Average Error: 2.0 → 2.0
Time: 3.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{x}{y} \cdot \left(z - t\right) + t
double f(double x, double y, double z, double t) {
        double r480545 = x;
        double r480546 = y;
        double r480547 = r480545 / r480546;
        double r480548 = z;
        double r480549 = t;
        double r480550 = r480548 - r480549;
        double r480551 = r480547 * r480550;
        double r480552 = r480551 + r480549;
        return r480552;
}
↓
double f(double x, double y, double z, double t) {
        double r480553 = x;
        double r480554 = y;
        double r480555 = r480553 / r480554;
        double r480556 = z;
        double r480557 = t;
        double r480558 = r480556 - r480557;
        double r480559 = r480555 * r480558;
        double r480560 = r480559 + r480557;
        return r480560;
}

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
Target2.2
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  2. Final simplification2.0

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :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))