Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	6	8
1	9	3
2	11	3
done	11	3

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b	(hypot x y)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `hypot-udef` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot x y)

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(hypot x y)

simplify1.1s

Counts

13 → 13

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	17	60
1	22	58
2	25	52
3	30	52
4	36	52
5	46	52
6	69	52
7	134	52
8	350	52
9	1294	52
done	5001	52

prune33.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot x y))
0.0b	(hypot x y)
0.0b	(hypot x y)
0.5b	(* (sqrt (hypot x y)) (sqrt (hypot x y)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (hypot x y))
0.0ms	(hypot x y)
0.0ms	(hypot x y)
10.0ms	(* (sqrt (hypot x y)) (sqrt (hypot x y)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (hypot x y))
48.0ms	(hypot x y)
51.0ms	(hypot x y)
49.0ms	(* (sqrt (hypot x y)) (sqrt (hypot x y)))

simplify1.5s

Counts

98 → 98

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	86	890
1	163	565
2	437	505
3	1129	486
4	2524	479
done	5000	475

prune207.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot x y)))
0.1b	(sqrt (sqrt (hypot x y)))
0.2b	(* (pow (sqrt (sqrt (hypot x y))) 3) (sqrt (sqrt (hypot x y))))
0.7b	(pow (sqrt (sqrt (hypot x y))) 3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

107×	`sqrt-prod`
74×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l` `unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`add-exp-log`
9×	`associate-r`
7×	`add-cbrt-cube`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

1.0ms	(sqrt (sqrt (hypot x y)))
1.0ms	(sqrt (sqrt (hypot x y)))
22.0ms	(* (pow (sqrt (sqrt (hypot x y))) 3) (sqrt (sqrt (hypot x y))))
4.0ms	(pow (sqrt (sqrt (hypot x y))) 3)

series492.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(sqrt (sqrt (hypot x y)))
138.0ms	(sqrt (sqrt (hypot x y)))
51.0ms	(* (pow (sqrt (sqrt (hypot x y))) 3) (sqrt (sqrt (hypot x y))))
163.0ms	(pow (sqrt (sqrt (hypot x y))) 3)

simplify39.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	130	2348