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

Average Error: 2.1 → 1.8

Time: 13.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -2.429342480740140650041385945281389977987 \cdot 10^{-176} \lor \neg \left(t \le 3.038275486400102813641711171286818002615 \cdot 10^{-154}\right):\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r390374 = x;
        double r390375 = y;
        double r390376 = r390374 / r390375;
        double r390377 = z;
        double r390378 = t;
        double r390379 = r390377 - r390378;
        double r390380 = r390376 * r390379;
        double r390381 = r390380 + r390378;
        return r390381;
}

↓

double f(double x, double y, double z, double t) {
        double r390382 = t;
        double r390383 = -2.4293424807401407e-176;
        bool r390384 = r390382 <= r390383;
        double r390385 = 3.038275486400103e-154;
        bool r390386 = r390382 <= r390385;
        double r390387 = !r390386;
        bool r390388 = r390384 || r390387;
        double r390389 = z;
        double r390390 = r390389 - r390382;
        double r390391 = x;
        double r390392 = y;
        double r390393 = r390391 / r390392;
        double r390394 = r390390 * r390393;
        double r390395 = r390382 + r390394;
        double r390396 = r390392 / r390390;
        double r390397 = r390391 / r390396;
        double r390398 = r390397 + r390382;
        double r390399 = r390388 ? r390395 : r390398;
        return r390399;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.4
Herbie	1.8

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

Derivation

1. Split input into 2 regimes

2. if t < -2.4293424807401407e-176 or 3.038275486400103e-154 < t

   1. Initial program 0.9

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

   if -2.4293424807401407e-176 < t < 3.038275486400103e-154

   1. Initial program 5.6

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

   3. Applied *-un-lft-identity 5.6

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

   4. Applied *-un-lft-identity 5.6

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

   5. Applied times-frac 5.6

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

   6. Applied associate-*l* 5.6

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

   7. Simplified 4.6

      \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{x}{\frac{y}{z - t}}} + t\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.429342480740140650041385945281389977987 \cdot 10^{-176} \lor \neg \left(t \le 3.038275486400102813641711171286818002615 \cdot 10^{-154}\right):\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :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))