Average Error: 6.5 → 1.6
Time: 3.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.3470219673435147 \cdot 10^{-109} \lor \neg \left(t \le 7.16783763326229843 \cdot 10^{-96}\right):\\ \;\;\;\;1 \cdot \left(x + \frac{y - x}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.3470219673435147 \cdot 10^{-109} \lor \neg \left(t \le 7.16783763326229843 \cdot 10^{-96}\right):\\
\;\;\;\;1 \cdot \left(x + \frac{y - x}{\frac{t}{z}}\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 r556323 = x;
        double r556324 = y;
        double r556325 = r556324 - r556323;
        double r556326 = z;
        double r556327 = r556325 * r556326;
        double r556328 = t;
        double r556329 = r556327 / r556328;
        double r556330 = r556323 + r556329;
        return r556330;
}
↓
double f(double x, double y, double z, double t) {
        double r556331 = t;
        double r556332 = -9.347021967343515e-109;
        bool r556333 = r556331 <= r556332;
        double r556334 = 7.1678376332622984e-96;
        bool r556335 = r556331 <= r556334;
        double r556336 = !r556335;
        bool r556337 = r556333 || r556336;
        double r556338 = 1.0;
        double r556339 = x;
        double r556340 = y;
        double r556341 = r556340 - r556339;
        double r556342 = z;
        double r556343 = r556331 / r556342;
        double r556344 = r556341 / r556343;
        double r556345 = r556339 + r556344;
        double r556346 = r556338 * r556345;
        double r556347 = r556341 * r556342;
        double r556348 = r556347 / r556331;
        double r556349 = r556339 + r556348;
        double r556350 = r556337 ? r556346 : r556349;
        return r556350;
}

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

Original6.5
Target2.0
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -9.347021967343515e-109 or 7.1678376332622984e-96 < t

    1. Initial program 7.4

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

    3. Applied associate-/l*1.2

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

    5. Applied *-un-lft-identity1.2

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

    if -9.347021967343515e-109 < t < 7.1678376332622984e-96

    1. Initial program 3.2

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.3470219673435147 \cdot 10^{-109} \lor \neg \left(t \le 7.16783763326229843 \cdot 10^{-96}\right):\\ \;\;\;\;1 \cdot \left(x + \frac{y - x}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(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)))