Average Error: 2.0 → 2.0
Time: 4.8s
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 r287373 = x;
        double r287374 = y;
        double r287375 = r287373 / r287374;
        double r287376 = z;
        double r287377 = t;
        double r287378 = r287376 - r287377;
        double r287379 = r287375 * r287378;
        double r287380 = r287379 + r287377;
        return r287380;
}
↓
double f(double x, double y, double z, double t) {
        double r287381 = x;
        double r287382 = y;
        double r287383 = r287381 / r287382;
        double r287384 = z;
        double r287385 = t;
        double r287386 = r287384 - r287385;
        double r287387 = r287383 * r287386;
        double r287388 = r287387 + r287385;
        return r287388;
}

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
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  3. Applied sub-neg2.0

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

  4. Applied distribute-rgt-in2.0

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

  5. Applied associate-+l+2.0

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

  6. Simplified2.0

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

  8. Applied add-cube-cbrt2.4

    \[\leadsto \color{blue}{\left(\sqrt[3]{z \cdot \frac{x}{y}} \cdot \sqrt[3]{z \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{z \cdot \frac{x}{y}}} + \left(t - t \cdot \frac{x}{y}\right)\]

  9. Final simplification2.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-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))