Average Error: 13.0 → 2.3
Time: 8.8s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.8543074289294527 \cdot 10^{47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \le -1.95697399262548232 \cdot 10^{-305}:\\ \;\;\;\;x + \left(-\frac{x \cdot z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.8543074289294527 \cdot 10^{47}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

\mathbf{elif}\;x \le -1.95697399262548232 \cdot 10^{-305}:\\
\;\;\;\;x + \left(-\frac{x \cdot z}{y}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\end{array}
double f(double x, double y, double z) {
        double r1341076 = x;
        double r1341077 = y;
        double r1341078 = z;
        double r1341079 = r1341077 - r1341078;
        double r1341080 = r1341076 * r1341079;
        double r1341081 = r1341080 / r1341077;
        return r1341081;
}
↓
double f(double x, double y, double z) {
        double r1341082 = x;
        double r1341083 = -1.8543074289294527e+47;
        bool r1341084 = r1341082 <= r1341083;
        double r1341085 = 1.0;
        double r1341086 = z;
        double r1341087 = y;
        double r1341088 = r1341086 / r1341087;
        double r1341089 = r1341085 - r1341088;
        double r1341090 = r1341082 * r1341089;
        double r1341091 = -1.9569739926254823e-305;
        bool r1341092 = r1341082 <= r1341091;
        double r1341093 = r1341082 * r1341086;
        double r1341094 = r1341093 / r1341087;
        double r1341095 = -r1341094;
        double r1341096 = r1341082 + r1341095;
        double r1341097 = r1341087 - r1341086;
        double r1341098 = r1341087 / r1341097;
        double r1341099 = r1341082 / r1341098;
        double r1341100 = r1341092 ? r1341096 : r1341099;
        double r1341101 = r1341084 ? r1341090 : r1341100;
        return r1341101;
}

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

Original13.0
Target2.9
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.8543074289294527e+47

    1. Initial program 27.0

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

    3. Applied *-un-lft-identity27.0

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    6. Simplified0.1

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

    if -1.8543074289294527e+47 < x < -1.9569739926254823e-305

    1. Initial program 4.8

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

    3. Applied *-un-lft-identity4.8

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

    4. Applied times-frac4.4

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

    5. Simplified4.4

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

    6. Simplified4.4

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

    8. Applied sub-neg4.4

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

    9. Applied distribute-lft-in4.4

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

    10. Simplified4.4

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

    11. Simplified2.6

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

    if -1.9569739926254823e-305 < x

    1. Initial program 13.2

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

    3. Applied associate-/l*2.8

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.8543074289294527 \cdot 10^{47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \le -1.95697399262548232 \cdot 10^{-305}:\\ \;\;\;\;x + \left(-\frac{x \cdot z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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