Average Error: 2.2 → 2.4
Time: 13.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\frac{x}{y} \cdot z + \sqrt[3]{\frac{x}{y}} \cdot \left(\left(\sqrt[3]{\frac{x}{y}} \cdot t\right) \cdot \left(-\sqrt[3]{\frac{x}{y}}\right)\right)\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\frac{x}{y} \cdot z + \sqrt[3]{\frac{x}{y}} \cdot \left(\left(\sqrt[3]{\frac{x}{y}} \cdot t\right) \cdot \left(-\sqrt[3]{\frac{x}{y}}\right)\right)\right) + t
double f(double x, double y, double z, double t) {
        double r313595 = x;
        double r313596 = y;
        double r313597 = r313595 / r313596;
        double r313598 = z;
        double r313599 = t;
        double r313600 = r313598 - r313599;
        double r313601 = r313597 * r313600;
        double r313602 = r313601 + r313599;
        return r313602;
}
↓
double f(double x, double y, double z, double t) {
        double r313603 = x;
        double r313604 = y;
        double r313605 = r313603 / r313604;
        double r313606 = z;
        double r313607 = r313605 * r313606;
        double r313608 = cbrt(r313605);
        double r313609 = t;
        double r313610 = r313608 * r313609;
        double r313611 = -r313608;
        double r313612 = r313610 * r313611;
        double r313613 = r313608 * r313612;
        double r313614 = r313607 + r313613;
        double r313615 = r313614 + r313609;
        return r313615;
}

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

Original2.2
Target2.5
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.2

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

  3. Applied sub-neg2.2

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

  4. Applied distribute-lft-in2.2

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

  5. Simplified2.2

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

  7. Applied *-un-lft-identity2.2

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

  9. Applied add-cube-cbrt2.4

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

  10. Applied associate-*r*2.4

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

  11. Simplified2.4

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

  12. Final simplification2.4

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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