Details

sample138.0ms

Algorithm

intervals

Results

73.0ms	58×	body	1280	valid
22.0ms	35×	body	640	valid
19.0ms	141×	body	80	valid
7.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify394.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	324
1	20	324
2	35	324
3	71	324
4	134	324
5	226	324
6	274	324
7	275	324
done	275	324

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 79

Calls

3 calls:

64.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
48.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series241.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
65.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
101.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify3.2s

Counts

88 → 88

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	163	29646
1	411	27013
2	1399	26652
done	5000	25972

prune482.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.1b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`add-log-exp`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 94

Calls

3 calls:

18.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
9.0ms	(/ (sin (* x 0.5)) (sin x))
46.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
73.0ms	(/ (sin (* x 0.5)) (sin x))
101.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify3.7s

Counts

103 → 103

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	175	38056
1	478	35402
2	1942	34799
done	5001	33678

prune555.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.1b	(/ 1 (sin x))
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (* (sin (* x 0.5)) (/ 1 (sin x))))
0.2b	(* (sin (* x 0.5)) (/ 1 (sin x)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
52×	`add-cbrt-cube`
37×	`prod-exp`
31×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`div-exp`
21×	`cbrt-unprod`
14×	`associate-r`
13×	`cbrt-undiv`
12×	`pow1`
10×	`associate-l`
6×	`associate-/r*`
5×	`rec-exp` `1-exp` `associate-*r/`
4×	`pow-prod-down` `div-inv` `associate-/l*` `add-log-exp`
3×	`un-div-inv` `unswap-sqr`
2×	`frac-times` `clear-num` `frac-2neg` `*-commutative`
1×	`associate-*l/` `pow-flip` `inv-pow`

Counts

4 → 135

Calls

4 calls:

28.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
5.0ms	(/ 1 (sin x))
59.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (* (sin (* x 0.5)) (/ 1 (sin x))))
42.0ms	(* (sin (* x 0.5)) (/ 1 (sin x)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
17.0ms	(/ 1 (sin x))
114.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (* (sin (* x 0.5)) (/ 1 (sin x))))
52.0ms	(* (sin (* x 0.5)) (/ 1 (sin x)))

simplify281.0ms

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	217	51382