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

↓

\[\mathsf{fma}\left(\frac{1}{\frac{z - a}{z - t}}, y, x\right)\]

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

↓

\mathsf{fma}\left(\frac{1}{\frac{z - a}{z - t}}, y, x\right)

double f(double x, double y, double z, double t, double a) {
        double r457671 = x;
        double r457672 = y;
        double r457673 = z;
        double r457674 = t;
        double r457675 = r457673 - r457674;
        double r457676 = a;
        double r457677 = r457673 - r457676;
        double r457678 = r457675 / r457677;
        double r457679 = r457672 * r457678;
        double r457680 = r457671 + r457679;
        return r457680;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r457681 = 1.0;
        double r457682 = z;
        double r457683 = a;
        double r457684 = r457682 - r457683;
        double r457685 = t;
        double r457686 = r457682 - r457685;
        double r457687 = r457684 / r457686;
        double r457688 = r457681 / r457687;
        double r457689 = y;
        double r457690 = x;
        double r457691 = fma(r457688, r457689, r457690);
        return r457691;
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Original	1.4
Target	1.3
Herbie	1.4

Derivation

Initial program 1.4
\[x + y \cdot \frac{z - t}{z - a}\]
Simplified1.4
\[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)}\]
Using strategy rm
Applied clear-num1.4
\[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{z - a}{z - t}}}, y, x\right)\]
Final simplification1.4
\[\leadsto \mathsf{fma}\left(\frac{1}{\frac{z - a}{z - t}}, y, x\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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

Error

Target

Derivation

Reproduce