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

↓

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

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 r1047570 = x;
        double r1047571 = y;
        double r1047572 = z;
        double r1047573 = t;
        double r1047574 = r1047572 - r1047573;
        double r1047575 = a;
        double r1047576 = r1047572 - r1047575;
        double r1047577 = r1047574 / r1047576;
        double r1047578 = r1047571 * r1047577;
        double r1047579 = r1047570 + r1047578;
        return r1047579;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r1047580 = 1.0;
        double r1047581 = z;
        double r1047582 = a;
        double r1047583 = r1047581 - r1047582;
        double r1047584 = t;
        double r1047585 = r1047581 - r1047584;
        double r1047586 = r1047583 / r1047585;
        double r1047587 = r1047580 / r1047586;
        double r1047588 = y;
        double r1047589 = x;
        double r1047590 = fma(r1047587, r1047588, r1047589);
        return r1047590;
}

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