Average Error: 1.3 → 1.3
Time: 20.0s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)
double f(double x, double y, double z, double t, double a) {
        double r22968307 = x;
        double r22968308 = y;
        double r22968309 = z;
        double r22968310 = t;
        double r22968311 = r22968309 - r22968310;
        double r22968312 = a;
        double r22968313 = r22968309 - r22968312;
        double r22968314 = r22968311 / r22968313;
        double r22968315 = r22968308 * r22968314;
        double r22968316 = r22968307 + r22968315;
        return r22968316;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r22968317 = z;
        double r22968318 = t;
        double r22968319 = r22968317 - r22968318;
        double r22968320 = a;
        double r22968321 = r22968317 - r22968320;
        double r22968322 = r22968319 / r22968321;
        double r22968323 = y;
        double r22968324 = x;
        double r22968325 = fma(r22968322, r22968323, r22968324);
        return r22968325;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original1.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  2. Simplified1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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