Average Error: 1.8 → 1.8
Time: 52.7s
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 r26720553 = x;
        double r26720554 = y;
        double r26720555 = r26720553 / r26720554;
        double r26720556 = z;
        double r26720557 = t;
        double r26720558 = r26720556 - r26720557;
        double r26720559 = r26720555 * r26720558;
        double r26720560 = r26720559 + r26720557;
        return r26720560;
}
↓
double f(double x, double y, double z, double t) {
        double r26720561 = t;
        double r26720562 = z;
        double r26720563 = r26720562 - r26720561;
        double r26720564 = x;
        double r26720565 = y;
        double r26720566 = r26720564 / r26720565;
        double r26720567 = r26720563 * r26720566;
        double r26720568 = r26720561 + r26720567;
        return r26720568;
}

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

Original1.8
Target2.1
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 1.8

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

  3. Applied *-commutative1.8

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

  4. Final simplification1.8

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

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))