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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -3.007379862259038223700121580907401945548 \cdot 10^{-291}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \mathbf{elif}\;x \le 1.512634081989243287548036584812913373901 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}} + x\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -3.007379862259038223700121580907401945548 \cdot 10^{-291}:\\
\;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\

\mathbf{elif}\;x \le 1.512634081989243287548036584812913373901 \cdot 10^{-54}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\

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

\end{array}

double f(double x, double y, double z, double t) {
        double r305329 = x;
        double r305330 = y;
        double r305331 = r305330 - r305329;
        double r305332 = z;
        double r305333 = r305331 * r305332;
        double r305334 = t;
        double r305335 = r305333 / r305334;
        double r305336 = r305329 + r305335;
        return r305336;
}

↓

double f(double x, double y, double z, double t) {
        double r305337 = x;
        double r305338 = -3.0073798622590382e-291;
        bool r305339 = r305337 <= r305338;
        double r305340 = y;
        double r305341 = r305340 - r305337;
        double r305342 = z;
        double r305343 = t;
        double r305344 = r305342 / r305343;
        double r305345 = fma(r305341, r305344, r305337);
        double r305346 = 1.5126340819892433e-54;
        bool r305347 = r305337 <= r305346;
        double r305348 = r305341 / r305343;
        double r305349 = fma(r305348, r305342, r305337);
        double r305350 = r305343 / r305342;
        double r305351 = r305341 / r305350;
        double r305352 = r305351 + r305337;
        double r305353 = r305347 ? r305349 : r305352;
        double r305354 = r305339 ? r305345 : r305353;
        return r305354;
}

Original	6.7
Target	2.1
Herbie	2.0

Derivation

Split input into 3 regimes
if x < -3.0073798622590382e-291
1. Initial program 6.6
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Simplified1.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)}\]
if -3.0073798622590382e-291 < x < 1.5126340819892433e-54
1. Initial program 5.3
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Using strategy rm
3. Applied *-un-lft-identity5.3
  \[\leadsto x + \color{blue}{1 \cdot \frac{\left(y - x\right) \cdot z}{t}}\]
4. Applied *-un-lft-identity5.3
  \[\leadsto \color{blue}{1 \cdot x} + 1 \cdot \frac{\left(y - x\right) \cdot z}{t}\]
5. Applied distribute-lft-out5.3
  \[\leadsto \color{blue}{1 \cdot \left(x + \frac{\left(y - x\right) \cdot z}{t}\right)}\]
6. Simplified4.5
  \[\leadsto 1 \cdot \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]
if 1.5126340819892433e-54 < x
1. Initial program 8.2
  \[x + \frac{\left(y - x\right) \cdot z}{t}\]
2. Using strategy rm
3. Applied associate-/l*0.2
  \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
Recombined 3 regimes into one program.
Final simplification2.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.007379862259038223700121580907401945548 \cdot 10^{-291}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \mathbf{elif}\;x \le 1.512634081989243287548036584812913373901 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"

  :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 < -3.0073798622590382e-291`

`if -3.0073798622590382e-291 < x < 1.5126340819892433e-54`

`if 1.5126340819892433e-54 < x`

Reproduce