Average Error: 1.7 → 1.7
Time: 12.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[t + \left(z - t\right) \cdot \frac{x}{y}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
t + \left(z - t\right) \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r24366513 = x;
        double r24366514 = y;
        double r24366515 = r24366513 / r24366514;
        double r24366516 = z;
        double r24366517 = t;
        double r24366518 = r24366516 - r24366517;
        double r24366519 = r24366515 * r24366518;
        double r24366520 = r24366519 + r24366517;
        return r24366520;
}
↓
double f(double x, double y, double z, double t) {
        double r24366521 = t;
        double r24366522 = z;
        double r24366523 = r24366522 - r24366521;
        double r24366524 = x;
        double r24366525 = y;
        double r24366526 = r24366524 / r24366525;
        double r24366527 = r24366523 * r24366526;
        double r24366528 = r24366521 + r24366527;
        return r24366528;
}

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

Original1.7
Target2.0
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 1.7

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

  3. Applied *-commutative1.7

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

  4. Final simplification1.7

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

Reproduce

herbie shell --seed 2019165 
(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))