Average Error: 6.2 → 2.4
Time: 23.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\frac{\sqrt[3]{y}}{\frac{t}{\sqrt[3]{z - x}}} \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}\right)\right) + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\frac{\sqrt[3]{y}}{\frac{t}{\sqrt[3]{z - x}}} \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}\right)\right) + x
double f(double x, double y, double z, double t) {
        double r15977402 = x;
        double r15977403 = y;
        double r15977404 = z;
        double r15977405 = r15977404 - r15977402;
        double r15977406 = r15977403 * r15977405;
        double r15977407 = t;
        double r15977408 = r15977406 / r15977407;
        double r15977409 = r15977402 + r15977408;
        return r15977409;
}
↓
double f(double x, double y, double z, double t) {
        double r15977410 = y;
        double r15977411 = cbrt(r15977410);
        double r15977412 = t;
        double r15977413 = z;
        double r15977414 = x;
        double r15977415 = r15977413 - r15977414;
        double r15977416 = cbrt(r15977415);
        double r15977417 = r15977412 / r15977416;
        double r15977418 = r15977411 / r15977417;
        double r15977419 = r15977411 * r15977411;
        double r15977420 = r15977416 * r15977416;
        double r15977421 = r15977419 * r15977420;
        double r15977422 = r15977418 * r15977421;
        double r15977423 = r15977422 + r15977414;
        return r15977423;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Target

Original6.2
Target2.0
Herbie2.4
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.2

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

  3. Applied associate-/l*5.7

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

  5. Applied add-cube-cbrt6.2

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

  6. Applied *-un-lft-identity6.2

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

  7. Applied times-frac6.2

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

  8. Applied add-cube-cbrt6.3

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

  9. Applied times-frac2.4

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

  10. Simplified2.4

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

  11. Final simplification2.4

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

Reproduce

herbie shell --seed 2019162 +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)))