Average Error: 2.0 → 5.8
Time: 10.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{x}{\frac{y}{z - t}} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{x}{\frac{y}{z - t}} + t
double f(double x, double y, double z, double t) {
        double r334119 = x;
        double r334120 = y;
        double r334121 = r334119 / r334120;
        double r334122 = z;
        double r334123 = t;
        double r334124 = r334122 - r334123;
        double r334125 = r334121 * r334124;
        double r334126 = r334125 + r334123;
        return r334126;
}
↓
double f(double x, double y, double z, double t) {
        double r334127 = x;
        double r334128 = y;
        double r334129 = z;
        double r334130 = t;
        double r334131 = r334129 - r334130;
        double r334132 = r334128 / r334131;
        double r334133 = r334127 / r334132;
        double r334134 = r334133 + r334130;
        return r334134;
}

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
Herbie5.8
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < -8.800041534266765e+168

    1. Initial program 15.7

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

    3. Applied associate-*l/3.3

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

    5. Applied associate-/l*1.4

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

    if -8.800041534266765e+168 < (/ x y)

    1. Initial program 1.4

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

    3. Applied sub-neg1.4

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

    4. Applied distribute-lft-in1.4

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

  4. Final simplification5.8

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

Reproduce

herbie shell --seed 2019297 
(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))