Average Error: 5.8 → 5.9
Time: 2.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.4618509963497409 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.4618509963497409 \cdot 10^{-77}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((x <= -2.461850996349741e-77)) {
		VAR = ((double) (((double) (x / z)) * y));
	} else {
		VAR = ((double) (x * ((double) (y / z))));
	}
	return VAR;
}

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

Original5.8
Target6.1
Herbie5.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.461850996349741e-77

    1. Initial program 6.1

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

    3. Applied *-un-lft-identity6.1

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

    4. Applied associate-*r*6.1

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

    5. Applied associate-/l*6.3

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

    7. Applied div-inv6.3

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

    8. Applied times-frac6.0

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

    9. Simplified5.9

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

    if -2.461850996349741e-77 < x

    1. Initial program 5.7

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

    3. Applied *-un-lft-identity5.7

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

    4. Applied times-frac5.8

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

    5. Simplified5.8

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

  4. Final simplification5.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.4618509963497409 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 
(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))