Average Error: 0.0 → 0.4
Time: 9.9s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\left(\left(y - z\right) \cdot t + x\right) + \left(-\left(\sqrt[3]{y - z} \cdot x\right) \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right)\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\left(\left(y - z\right) \cdot t + x\right) + \left(-\left(\sqrt[3]{y - z} \cdot x\right) \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right)\right)
double f(double x, double y, double z, double t) {
        double r14314629 = x;
        double r14314630 = y;
        double r14314631 = z;
        double r14314632 = r14314630 - r14314631;
        double r14314633 = t;
        double r14314634 = r14314633 - r14314629;
        double r14314635 = r14314632 * r14314634;
        double r14314636 = r14314629 + r14314635;
        return r14314636;
}
↓
double f(double x, double y, double z, double t) {
        double r14314637 = y;
        double r14314638 = z;
        double r14314639 = r14314637 - r14314638;
        double r14314640 = t;
        double r14314641 = r14314639 * r14314640;
        double r14314642 = x;
        double r14314643 = r14314641 + r14314642;
        double r14314644 = cbrt(r14314639);
        double r14314645 = r14314644 * r14314642;
        double r14314646 = r14314644 * r14314644;
        double r14314647 = r14314645 * r14314646;
        double r14314648 = -r14314647;
        double r14314649 = r14314643 + r14314648;
        return r14314649;
}

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

Original0.0
Target0.0
Herbie0.4
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

  1. Initial program 0.0

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

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  7. Applied add-cube-cbrt0.4

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

  8. Applied associate-*l*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))