Average Error: 6.0 → 3.4
Time: 7.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.4829212502580601 \cdot 10^{-130} \lor \neg \left(x \cdot y \le 3.353944357483643 \cdot 10^{-120}\right) \land x \cdot y \le 1.48436680561384441 \cdot 10^{38}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{1}{x}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -2.4829212502580601 \cdot 10^{-130} \lor \neg \left(x \cdot y \le 3.353944357483643 \cdot 10^{-120}\right) \land x \cdot y \le 1.48436680561384441 \cdot 10^{38}:\\
\;\;\;\;\frac{1}{z \cdot \frac{\frac{1}{x}}{y}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r829558 = x;
        double r829559 = y;
        double r829560 = r829558 * r829559;
        double r829561 = z;
        double r829562 = r829560 / r829561;
        return r829562;
}
↓
double f(double x, double y, double z) {
        double r829563 = x;
        double r829564 = y;
        double r829565 = r829563 * r829564;
        double r829566 = -2.48292125025806e-130;
        bool r829567 = r829565 <= r829566;
        double r829568 = 3.353944357483643e-120;
        bool r829569 = r829565 <= r829568;
        double r829570 = !r829569;
        double r829571 = 1.4843668056138444e+38;
        bool r829572 = r829565 <= r829571;
        bool r829573 = r829570 && r829572;
        bool r829574 = r829567 || r829573;
        double r829575 = 1.0;
        double r829576 = z;
        double r829577 = r829575 / r829563;
        double r829578 = r829577 / r829564;
        double r829579 = r829576 * r829578;
        double r829580 = r829575 / r829579;
        double r829581 = r829576 / r829564;
        double r829582 = r829563 / r829581;
        double r829583 = r829574 ? r829580 : r829582;
        return r829583;
}

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

Original6.0
Target6.6
Herbie3.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -2.48292125025806e-130 or 3.353944357483643e-120 < (* x y) < 1.4843668056138444e+38

    1. Initial program 3.8

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*10.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
    4. Using strategy rm

    5. Applied clear-num10.5

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{y}}{x}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity10.5

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

    8. Applied div-inv10.6

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

    9. Applied times-frac3.9

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

    10. Simplified3.9

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

    11. Simplified3.9

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

    if -2.48292125025806e-130 < (* x y) < 3.353944357483643e-120 or 1.4843668056138444e+38 < (* x y)

    1. Initial program 7.9

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*3.0

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -2.4829212502580601 \cdot 10^{-130} \lor \neg \left(x \cdot y \le 3.353944357483643 \cdot 10^{-120}\right) \land x \cdot y \le 1.48436680561384441 \cdot 10^{38}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{1}{x}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))