Average Error: 2.0 → 6.3
Time: 8.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[x \cdot \frac{z - t}{y} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
x \cdot \frac{z - t}{y} + t
double f(double x, double y, double z, double t) {
        double r433896 = x;
        double r433897 = y;
        double r433898 = r433896 / r433897;
        double r433899 = z;
        double r433900 = t;
        double r433901 = r433899 - r433900;
        double r433902 = r433898 * r433901;
        double r433903 = r433902 + r433900;
        return r433903;
}
↓
double f(double x, double y, double z, double t) {
        double r433904 = x;
        double r433905 = z;
        double r433906 = t;
        double r433907 = r433905 - r433906;
        double r433908 = y;
        double r433909 = r433907 / r433908;
        double r433910 = r433904 * r433909;
        double r433911 = r433910 + r433906;
        return r433911;
}

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
Target2.4
Herbie6.3
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.0788925605168588e-242 or 2.6094425953641534e+23 < t

    1. Initial program 1.1

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

    3. Applied sub-neg1.1

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

    4. Applied distribute-lft-in1.1

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

    if -1.0788925605168588e-242 < t < 2.6094425953641534e+23

    1. Initial program 3.7

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

    3. Applied div-inv3.8

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot \left(z - t\right) + t\]

    4. Applied associate-*l*4.1

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{y} \cdot \left(z - t\right)\right)} + t\]

    5. Simplified4.0

      \[\leadsto x \cdot \color{blue}{\frac{z - t}{y}} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.3

    \[\leadsto x \cdot \frac{z - t}{y} + t\]

Reproduce

herbie shell --seed 2019298 
(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))