Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Average Error: 2.2 → 1.9

Time: 3.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -1.329770551630262009868286464899679933254 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \mathbf{elif}\;x \le -1.674371725197054530420515707920578774098 \cdot 10^{-177}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r524503 = x;
        double r524504 = y;
        double r524505 = r524503 / r524504;
        double r524506 = z;
        double r524507 = t;
        double r524508 = r524506 - r524507;
        double r524509 = r524505 * r524508;
        double r524510 = r524509 + r524507;
        return r524510;
}

↓

double f(double x, double y, double z, double t) {
        double r524511 = x;
        double r524512 = -1.329770551630262e-82;
        bool r524513 = r524511 <= r524512;
        double r524514 = y;
        double r524515 = z;
        double r524516 = t;
        double r524517 = r524515 - r524516;
        double r524518 = r524514 / r524517;
        double r524519 = r524511 / r524518;
        double r524520 = r524519 + r524516;
        double r524521 = -1.6743717251970545e-177;
        bool r524522 = r524511 <= r524521;
        double r524523 = r524511 * r524517;
        double r524524 = r524523 / r524514;
        double r524525 = r524524 + r524516;
        double r524526 = r524511 / r524514;
        double r524527 = r524526 * r524517;
        double r524528 = r524527 + r524516;
        double r524529 = r524522 ? r524525 : r524528;
        double r524530 = r524513 ? r524520 : r524529;
        return r524530;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.4
Herbie	1.9

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

Derivation

1. Split input into 3 regimes

2. if x < -1.329770551630262e-82

   1. Initial program 3.1

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

   3. Applied associate-*l/ 11.0

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

   5. Applied associate-/l* 2.0

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

   if -1.329770551630262e-82 < x < -1.6743717251970545e-177

   1. Initial program 0.9

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

   3. Applied associate-*l/ 0.7

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

   if -1.6743717251970545e-177 < x

   1. Initial program 2.0

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

4. Final simplification 1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.329770551630262009868286464899679933254 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \mathbf{elif}\;x \le -1.674371725197054530420515707920578774098 \cdot 10^{-177}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(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))