Average Error: 9.7 → 0.2
Time: 9.0s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.5083267701132725 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 5724342807205024770:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.5083267701132725 \cdot 10^{-75}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;z \le 5724342807205024770:\\
\;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r503154 = x;
        double r503155 = y;
        double r503156 = z;
        double r503157 = r503155 - r503156;
        double r503158 = 1.0;
        double r503159 = r503157 + r503158;
        double r503160 = r503154 * r503159;
        double r503161 = r503160 / r503156;
        return r503161;
}
↓
double f(double x, double y, double z) {
        double r503162 = z;
        double r503163 = -1.5083267701132725e-75;
        bool r503164 = r503162 <= r503163;
        double r503165 = x;
        double r503166 = y;
        double r503167 = r503166 - r503162;
        double r503168 = 1.0;
        double r503169 = r503167 + r503168;
        double r503170 = r503162 / r503169;
        double r503171 = r503165 / r503170;
        double r503172 = 5.724342807205025e+18;
        bool r503173 = r503162 <= r503172;
        double r503174 = r503165 / r503162;
        double r503175 = r503174 * r503169;
        double r503176 = r503169 / r503162;
        double r503177 = r503165 * r503176;
        double r503178 = r503173 ? r503175 : r503177;
        double r503179 = r503164 ? r503171 : r503178;
        return r503179;
}

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

Original9.7
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.5083267701132725e-75

    1. Initial program 13.1

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

    3. Applied associate-/l*0.4

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

    if -1.5083267701132725e-75 < z < 5.724342807205025e+18

    1. Initial program 0.1

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

    3. Applied associate-/l*8.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.2

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

    if 5.724342807205025e+18 < z

    1. Initial program 17.0

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

    3. Applied *-un-lft-identity17.0

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.5083267701132725 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 5724342807205024770:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(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))