Average Error: 10.4 → 0.2
Time: 3.1s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4537181300022055465139962904576:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{elif}\;z \le 10852378853767397241265820316179722403840:\\ \;\;\;\;\frac{x \cdot \left(y - z\right) + x \cdot 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4537181300022055465139962904576:\\
\;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\

\mathbf{elif}\;z \le 10852378853767397241265820316179722403840:\\
\;\;\;\;\frac{x \cdot \left(y - z\right) + x \cdot 1}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r704149 = x;
        double r704150 = y;
        double r704151 = z;
        double r704152 = r704150 - r704151;
        double r704153 = 1.0;
        double r704154 = r704152 + r704153;
        double r704155 = r704149 * r704154;
        double r704156 = r704155 / r704151;
        return r704156;
}
↓
double f(double x, double y, double z) {
        double r704157 = z;
        double r704158 = -4.5371813000220555e+30;
        bool r704159 = r704157 <= r704158;
        double r704160 = x;
        double r704161 = y;
        double r704162 = r704161 - r704157;
        double r704163 = 1.0;
        double r704164 = r704162 + r704163;
        double r704165 = r704164 / r704157;
        double r704166 = r704160 * r704165;
        double r704167 = 1.0852378853767397e+40;
        bool r704168 = r704157 <= r704167;
        double r704169 = r704160 * r704162;
        double r704170 = r704160 * r704163;
        double r704171 = r704169 + r704170;
        double r704172 = r704171 / r704157;
        double r704173 = r704157 / r704164;
        double r704174 = r704160 / r704173;
        double r704175 = r704168 ? r704172 : r704174;
        double r704176 = r704159 ? r704166 : r704175;
        return r704176;
}

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

Original10.4
Target0.4
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 3 regimes

  2. if z < -4.5371813000220555e+30

    1. Initial program 18.8

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

    3. Applied *-un-lft-identity18.8

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -4.5371813000220555e+30 < z < 1.0852378853767397e+40

    1. Initial program 0.3

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

    3. Applied distribute-lft-in0.3

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

    if 1.0852378853767397e+40 < z

    1. Initial program 19.2

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

    3. Applied associate-/l*0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4537181300022055465139962904576:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{elif}\;z \le 10852378853767397241265820316179722403840:\\ \;\;\;\;\frac{x \cdot \left(y - z\right) + x \cdot 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))