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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.53657593812259464 \cdot 10^{301}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.53657593812259464 \cdot 10^{301}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r488461 = x;
        double r488462 = y;
        double r488463 = z;
        double r488464 = t;
        double r488465 = r488463 - r488464;
        double r488466 = r488462 * r488465;
        double r488467 = a;
        double r488468 = r488463 - r488467;
        double r488469 = r488466 / r488468;
        double r488470 = r488461 + r488469;
        return r488470;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r488471 = y;
        double r488472 = z;
        double r488473 = t;
        double r488474 = r488472 - r488473;
        double r488475 = r488471 * r488474;
        double r488476 = a;
        double r488477 = r488472 - r488476;
        double r488478 = r488475 / r488477;
        double r488479 = -inf.0;
        bool r488480 = r488478 <= r488479;
        double r488481 = 2.5365759381225946e+301;
        bool r488482 = r488478 <= r488481;
        double r488483 = !r488482;
        bool r488484 = r488480 || r488483;
        double r488485 = r488474 / r488477;
        double r488486 = x;
        double r488487 = fma(r488485, r488471, r488486);
        double r488488 = r488486 + r488478;
        double r488489 = r488484 ? r488487 : r488488;
        return r488489;
}

Original	10.9
Target	1.3
Herbie	0.2

Derivation

Split input into 2 regimes
if (/ (* y (- z t)) (- z a)) < -inf.0 or 2.5365759381225946e+301 < (/ (* y (- z t)) (- z a))
1. Initial program 63.8
  \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
2. Simplified0.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)}\]
3. Using strategy rm
4. Applied clear-num0.3
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{z - a}{y}}}, z - t, x\right)\]
5. Using strategy rm
6. Applied fma-udef0.3
  \[\leadsto \color{blue}{\frac{1}{\frac{z - a}{y}} \cdot \left(z - t\right) + x}\]
7. Simplified0.2
  \[\leadsto \color{blue}{\frac{z - t}{\frac{z - a}{y}}} + x\]
8. Using strategy rm
9. Applied associate-/r/0.2
  \[\leadsto \color{blue}{\frac{z - t}{z - a} \cdot y} + x\]
10. Applied fma-def0.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)}\]
if -inf.0 < (/ (* y (- z t)) (- z a)) < 2.5365759381225946e+301
1. Initial program 0.2
  \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.53657593812259464 \cdot 10^{301}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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

Error

Target

Derivation

`if (/ (* y (- z t)) (- z a)) < -inf.0 or 2.5365759381225946e+301 < (/ (* y (- z t)) (- z a))`

`if -inf.0 < (/ (* y (- z t)) (- z a)) < 2.5365759381225946e+301`

Reproduce