Average Error: 6.6 → 2.0
Time: 14.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.800389692060424312600133254503662266438 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le -3.615258638221127683072678174846267896082 \cdot 10^{-215}:\\ \;\;\;\;\frac{\frac{y - x}{t}}{\frac{1}{z}} + x\\ \mathbf{elif}\;x \le 1.013053324772574326625267410473662208197 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le 6.938243238828456220383561175139930807294 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}} + x\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.800389692060424312600133254503662266438 \cdot 10^{-86}:\\
\;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\

\mathbf{elif}\;x \le -3.615258638221127683072678174846267896082 \cdot 10^{-215}:\\
\;\;\;\;\frac{\frac{y - x}{t}}{\frac{1}{z}} + x\\

\mathbf{elif}\;x \le 1.013053324772574326625267410473662208197 \cdot 10^{-244}:\\
\;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\

\mathbf{elif}\;x \le 6.938243238828456220383561175139930807294 \cdot 10^{-144}:\\
\;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r26323334 = x;
        double r26323335 = y;
        double r26323336 = r26323335 - r26323334;
        double r26323337 = z;
        double r26323338 = r26323336 * r26323337;
        double r26323339 = t;
        double r26323340 = r26323338 / r26323339;
        double r26323341 = r26323334 + r26323340;
        return r26323341;
}
↓
double f(double x, double y, double z, double t) {
        double r26323342 = x;
        double r26323343 = -4.800389692060424e-86;
        bool r26323344 = r26323342 <= r26323343;
        double r26323345 = z;
        double r26323346 = t;
        double r26323347 = r26323345 / r26323346;
        double r26323348 = y;
        double r26323349 = r26323348 - r26323342;
        double r26323350 = r26323347 * r26323349;
        double r26323351 = r26323342 + r26323350;
        double r26323352 = -3.6152586382211277e-215;
        bool r26323353 = r26323342 <= r26323352;
        double r26323354 = r26323349 / r26323346;
        double r26323355 = 1.0;
        double r26323356 = r26323355 / r26323345;
        double r26323357 = r26323354 / r26323356;
        double r26323358 = r26323357 + r26323342;
        double r26323359 = 1.0130533247725743e-244;
        bool r26323360 = r26323342 <= r26323359;
        double r26323361 = 6.938243238828456e-144;
        bool r26323362 = r26323342 <= r26323361;
        double r26323363 = r26323349 * r26323345;
        double r26323364 = r26323363 / r26323346;
        double r26323365 = r26323364 + r26323342;
        double r26323366 = r26323346 / r26323345;
        double r26323367 = r26323349 / r26323366;
        double r26323368 = r26323367 + r26323342;
        double r26323369 = r26323362 ? r26323365 : r26323368;
        double r26323370 = r26323360 ? r26323351 : r26323369;
        double r26323371 = r26323353 ? r26323358 : r26323370;
        double r26323372 = r26323344 ? r26323351 : r26323371;
        return r26323372;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.6
Target1.9
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -4.800389692060424e-86 or -3.6152586382211277e-215 < x < 1.0130533247725743e-244

    1. Initial program 6.8

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity6.8

      \[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{1 \cdot t}}\]

    4. Applied times-frac2.0

      \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]

    5. Simplified2.0

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

    if -4.800389692060424e-86 < x < -3.6152586382211277e-215

    1. Initial program 4.6

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
    2. Using strategy rm

    3. Applied associate-/l*3.1

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
    4. Using strategy rm

    5. Applied div-inv3.2

      \[\leadsto x + \frac{y - x}{\color{blue}{t \cdot \frac{1}{z}}}\]

    6. Applied associate-/r*4.5

      \[\leadsto x + \color{blue}{\frac{\frac{y - x}{t}}{\frac{1}{z}}}\]

    if 1.0130533247725743e-244 < x < 6.938243238828456e-144

    1. Initial program 4.3

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

    if 6.938243238828456e-144 < x

    1. Initial program 7.6

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
    2. Using strategy rm

    3. Applied associate-/l*0.7

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.800389692060424312600133254503662266438 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le -3.615258638221127683072678174846267896082 \cdot 10^{-215}:\\ \;\;\;\;\frac{\frac{y - x}{t}}{\frac{1}{z}} + x\\ \mathbf{elif}\;x \le 1.013053324772574326625267410473662208197 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le 6.938243238828456220383561175139930807294 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(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)))