Average Error: 6.6 → 0.3
Time: 1.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -7.92636400136768842 \cdot 10^{-208}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.68166276423310295 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 7.8533070445434405 \cdot 10^{220}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{y}}{x}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -\infty:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -7.92636400136768842 \cdot 10^{-208}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 2.68166276423310295 \cdot 10^{-233}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 7.8533070445434405 \cdot 10^{220}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{y}}{x}}\\

\end{array}
double f(double x, double y, double z) {
        double r722549 = x;
        double r722550 = y;
        double r722551 = r722549 * r722550;
        double r722552 = z;
        double r722553 = r722551 / r722552;
        return r722553;
}
↓
double f(double x, double y, double z) {
        double r722554 = x;
        double r722555 = y;
        double r722556 = r722554 * r722555;
        double r722557 = -inf.0;
        bool r722558 = r722556 <= r722557;
        double r722559 = z;
        double r722560 = r722559 / r722555;
        double r722561 = r722554 / r722560;
        double r722562 = -7.926364001367688e-208;
        bool r722563 = r722556 <= r722562;
        double r722564 = r722556 / r722559;
        double r722565 = 2.681662764233103e-233;
        bool r722566 = r722556 <= r722565;
        double r722567 = r722555 / r722559;
        double r722568 = r722554 * r722567;
        double r722569 = 7.85330704454344e+220;
        bool r722570 = r722556 <= r722569;
        double r722571 = 1.0;
        double r722572 = r722560 / r722554;
        double r722573 = r722571 / r722572;
        double r722574 = r722570 ? r722564 : r722573;
        double r722575 = r722566 ? r722568 : r722574;
        double r722576 = r722563 ? r722564 : r722575;
        double r722577 = r722558 ? r722561 : r722576;
        return r722577;
}

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

Original6.6
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 4 regimes

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

    1. Initial program 64.0

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

    3. Applied associate-/l*0.3

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

    if -inf.0 < (* x y) < -7.926364001367688e-208 or 2.681662764233103e-233 < (* x y) < 7.85330704454344e+220

    1. Initial program 0.3

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

    if -7.926364001367688e-208 < (* x y) < 2.681662764233103e-233

    1. Initial program 11.8

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

    3. Applied *-un-lft-identity11.8

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    if 7.85330704454344e+220 < (* x y)

    1. Initial program 31.8

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

    3. Applied associate-/l*0.8

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

    5. Applied clear-num0.9

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{y}}{x}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -7.92636400136768842 \cdot 10^{-208}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.68166276423310295 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 7.8533070445434405 \cdot 10^{220}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{y}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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))