cbrt(r391586);
        double r391599 = r391598 / r391594;
        double r391600 = r391589 / r391599;
        double r391601 = r391597 * r391600;
        double r391602 = r391583 + r391601;
        return r391602;
}

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

Original6.7
Target2.0
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.7

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

  3. Applied associate-/l*5.6

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

  5. Applied *-un-lft-identity5.6

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

  6. Applied add-cube-cbrt6.1

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

  7. Applied times-frac6.1

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

  8. Applied associate-/r*2.4

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

  9. Simplified2.4

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

  11. Applied add-cube-cbrt2.5

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

  12. Applied add-cube-cbrt2.6

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

  13. Applied cbrt-prod2.6

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

  14. Applied times-frac2.6

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

  15. Applied add-cube-cbrt2.7

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

  16. Applied times-frac1.7

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

  17. Final simplification1.7

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

Reproduce

herbie shell --seed 2020056 
(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)))