Average Error: 10.5 → 0.2
Time: 12.6s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.001862668948682683719019062200331892161 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 1900831.650325161404907703399658203125:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.001862668948682683719019062200331892161 \cdot 10^{54}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;z \le 1900831.650325161404907703399658203125:\\
\;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\end{array}
double f(double x, double y, double z) {
        double r47647319 = x;
        double r47647320 = y;
        double r47647321 = z;
        double r47647322 = r47647320 - r47647321;
        double r47647323 = 1.0;
        double r47647324 = r47647322 + r47647323;
        double r47647325 = r47647319 * r47647324;
        double r47647326 = r47647325 / r47647321;
        return r47647326;
}
↓
double f(double x, double y, double z) {
        double r47647327 = z;
        double r47647328 = -2.0018626689486827e+54;
        bool r47647329 = r47647327 <= r47647328;
        double r47647330 = x;
        double r47647331 = y;
        double r47647332 = r47647331 - r47647327;
        double r47647333 = 1.0;
        double r47647334 = r47647332 + r47647333;
        double r47647335 = r47647327 / r47647334;
        double r47647336 = r47647330 / r47647335;
        double r47647337 = 1900831.6503251614;
        bool r47647338 = r47647327 <= r47647337;
        double r47647339 = r47647330 * r47647334;
        double r47647340 = r47647339 / r47647327;
        double r47647341 = r47647338 ? r47647340 : r47647336;
        double r47647342 = r47647329 ? r47647336 : r47647341;
        return r47647342;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.5
Target0.5
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.0018626689486827e+54 or 1900831.6503251614 < z

    1. Initial program 18.4

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.1

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

    if -2.0018626689486827e+54 < z < 1900831.6503251614

    1. Initial program 0.5

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.001862668948682683719019062200331892161 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 1900831.650325161404907703399658203125:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))