Average Error: 6.2 → 1.0
Time: 5.0s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \leq -4.0229076533194283 \cdot 10^{+288}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq -5.5812861840269 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq 0:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq 2.0819988659681098 \cdot 10^{+261}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} \leq -4.0229076533194283 \cdot 10^{+288}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \leq -5.5812861840269 \cdot 10^{-317}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \leq 0:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \leq 2.0819988659681098 \cdot 10^{+261}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x y) z) -4.0229076533194283e+288)
   (/ x (/ z y))
   (if (<= (/ (* x y) z) -5.5812861840269e-317)
     (/ (* x y) z)
     (if (<= (/ (* x y) z) 0.0)
       (/ (/ y z) (/ 1.0 x))
       (if (<= (/ (* x y) z) 2.0819988659681098e+261)
         (* (* x y) (/ 1.0 z))
         (* x (/ y z)))))))
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) / z) <= -4.0229076533194283e+288) {
		tmp = x / (z / y);
	} else if (((x * y) / z) <= -5.5812861840269e-317) {
		tmp = (x * y) / z;
	} else if (((x * y) / z) <= 0.0) {
		tmp = (y / z) / (1.0 / x);
	} else if (((x * y) / z) <= 2.0819988659681098e+261) {
		tmp = (x * y) * (1.0 / z);
	} else {
		tmp = x * (y / z);
	}
	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

Original6.2
Target6.2
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if (/.f64 (*.f64 x y) z) < -4.02290765331942828e288

    1. Initial program 50.3

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

    3. Applied associate-/l*_binary64_170733.8

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

    if -4.02290765331942828e288 < (/.f64 (*.f64 x y) z) < -5.58128618e-317

    1. Initial program 0.5

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

    if -5.58128618e-317 < (/.f64 (*.f64 x y) z) < 0.0

    1. Initial program 11.9

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

    3. Applied add-cube-cbrt_binary64_1716311.9

      \[\leadsto \frac{x \cdot y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied associate-/r*_binary64_1707211.9

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}}\]

    5. Simplified2.6

      \[\leadsto \frac{\color{blue}{y \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{z}}\]
    6. Using strategy rm

    7. Applied associate-/l*_binary64_170730.3

      \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt[3]{z}}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}}\]

    8. Simplified0.1

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

    10. Applied div-inv_binary64_171250.1

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

    11. Applied associate-/r*_binary64_170720.1

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

    if 0.0 < (/.f64 (*.f64 x y) z) < 2.08199886596810975e261

    1. Initial program 0.5

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

    3. Applied add-cube-cbrt_binary64_171631.6

      \[\leadsto \frac{x \cdot y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied associate-/r*_binary64_170721.6

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}}\]

    5. Simplified5.0

      \[\leadsto \frac{\color{blue}{y \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{z}}\]
    6. Using strategy rm

    7. Applied associate-/l*_binary64_170739.1

      \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt[3]{z}}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}}\]

    8. Simplified8.2

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

    10. Applied div-inv_binary64_171258.3

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

    11. Applied *-un-lft-identity_binary64_171288.3

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

    12. Applied times-frac_binary64_171340.7

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

    13. Simplified0.6

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

    if 2.08199886596810975e261 < (/.f64 (*.f64 x y) z)

    1. Initial program 34.2

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

    3. Applied add-cube-cbrt_binary64_1716334.8

      \[\leadsto \frac{x \cdot y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied associate-/r*_binary64_1707234.8

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}}\]

    5. Simplified16.6

      \[\leadsto \frac{\color{blue}{y \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{z}}\]
    6. Using strategy rm

    7. Applied associate-/l*_binary64_170739.4

      \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt[3]{z}}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}}\]

    8. Simplified8.4

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

    10. Applied associate-/r/_binary64_170749.9

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \leq -4.0229076533194283 \cdot 10^{+288}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq -5.5812861840269 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq 0:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq 2.0819988659681098 \cdot 10^{+261}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021102 
(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))