Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Error: 24.2 → 10.3

Time: 14.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -4.2852583466209365 \cdot 10^{-144} \lor \neg \left(a \le 2.0695378041879823 \cdot 10^{-147}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r748363 = x;
        double r748364 = y;
        double r748365 = r748364 - r748363;
        double r748366 = z;
        double r748367 = t;
        double r748368 = r748366 - r748367;
        double r748369 = r748365 * r748368;
        double r748370 = a;
        double r748371 = r748370 - r748367;
        double r748372 = r748369 / r748371;
        double r748373 = r748363 + r748372;
        return r748373;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r748374 = a;
        double r748375 = -4.2852583466209365e-144;
        bool r748376 = r748374 <= r748375;
        double r748377 = 2.0695378041879823e-147;
        bool r748378 = r748374 <= r748377;
        double r748379 = !r748378;
        bool r748380 = r748376 || r748379;
        double r748381 = x;
        double r748382 = y;
        double r748383 = r748382 - r748381;
        double r748384 = t;
        double r748385 = r748374 - r748384;
        double r748386 = z;
        double r748387 = r748386 - r748384;
        double r748388 = r748385 / r748387;
        double r748389 = r748383 / r748388;
        double r748390 = r748381 + r748389;
        double r748391 = r748381 * r748386;
        double r748392 = r748391 / r748384;
        double r748393 = r748382 + r748392;
        double r748394 = r748386 * r748382;
        double r748395 = r748394 / r748384;
        double r748396 = r748393 - r748395;
        double r748397 = r748380 ? r748390 : r748396;
        return r748397;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	24.2
Target	9.3
Herbie	10.3

\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if a < -4.2852583466209365e-144 or 2.0695378041879823e-147 < a

   1. Initial program 22.4

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

   3. Applied associate-/l* 9.2

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

   if -4.2852583466209365e-144 < a < 2.0695378041879823e-147

   1. Initial program 30.0

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

   2. Taylor expanded around inf 14.1

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

4. Final simplification 10.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.2852583466209365 \cdot 10^{-144} \lor \neg \left(a \le 2.0695378041879823 \cdot 10^{-147}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))