Average Error: 6.5 → 1.4
Time: 3.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.782228900807808857038191301769811324591 \cdot 10^{-260}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.782228900807808857038191301769811324591 \cdot 10^{-260}\right):\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r504269 = x;
        double r504270 = y;
        double r504271 = r504270 - r504269;
        double r504272 = z;
        double r504273 = r504271 * r504272;
        double r504274 = t;
        double r504275 = r504273 / r504274;
        double r504276 = r504269 + r504275;
        return r504276;
}
↓
double f(double x, double y, double z, double t) {
        double r504277 = x;
        double r504278 = y;
        double r504279 = r504278 - r504277;
        double r504280 = z;
        double r504281 = r504279 * r504280;
        double r504282 = t;
        double r504283 = r504281 / r504282;
        double r504284 = r504277 + r504283;
        double r504285 = -inf.0;
        bool r504286 = r504284 <= r504285;
        double r504287 = 4.782228900807809e-260;
        bool r504288 = r504284 <= r504287;
        double r504289 = !r504288;
        bool r504290 = r504286 || r504289;
        double r504291 = 1.0;
        double r504292 = r504282 / r504280;
        double r504293 = r504292 / r504279;
        double r504294 = r504291 / r504293;
        double r504295 = r504277 + r504294;
        double r504296 = r504290 ? r504295 : r504284;
        return r504296;
}

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
Target2.2
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0 or 4.782228900807809e-260 < (+ x (/ (* (- y x) z) t))

    1. Initial program 11.4

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

    3. Applied associate-/l*1.7

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

    5. Applied clear-num1.8

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 4.782228900807809e-260

    1. Initial program 0.9

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.782228900807808857038191301769811324591 \cdot 10^{-260}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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)))