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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -3.766965029138646 \cdot 10^{211} \lor \neg \left(z \le 1.0645799767702823 \cdot 10^{217}\right):\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot \left(t - x\right) + x\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -3.766965029138646 \cdot 10^{211} \lor \neg \left(z \le 1.0645799767702823 \cdot 10^{217}\right):\\
\;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r600485 = x;
        double r600486 = y;
        double r600487 = z;
        double r600488 = r600486 - r600487;
        double r600489 = t;
        double r600490 = r600489 - r600485;
        double r600491 = r600488 * r600490;
        double r600492 = a;
        double r600493 = r600492 - r600487;
        double r600494 = r600491 / r600493;
        double r600495 = r600485 + r600494;
        return r600495;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r600496 = z;
        double r600497 = -3.7669650291386463e+211;
        bool r600498 = r600496 <= r600497;
        double r600499 = 1.0645799767702823e+217;
        bool r600500 = r600496 <= r600499;
        double r600501 = !r600500;
        bool r600502 = r600498 || r600501;
        double r600503 = y;
        double r600504 = x;
        double r600505 = r600504 / r600496;
        double r600506 = t;
        double r600507 = r600506 / r600496;
        double r600508 = r600505 - r600507;
        double r600509 = fma(r600503, r600508, r600506);
        double r600510 = r600503 - r600496;
        double r600511 = a;
        double r600512 = r600511 - r600496;
        double r600513 = r600510 / r600512;
        double r600514 = r600506 - r600504;
        double r600515 = r600513 * r600514;
        double r600516 = r600515 + r600504;
        double r600517 = r600502 ? r600509 : r600516;
        return r600517;
}

Original	25.2
Target	11.8
Herbie	9.6

Derivation

Split input into 2 regimes
if z < -3.7669650291386463e+211 or 1.0645799767702823e+217 < z
1. Initial program 51.5
  \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
2. Simplified25.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)}\]
3. Taylor expanded around inf 22.8
  \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]
4. Simplified12.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)}\]
if -3.7669650291386463e+211 < z < 1.0645799767702823e+217
1. Initial program 19.5
  \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
2. Simplified9.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)}\]
3. Using strategy rm
4. Applied fma-udef9.0
  \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x}\]
Recombined 2 regimes into one program.
Final simplification9.6
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.766965029138646 \cdot 10^{211} \lor \neg \left(z \le 1.0645799767702823 \cdot 10^{217}\right):\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot \left(t - x\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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

Error

Target

Derivation

`if z < -3.7669650291386463e+211 or 1.0645799767702823e+217 < z`

`if -3.7669650291386463e+211 < z < 1.0645799767702823e+217`

Reproduce