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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le -2.12540069280457327 \cdot 10^{-224}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le -2.12540069280457327 \cdot 10^{-224}\right):\\
\;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\

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

\end{array}

double f(double x, double y, double z, double t) {
        double r444638 = x;
        double r444639 = y;
        double r444640 = r444639 - r444638;
        double r444641 = z;
        double r444642 = r444640 * r444641;
        double r444643 = t;
        double r444644 = r444642 / r444643;
        double r444645 = r444638 + r444644;
        return r444645;
}

↓

double f(double x, double y, double z, double t) {
        double r444646 = x;
        double r444647 = y;
        double r444648 = r444647 - r444646;
        double r444649 = z;
        double r444650 = r444648 * r444649;
        double r444651 = t;
        double r444652 = r444650 / r444651;
        double r444653 = r444646 + r444652;
        double r444654 = -inf.0;
        bool r444655 = r444653 <= r444654;
        double r444656 = -2.1254006928045733e-224;
        bool r444657 = r444653 <= r444656;
        double r444658 = !r444657;
        bool r444659 = r444655 || r444658;
        double r444660 = r444649 / r444651;
        double r444661 = fma(r444648, r444660, r444646);
        double r444662 = r444659 ? r444661 : r444653;
        return r444662;
}

Original	6.1
Target	2.0
Herbie	1.3

Derivation

Split input into 2 regimes
if (+ x (/ (* (- y x) z) t)) < -inf.0 or -2.1254006928045733e-224 < (+ x (/ (* (- y x) z) t))
1. Initial program 10.4
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Simplified5.6
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]
3. Using strategy rm
4. Applied fma-udef5.6
  \[\leadsto \color{blue}{\frac{y - x}{t} \cdot z + x}\]
5. Using strategy rm
6. Applied div-inv5.6
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \frac{1}{t}\right)} \cdot z + x\]
7. Applied associate-*l*2.0
  \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(\frac{1}{t} \cdot z\right)} + x\]
8. Simplified2.0
  \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z}{t}} + x\]
9. Using strategy rm
10. Applied fma-def2.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)}\]
if -inf.0 < (+ x (/ (* (- y x) z) t)) < -2.1254006928045733e-224
1. Initial program 0.4
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
Recombined 2 regimes into one program.
Final simplification1.3
\[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le -2.12540069280457327 \cdot 10^{-224}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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

Error

Target

Derivation

`if (+ x (/ (* (- y x) z) t)) < -inf.0 or -2.1254006928045733e-224 < (+ x (/ (* (- y x) z) t))`

`if -inf.0 < (+ x (/ (* (- y x) z) t)) < -2.1254006928045733e-224`

Reproduce