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

↓

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

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 r570296 = x;
        double r570297 = y;
        double r570298 = r570297 - r570296;
        double r570299 = z;
        double r570300 = t;
        double r570301 = r570299 / r570300;
        double r570302 = r570298 * r570301;
        double r570303 = r570296 + r570302;
        return r570303;
}

↓

double f(double x, double y, double z, double t) {
        double r570304 = y;
        double r570305 = x;
        double r570306 = r570304 - r570305;
        double r570307 = z;
        double r570308 = t;
        double r570309 = r570307 / r570308;
        double r570310 = fma(r570306, r570309, r570305);
        return r570310;
}

Error

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

Target

Original	1.9
Target	2.0
Herbie	1.9

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

Initial program 1.9
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
Simplified1.9
\[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)}\]
Final simplification1.9
\[\leadsto \mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\]

Reproduce

herbie shell --seed 2020021 +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))))