Average Error: 2.0 → 2.0
Time: 13.0s
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 r377191 = x;
        double r377192 = y;
        double r377193 = r377191 / r377192;
        double r377194 = z;
        double r377195 = t;
        double r377196 = r377194 - r377195;
        double r377197 = r377193 * r377196;
        double r377198 = r377197 + r377195;
        return r377198;
}
↓
double f(double x, double y, double z, double t) {
        double r377199 = x;
        double r377200 = y;
        double r377201 = r377199 / r377200;
        double r377202 = z;
        double r377203 = t;
        double r377204 = r377202 - r377203;
        double r377205 = r377201 * r377204;
        double r377206 = r377205 + r377203;
        return r377206;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < -9.977563095314812e+140 or 4.073187398339556e+236 < (/ x y)

    1. Initial program 15.9

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

    3. Applied div-inv16.0

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

    4. Applied associate-*l*2.8

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

    5. Simplified2.7

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

    if -9.977563095314812e+140 < (/ x y) < 4.073187398339556e+236

    1. Initial program 0.7

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

  4. Final simplification2.0

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

Reproduce

herbie shell --seed 2019294 
(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))