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

↓

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

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 r540664 = x;
        double r540665 = y;
        double r540666 = r540665 - r540664;
        double r540667 = z;
        double r540668 = r540666 * r540667;
        double r540669 = t;
        double r540670 = r540668 / r540669;
        double r540671 = r540664 + r540670;
        return r540671;
}

↓

double f(double x, double y, double z, double t) {
        double r540672 = z;
        double r540673 = 8.722376555020404e-83;
        bool r540674 = r540672 <= r540673;
        double r540675 = x;
        double r540676 = y;
        double r540677 = r540676 - r540675;
        double r540678 = t;
        double r540679 = r540672 / r540678;
        double r540680 = r540677 * r540679;
        double r540681 = r540675 + r540680;
        double r540682 = 2.11625050668119e+206;
        bool r540683 = r540672 <= r540682;
        double r540684 = r540677 / r540678;
        double r540685 = fma(r540684, r540672, r540675);
        double r540686 = r540678 / r540672;
        double r540687 = r540677 / r540686;
        double r540688 = r540675 + r540687;
        double r540689 = r540683 ? r540685 : r540688;
        double r540690 = r540674 ? r540681 : r540689;
        return r540690;
}

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