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

↓

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

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

↓

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

double f(double x, double y, double z, double t) {
        double r298430 = x;
        double r298431 = y;
        double r298432 = r298431 - r298430;
        double r298433 = z;
        double r298434 = t;
        double r298435 = r298433 / r298434;
        double r298436 = r298432 * r298435;
        double r298437 = r298430 + r298436;
        return r298437;
}

↓

double f(double x, double y, double z, double t) {
        double r298438 = y;
        double r298439 = x;
        double r298440 = r298438 - r298439;
        double r298441 = z;
        double r298442 = t;
        double r298443 = r298441 / r298442;
        double r298444 = fma(r298440, r298443, r298439);
        return r298444;
}

Error

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

Target

Original	2.1
Target	2.3
Herbie	2.1

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

Derivation

Initial program 2.1
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
Simplified2.1
\[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)}\]
Final simplification2.1
\[\leadsto \mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ 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))))