Average Error: 6.4 → 0.6
Time: 2.9s
Precision: binary64
Cost: 1613
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.2583117062414792 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \leq -3.465479670824521 \cdot 10^{-205} \lor \neg \left(x \cdot y \leq 2.9882567291840723 \cdot 10^{-243}\right) \land x \cdot y \leq 7.971146091977197 \cdot 10^{+161}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -1.2583117062414792 \cdot 10^{+189}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \leq -3.465479670824521 \cdot 10^{-205} \lor \neg \left(x \cdot y \leq 2.9882567291840723 \cdot 10^{-243}\right) \land x \cdot y \leq 7.971146091977197 \cdot 10^{+161}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* x y) -1.2583117062414792e+189)
   (* x (/ y z))
   (if (or (<= (* x y) -3.465479670824521e-205)
           (and (not (<= (* x y) 2.9882567291840723e-243))
                (<= (* x y) 7.971146091977197e+161)))
     (/ (* x y) z)
     (/ x (/ z y)))))
double code(double x, double y, double z) {
	return (x * y) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((x * y) <= -1.2583117062414792e+189) {
		tmp = x * (y / z);
	} else if (((x * y) <= -3.465479670824521e-205) || (!((x * y) <= 2.9882567291840723e-243) && ((x * y) <= 7.971146091977197e+161))) {
		tmp = (x * y) / z;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

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
Target6.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Alternatives

Alternative 1
Error6.1
Cost1283
\[\begin{array}{l} \mathbf{if}\;x \leq -2.0209041450172942 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 3.237680869149344 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq 1.5035835833618667 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
Alternative 2
Error6.2
Cost320
\[x \cdot \frac{y}{z}\]
Alternative 3
Error6.1
Cost320
\[\frac{x}{\frac{z}{y}}\]
Alternative 4
Error49.5
Cost64
\[0\]
Alternative 5
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x y) < -1.25831170624147922e189

    1. Initial program 24.5

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

    3. Applied *-un-lft-identity_binary64_2053824.5

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

    4. Applied times-frac_binary64_205441.9

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

    5. Simplified1.9

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

    6. Simplified1.9

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

    if -1.25831170624147922e189 < (*.f64 x y) < -3.46547967082452108e-205 or 2.9882567291840723e-243 < (*.f64 x y) < 7.97114609197719727e161

    1. Initial program 0.2

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

    2. Simplified0.2

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

    if -3.46547967082452108e-205 < (*.f64 x y) < 2.9882567291840723e-243 or 7.97114609197719727e161 < (*.f64 x y)

    1. Initial program 14.0

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

    3. Applied associate-/l*_binary64_204830.9

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

    4. Simplified0.9

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.2583117062414792 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \leq -3.465479670824521 \cdot 10^{-205} \lor \neg \left(x \cdot y \leq 2.9882567291840723 \cdot 10^{-243}\right) \land x \cdot y \leq 7.971146091977197 \cdot 10^{+161}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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))