Details

sample161.0ms

Algorithm

intervals

Results

79.0ms	101×	body	1280	valid
25.0ms	74×	body	640	valid
21.0ms	274×	body	80	valid
10.0ms	42×	body	320	valid
3.0ms	21×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	197
1	15	197
2	30	197
3	65	197
4	126	197
5	236	197
6	607	197
7	1809	197
done	5004	197

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.0b	(/ (sinh y) y)
0.2b	(* (sin x) (/ (sinh y) y))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `sinh-def` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

3 → 68

Calls

3 calls:

2.0ms	(sinh y)
10.0ms	(/ (sinh y) y)
26.0ms	(* (sin x) (/ (sinh y) y))

series406.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(sinh y)
139.0ms	(/ (sinh y) y)
191.0ms	(* (sin x) (/ (sinh y) y))

simplify3.3s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	140	20306
1	342	18641
2	1042	17590
3	3664	16831
done	5013	16831

prune467.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sinh y)
0.0b	(/ y (sinh y))
0.0b	(/ 1 (/ y (sinh y)))
0.2b	(* (sin x) (/ 1 (/ y (sinh y))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
106×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
36×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`associate-/r*`
15×	`div-exp`
10×	`associate-/r/` `div-inv`
9×	`sinh-def`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

1.0ms	(sinh y)
4.0ms	(/ y (sinh y))
9.0ms	(/ 1 (/ y (sinh y)))
32.0ms	(* (sin x) (/ 1 (/ y (sinh y))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sinh y)
142.0ms	(/ y (sinh y))
126.0ms	(/ 1 (/ y (sinh y)))
142.0ms	(* (sin x) (/ 1 (/ y (sinh y))))

simplify3.6s

Counts

204 → 204

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	291	68093
1	794	55055
2	2394	50968
done	5001	47649

prune952.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/6 (* 1/120 (* y y)))
0.0b	(* (sin x) (+ (* (* y y) (+ 1/6 (* 1/120 (* y y)))) 1))
0.1b	(* 1/120 (* y y))
0.2b	(* (* y y) (+ 1/6 (* 1/120 (* y y))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`associate-*r/`
3×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`+-commutative` `sum-log`

Counts

4 → 75

Calls

4 calls:

10.0ms	(+ 1/6 (* 1/120 (* y y)))
70.0ms	(* (sin x) (+ (* (* y y) (+ 1/6 (* 1/120 (* y y)))) 1))
18.0ms	(* 1/120 (* y y))
21.0ms	(* (* y y) (+ 1/6 (* 1/120 (* y y))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ 1/6 (* 1/120 (* y y)))
157.0ms	(* (sin x) (+ (* (* y y) (+ 1/6 (* 1/120 (* y y)))) 1))
38.0ms	(* 1/120 (* y y))
97.0ms	(* (* y y) (+ 1/6 (* 1/120 (* y y))))

simplify2.7s

Counts

87 → 87

Iterations

Useful iterations: 2 (759.0ms)

Iter	Nodes	Cost
0	137	24869
1	454	19947
2	1886	19371
done	5000	19371

prune378.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/120 (* y y))
0.2b	(* (* y y) (+ 1/6 (* 1/120 (* y y))))
2.8b	(exp (log (* (* y y) (+ 1/6 (* 1/120 (* y y))))))
31.4b	(log (* (* y y) (+ 1/6 (* 1/120 (* y y)))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
20×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `prod-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod` `associate-*r/` `log-pow` `cbrt-unprod`
4×	`log-div` `associate-r` `associate-l` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
2×	`log-prod` `exp-diff` `*-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `exp-sum` `rem-exp-log`

Counts

4 → 75

Calls

4 calls:

26.0ms	(* 1/120 (* y y))
30.0ms	(* (* y y) (+ 1/6 (* 1/120 (* y y))))
93.0ms	(exp (log (* (* y y) (+ 1/6 (* 1/120 (* y y))))))
32.0ms	(log (* (* y y) (+ 1/6 (* 1/120 (* y y)))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 1/120 (* y y))
144.0ms	(* (* y y) (+ 1/6 (* 1/120 (* y y))))
118.0ms	(exp (log (* (* y y) (+ 1/6 (* 1/120 (* y y))))))
113.0ms	(log (* (* y y) (+ 1/6 (* 1/120 (* y y)))))

simplify105.0ms

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	135	25614