Average Error: 2.0 → 1.9
Time: 20.2s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[t + \frac{z - t}{\frac{y}{x}}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
t + \frac{z - t}{\frac{y}{x}}
double f(double x, double y, double z, double t) {
        double r21569349 = x;
        double r21569350 = y;
        double r21569351 = r21569349 / r21569350;
        double r21569352 = z;
        double r21569353 = t;
        double r21569354 = r21569352 - r21569353;
        double r21569355 = r21569351 * r21569354;
        double r21569356 = r21569355 + r21569353;
        return r21569356;
}
↓
double f(double x, double y, double z, double t) {
        double r21569357 = t;
        double r21569358 = z;
        double r21569359 = r21569358 - r21569357;
        double r21569360 = y;
        double r21569361 = x;
        double r21569362 = r21569360 / r21569361;
        double r21569363 = r21569359 / r21569362;
        double r21569364 = r21569357 + r21569363;
        return r21569364;
}

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

Original2.0
Target2.3
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  2. Taylor expanded around 0 6.0

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

  3. Simplified1.9

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

  4. Final simplification1.9

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(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))