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

Average Error: 24.3 → 10.4

Time: 26.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -1.9083083361715035 \cdot 10^{-150} \lor \neg \left(a \le 2.0184421630927511 \cdot 10^{-153}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r507617 = x;
        double r507618 = y;
        double r507619 = r507618 - r507617;
        double r507620 = z;
        double r507621 = t;
        double r507622 = r507620 - r507621;
        double r507623 = r507619 * r507622;
        double r507624 = a;
        double r507625 = r507624 - r507621;
        double r507626 = r507623 / r507625;
        double r507627 = r507617 + r507626;
        return r507627;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r507628 = a;
        double r507629 = -1.9083083361715035e-150;
        bool r507630 = r507628 <= r507629;
        double r507631 = 2.018442163092751e-153;
        bool r507632 = r507628 <= r507631;
        double r507633 = !r507632;
        bool r507634 = r507630 || r507633;
        double r507635 = x;
        double r507636 = y;
        double r507637 = r507636 - r507635;
        double r507638 = t;
        double r507639 = r507628 - r507638;
        double r507640 = z;
        double r507641 = r507640 - r507638;
        double r507642 = r507639 / r507641;
        double r507643 = r507637 / r507642;
        double r507644 = r507635 + r507643;
        double r507645 = r507635 * r507640;
        double r507646 = r507645 / r507638;
        double r507647 = r507636 + r507646;
        double r507648 = r507640 * r507636;
        double r507649 = r507648 / r507638;
        double r507650 = r507647 - r507649;
        double r507651 = r507634 ? r507644 : r507650;
        return r507651;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	24.3
Target	9.5
Herbie	10.4

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

Derivation

1. Split input into 2 regimes

2. if a < -1.9083083361715035e-150 or 2.018442163092751e-153 < a

   1. Initial program 23.0

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

   3. Applied associate-/l* 9.4

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

   if -1.9083083361715035e-150 < a < 2.018442163092751e-153

   1. Initial program 28.8

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

   2. Taylor expanded around inf 14.0

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

4. Final simplification 10.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.9083083361715035 \cdot 10^{-150} \lor \neg \left(a \le 2.0184421630927511 \cdot 10^{-153}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(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) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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