Average Error: 2.0 → 2.0
Time: 14.9s
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 r546125 = x;
        double r546126 = y;
        double r546127 = r546125 / r546126;
        double r546128 = z;
        double r546129 = t;
        double r546130 = r546128 - r546129;
        double r546131 = r546127 * r546130;
        double r546132 = r546131 + r546129;
        return r546132;
}
↓
double f(double x, double y, double z, double t) {
        double r546133 = x;
        double r546134 = y;
        double r546135 = r546133 / r546134;
        double r546136 = z;
        double r546137 = t;
        double r546138 = r546136 - r546137;
        double r546139 = r546135 * r546138;
        double r546140 = r546139 + r546137;
        return r546140;
}

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
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 2020047 
(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))