Average Error: 10.0 → 0.2
Time: 30.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.462623845658977322749437144610251377998 \cdot 10^{-37}:\\ \;\;\;\;\left(1 \cdot \frac{x}{z} + \frac{x}{z} \cdot y\right) - x\\ \mathbf{elif}\;x \le 2.068539181220407868990844181630071705591 \cdot 10^{-54}:\\ \;\;\;\;\left(\frac{y \cdot x}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - \left(z - 1\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.462623845658977322749437144610251377998 \cdot 10^{-37}:\\
\;\;\;\;\left(1 \cdot \frac{x}{z} + \frac{x}{z} \cdot y\right) - x\\

\mathbf{elif}\;x \le 2.068539181220407868990844181630071705591 \cdot 10^{-54}:\\
\;\;\;\;\left(\frac{y \cdot x}{z} + 1 \cdot \frac{x}{z}\right) - x\\

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

\end{array}
double f(double x, double y, double z) {
        double r33111141 = x;
        double r33111142 = y;
        double r33111143 = z;
        double r33111144 = r33111142 - r33111143;
        double r33111145 = 1.0;
        double r33111146 = r33111144 + r33111145;
        double r33111147 = r33111141 * r33111146;
        double r33111148 = r33111147 / r33111143;
        return r33111148;
}
↓
double f(double x, double y, double z) {
        double r33111149 = x;
        double r33111150 = -1.4626238456589773e-37;
        bool r33111151 = r33111149 <= r33111150;
        double r33111152 = 1.0;
        double r33111153 = z;
        double r33111154 = r33111149 / r33111153;
        double r33111155 = r33111152 * r33111154;
        double r33111156 = y;
        double r33111157 = r33111154 * r33111156;
        double r33111158 = r33111155 + r33111157;
        double r33111159 = r33111158 - r33111149;
        double r33111160 = 2.068539181220408e-54;
        bool r33111161 = r33111149 <= r33111160;
        double r33111162 = r33111156 * r33111149;
        double r33111163 = r33111162 / r33111153;
        double r33111164 = r33111163 + r33111155;
        double r33111165 = r33111164 - r33111149;
        double r33111166 = r33111153 - r33111152;
        double r33111167 = r33111156 - r33111166;
        double r33111168 = r33111167 / r33111153;
        double r33111169 = r33111149 * r33111168;
        double r33111170 = r33111161 ? r33111165 : r33111169;
        double r33111171 = r33111151 ? r33111159 : r33111170;
        return r33111171;
}

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

Original10.0
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 3 regimes

  2. if x < -1.4626238456589773e-37

    1. Initial program 22.2

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

    3. Applied associate-/l*0.3

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

    4. Taylor expanded around 0 7.6

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

    5. Simplified0.1

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

    if -1.4626238456589773e-37 < x < 2.068539181220408e-54

    1. Initial program 0.2

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

    2. Taylor expanded around 0 0.1

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

    if 2.068539181220408e-54 < x

    1. Initial program 19.8

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

    3. Applied associate-/l*0.2

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

    5. Applied div-inv0.4

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

    6. Simplified0.4

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.462623845658977322749437144610251377998 \cdot 10^{-37}:\\ \;\;\;\;\left(1 \cdot \frac{x}{z} + \frac{x}{z} \cdot y\right) - x\\ \mathbf{elif}\;x \le 2.068539181220407868990844181630071705591 \cdot 10^{-54}:\\ \;\;\;\;\left(\frac{y \cdot x}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - \left(z - 1\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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))