Average Error: 6.6 → 2.2
Time: 3.4s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.01649379191452465 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.01649379191452465 \cdot 10^{-92}:\\
\;\;\;\;x + \frac{y - x}{t} \cdot z\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r520928 = x;
        double r520929 = y;
        double r520930 = r520929 - r520928;
        double r520931 = z;
        double r520932 = r520930 * r520931;
        double r520933 = t;
        double r520934 = r520932 / r520933;
        double r520935 = r520928 + r520934;
        return r520935;
}
↓
double f(double x, double y, double z, double t) {
        double r520936 = z;
        double r520937 = -4.0164937919145246e-92;
        bool r520938 = r520936 <= r520937;
        double r520939 = x;
        double r520940 = y;
        double r520941 = r520940 - r520939;
        double r520942 = t;
        double r520943 = r520941 / r520942;
        double r520944 = r520943 * r520936;
        double r520945 = r520939 + r520944;
        double r520946 = r520936 / r520942;
        double r520947 = r520941 * r520946;
        double r520948 = r520939 + r520947;
        double r520949 = r520938 ? r520945 : r520948;
        return r520949;
}

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
Target2.2
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.0164937919145246e-92

    1. Initial program 10.3

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

    3. Applied associate-/l*2.4

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

    5. Applied associate-/r/2.9

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

    if -4.0164937919145246e-92 < z

    1. Initial program 5.2

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

    3. Applied *-un-lft-identity5.2

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

    4. Applied times-frac2.0

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

    5. Simplified2.0

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.01649379191452465 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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)))