Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Average Error: 15.8 → 10.4

Time: 13.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -3.882750870169282 \cdot 10^{+54}:\\ \;\;\;\;x + \left(y - \left(y \cdot \frac{1}{a - t}\right) \cdot \left(z - t\right)\right)\\ \mathbf{elif}\;t \le 5.8516997634450565 \cdot 10^{+103}:\\ \;\;\;\;x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r29363706 = x;
        double r29363707 = y;
        double r29363708 = r29363706 + r29363707;
        double r29363709 = z;
        double r29363710 = t;
        double r29363711 = r29363709 - r29363710;
        double r29363712 = r29363711 * r29363707;
        double r29363713 = a;
        double r29363714 = r29363713 - r29363710;
        double r29363715 = r29363712 / r29363714;
        double r29363716 = r29363708 - r29363715;
        return r29363716;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r29363717 = t;
        double r29363718 = -3.882750870169282e+54;
        bool r29363719 = r29363717 <= r29363718;
        double r29363720 = x;
        double r29363721 = y;
        double r29363722 = 1.0;
        double r29363723 = a;
        double r29363724 = r29363723 - r29363717;
        double r29363725 = r29363722 / r29363724;
        double r29363726 = r29363721 * r29363725;
        double r29363727 = z;
        double r29363728 = r29363727 - r29363717;
        double r29363729 = r29363726 * r29363728;
        double r29363730 = r29363721 - r29363729;
        double r29363731 = r29363720 + r29363730;
        double r29363732 = 5.8516997634450565e+103;
        bool r29363733 = r29363717 <= r29363732;
        double r29363734 = r29363728 * r29363721;
        double r29363735 = r29363734 / r29363724;
        double r29363736 = r29363721 - r29363735;
        double r29363737 = r29363720 + r29363736;
        double r29363738 = r29363721 * r29363727;
        double r29363739 = r29363738 / r29363717;
        double r29363740 = r29363720 + r29363739;
        double r29363741 = r29363733 ? r29363737 : r29363740;
        double r29363742 = r29363719 ? r29363731 : r29363741;
        return r29363742;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	15.8
Target	8.3
Herbie	10.4

\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-07}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if t < -3.882750870169282e+54

   1. Initial program 26.7

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

   3. Applied associate--l+ 22.7

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

   5. Applied *-un-lft-identity 22.7

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

   6. Applied times-frac 12.7

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

   7. Simplified 12.7

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

   9. Applied div-inv 13.8

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

   if -3.882750870169282e+54 < t < 5.8516997634450565e+103

   1. Initial program 7.6

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

   3. Applied associate--l+ 6.9

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

   if 5.8516997634450565e+103 < t

   1. Initial program 30.7

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

   3. Applied associate--l+ 26.7

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

   5. Applied *-un-lft-identity 26.7

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

   6. Applied times-frac 15.6

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

   7. Simplified 15.6

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

   8. Taylor expanded around inf 18.3

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

4. Final simplification 10.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.882750870169282 \cdot 10^{+54}:\\ \;\;\;\;x + \left(y - \left(y \cdot \frac{1}{a - t}\right) \cdot \left(z - t\right)\right)\\ \mathbf{elif}\;t \le 5.8516997634450565 \cdot 10^{+103}:\\ \;\;\;\;x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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