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

Average Error: 23.9 → 8.2

Time: 18.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -1.5335432679341662 \cdot 10^{-301}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r32332349 = x;
        double r32332350 = y;
        double r32332351 = r32332350 - r32332349;
        double r32332352 = z;
        double r32332353 = t;
        double r32332354 = r32332352 - r32332353;
        double r32332355 = r32332351 * r32332354;
        double r32332356 = a;
        double r32332357 = r32332356 - r32332353;
        double r32332358 = r32332355 / r32332357;
        double r32332359 = r32332349 + r32332358;
        return r32332359;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r32332360 = x;
        double r32332361 = y;
        double r32332362 = r32332361 - r32332360;
        double r32332363 = z;
        double r32332364 = t;
        double r32332365 = r32332363 - r32332364;
        double r32332366 = r32332362 * r32332365;
        double r32332367 = a;
        double r32332368 = r32332367 - r32332364;
        double r32332369 = r32332366 / r32332368;
        double r32332370 = r32332360 + r32332369;
        double r32332371 = -1.5335432679341662e-301;
        bool r32332372 = r32332370 <= r32332371;
        double r32332373 = r32332368 / r32332365;
        double r32332374 = r32332362 / r32332373;
        double r32332375 = r32332374 + r32332360;
        double r32332376 = 0.0;
        bool r32332377 = r32332370 <= r32332376;
        double r32332378 = r32332363 * r32332360;
        double r32332379 = r32332378 / r32332364;
        double r32332380 = r32332379 + r32332361;
        double r32332381 = r32332363 * r32332361;
        double r32332382 = r32332381 / r32332364;
        double r32332383 = r32332380 - r32332382;
        double r32332384 = r32332377 ? r32332383 : r32332375;
        double r32332385 = r32332372 ? r32332375 : r32332384;
        return r32332385;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	23.9
Target	9.2
Herbie	8.2

\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -1.5335432679341662e-301 or 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

   1. Initial program 20.5

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

   3. Applied associate-/l* 7.3

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

   if -1.5335432679341662e-301 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

   1. Initial program 60.8

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

   2. Taylor expanded around inf 17.6

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

4. Final simplification 8.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -1.5335432679341662 \cdot 10^{-301}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"

  :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))))