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

Average Error: 10.4 → 1.5

Time: 30.6s

Precision: 64

Math

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

↓

\[\mathsf{fma}\left(y, \frac{z - t}{a - t}, x\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r21953998 = x;
        double r21953999 = y;
        double r21954000 = z;
        double r21954001 = t;
        double r21954002 = r21954000 - r21954001;
        double r21954003 = r21953999 * r21954002;
        double r21954004 = a;
        double r21954005 = r21954004 - r21954001;
        double r21954006 = r21954003 / r21954005;
        double r21954007 = r21953998 + r21954006;
        return r21954007;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r21954008 = y;
        double r21954009 = z;
        double r21954010 = t;
        double r21954011 = r21954009 - r21954010;
        double r21954012 = a;
        double r21954013 = r21954012 - r21954010;
        double r21954014 = r21954011 / r21954013;
        double r21954015 = x;
        double r21954016 = fma(r21954008, r21954014, r21954015);
        return r21954016;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.4
Target	1.3
Herbie	1.5

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

Derivation

1. Initial program 10.4

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

2. Simplified 1.5

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a - t}, x\right)}\]

3. Final simplification 1.5

   \[\leadsto \mathsf{fma}\left(y, \frac{z - t}{a - t}, x\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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