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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2.3206655123942797 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{elif}\;z \le 5.542680570447865 \cdot 10^{+157}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -2.3206655123942797 \cdot 10^{+53}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\

\mathbf{elif}\;z \le 5.542680570447865 \cdot 10^{+157}:\\
\;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\

\mathbf{else}:\\
\;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\

\end{array}

double f(double x, double y, double z, double t) {
        double r27581159 = x;
        double r27581160 = y;
        double r27581161 = r27581160 - r27581159;
        double r27581162 = z;
        double r27581163 = t;
        double r27581164 = r27581162 / r27581163;
        double r27581165 = r27581161 * r27581164;
        double r27581166 = r27581159 + r27581165;
        return r27581166;
}

↓

double f(double x, double y, double z, double t) {
        double r27581167 = z;
        double r27581168 = -2.3206655123942797e+53;
        bool r27581169 = r27581167 <= r27581168;
        double r27581170 = y;
        double r27581171 = x;
        double r27581172 = r27581170 - r27581171;
        double r27581173 = t;
        double r27581174 = r27581172 / r27581173;
        double r27581175 = fma(r27581174, r27581167, r27581171);
        double r27581176 = 5.542680570447865e+157;
        bool r27581177 = r27581167 <= r27581176;
        double r27581178 = r27581172 * r27581167;
        double r27581179 = r27581178 / r27581173;
        double r27581180 = r27581179 + r27581171;
        double r27581181 = r27581167 / r27581173;
        double r27581182 = r27581181 * r27581172;
        double r27581183 = r27581171 + r27581182;
        double r27581184 = r27581177 ? r27581180 : r27581183;
        double r27581185 = r27581169 ? r27581175 : r27581184;
        return r27581185;
}

Original	2.1
Target	2.3
Herbie	2.5

Derivation

Split input into 3 regimes
if z < -2.3206655123942797e+53
1. Initial program 5.6
  \[x + \left(y - x\right) \cdot \frac{z}{t}\]
2. Simplified2.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]
if -2.3206655123942797e+53 < z < 5.542680570447865e+157
1. Initial program 1.2
  \[x + \left(y - x\right) \cdot \frac{z}{t}\]
2. Using strategy rm
3. Applied associate-*r/2.3
  \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}}\]
if 5.542680570447865e+157 < z
1. Initial program 5.2
  \[x + \left(y - x\right) \cdot \frac{z}{t}\]
Recombined 3 regimes into one program.
Final simplification2.5
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.3206655123942797 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{elif}\;z \le 5.542680570447865 \cdot 10^{+157}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 +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))))

Error

Target

Derivation

`if z < -2.3206655123942797e+53`

`if -2.3206655123942797e+53 < z < 5.542680570447865e+157`

`if 5.542680570447865e+157 < z`

Reproduce