Details

sample135.0ms

Algorithm

intervals

Results

63.0ms	58×	body	1280	valid
25.0ms	35×	body	640	valid
20.0ms	141×	body	80	valid
8.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify467.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize39.0ms

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))

rewrite184.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 85

Calls

3 calls:

48.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
92.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series209.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
103.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify3.7s

Counts

94 → 94

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	169	31590
1	418	28857
2	1409	28496
done	5004	27801

prune533.0ms

Pruning

10 alts after pruning (10 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)))

rewrite100.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

28.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
24.0ms	(/ (sin (* x 0.5)) (sin x))
42.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series239.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
54.0ms	(/ (sin (* x 0.5)) (sin x))
139.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify3.4s

Counts

109 → 109

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	181	39956
1	490	37096
2	1857	36333
done	5001	35478

prune452.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-cbrt-cube` `add-exp-log`
21×	`times-frac`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/`
1×	`associate-l` `*-commutative` `associate-/l/`

Counts

3 → 94

Calls

3 calls:

21.0ms	(/ (sin (* x 0.5)) (sin x))
56.0ms	(/ (* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x))) 3.0)
51.0ms	(* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (sin (* x 0.5)) (sin x))
107.0ms	(/ (* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x))) 3.0)
138.0ms	(* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))

simplify3.1s

Counts

103 → 103

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	176	39728
1	469	36442
2	1810	35160
done	5001	35049

prune568.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize40.0ms

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)))

rewrite163.0ms

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×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `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 → 143

Calls

4 calls:

26.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
5.0ms	(/ 1 (sin x))
80.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (* (sin (* x 0.5)) (/ 1 (sin x))))
43.0ms	(* (sin (* x 0.5)) (/ 1 (sin x)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
15.0ms	(/ 1 (sin x))
107.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (* (sin (* x 0.5)) (/ 1 (sin x))))
57.0ms	(* (sin (* x 0.5)) (/ 1 (sin x)))

simplify209.0ms

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	225	53810