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

↓

\[\begin{array}{l} \mathbf{if}\;z \le 8.72237655502040412 \cdot 10^{-83}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \le 2.11625050668119009 \cdot 10^{206}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le 8.72237655502040412 \cdot 10^{-83}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;z \le 2.11625050668119009 \cdot 10^{206}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\end{array}

double f(double x, double y, double z, double t) {
        double r582581 = x;
        double r582582 = y;
        double r582583 = r582582 - r582581;
        double r582584 = z;
        double r582585 = r582583 * r582584;
        double r582586 = t;
        double r582587 = r582585 / r582586;
        double r582588 = r582581 + r582587;
        return r582588;
}

↓

double f(double x, double y, double z, double t) {
        double r582589 = z;
        double r582590 = 8.722376555020404e-83;
        bool r582591 = r582589 <= r582590;
        double r582592 = x;
        double r582593 = y;
        double r582594 = r582593 - r582592;
        double r582595 = t;
        double r582596 = r582589 / r582595;
        double r582597 = r582594 * r582596;
        double r582598 = r582592 + r582597;
        double r582599 = 2.11625050668119e+206;
        bool r582600 = r582589 <= r582599;
        double r582601 = r582594 / r582595;
        double r582602 = fma(r582601, r582589, r582592);
        double r582603 = r582595 / r582589;
        double r582604 = r582594 / r582603;
        double r582605 = r582592 + r582604;
        double r582606 = r582600 ? r582602 : r582605;
        double r582607 = r582591 ? r582598 : r582606;
        return r582607;
}

Original	6.5
Target	2.2
Herbie	2.0

Derivation

Split input into 3 regimes
if z < 8.722376555020404e-83
1. Initial program 5.0
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Using strategy rm
3. Applied *-un-lft-identity5.0
  \[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{1 \cdot t}}\]
4. Applied times-frac1.9
  \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]
5. Simplified1.9
  \[\leadsto x + \color{blue}{\left(y - x\right)} \cdot \frac{z}{t}\]
if 8.722376555020404e-83 < z < 2.11625050668119e+206
1. Initial program 7.7
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Simplified1.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]
if 2.11625050668119e+206 < z
1. Initial program 25.3
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Using strategy rm
3. Applied associate-/l*7.6
  \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
Recombined 3 regimes into one program.
Final simplification2.0
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le 8.72237655502040412 \cdot 10^{-83}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \le 2.11625050668119009 \cdot 10^{206}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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 z < 8.722376555020404e-83`

`if 8.722376555020404e-83 < z < 2.11625050668119e+206`

`if 2.11625050668119e+206 < z`

Reproduce