Average Error: 6.4 → 0.3
Time: 3.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -7.121739380084154 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 8.8208746245571606 \cdot 10^{264}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -\infty:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -7.121739380084154 \cdot 10^{-271}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le -0.0:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 8.8208746245571606 \cdot 10^{264}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r3522 = x;
        double r3523 = y;
        double r3524 = r3522 * r3523;
        double r3525 = z;
        double r3526 = r3524 / r3525;
        return r3526;
}
↓
double f(double x, double y, double z) {
        double r3527 = x;
        double r3528 = y;
        double r3529 = r3527 * r3528;
        double r3530 = -inf.0;
        bool r3531 = r3529 <= r3530;
        double r3532 = z;
        double r3533 = r3528 / r3532;
        double r3534 = r3527 * r3533;
        double r3535 = -7.121739380084154e-271;
        bool r3536 = r3529 <= r3535;
        double r3537 = r3529 / r3532;
        double r3538 = -0.0;
        bool r3539 = r3529 <= r3538;
        double r3540 = r3532 / r3528;
        double r3541 = r3527 / r3540;
        double r3542 = 8.82087462455716e+264;
        bool r3543 = r3529 <= r3542;
        double r3544 = r3543 ? r3537 : r3541;
        double r3545 = r3539 ? r3541 : r3544;
        double r3546 = r3536 ? r3537 : r3545;
        double r3547 = r3531 ? r3534 : r3546;
        return r3547;
}

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

Original6.4
Target6.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    if -inf.0 < (* x y) < -7.121739380084154e-271 or -0.0 < (* x y) < 8.82087462455716e+264

    1. Initial program 0.3

      \[\frac{x \cdot y}{z}\]

    if -7.121739380084154e-271 < (* x y) < -0.0 or 8.82087462455716e+264 < (* x y)

    1. Initial program 22.7

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

    3. Applied associate-/l*0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -7.121739380084154 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 8.8208746245571606 \cdot 10^{264}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(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))