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

↓

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

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

↓

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

double f(double x, double y, double z, double t) {
        double r20271668 = x;
        double r20271669 = y;
        double r20271670 = r20271669 - r20271668;
        double r20271671 = z;
        double r20271672 = t;
        double r20271673 = r20271671 / r20271672;
        double r20271674 = r20271670 * r20271673;
        double r20271675 = r20271668 + r20271674;
        return r20271675;
}

↓

double f(double x, double y, double z, double t) {
        double r20271676 = z;
        double r20271677 = t;
        double r20271678 = r20271676 / r20271677;
        double r20271679 = y;
        double r20271680 = x;
        double r20271681 = r20271679 - r20271680;
        double r20271682 = fma(r20271678, r20271681, r20271680);
        return r20271682;
}

Error

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

Target

Original	1.8
Target	2.0
Herbie	1.8

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

Initial program 1.8
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
Simplified1.8
\[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)}\]
Final simplification1.8
\[\leadsto \mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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