Details

sample104.0ms

Algorithm

intervals

Results

42.0ms	48×	body	2560	valid
24.0ms	52×	body	1280	valid
10.0ms	35×	body	640	valid
7.0ms	32×	body	320	valid
5.0ms	72×	body	80	valid
3.0ms	17×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize10.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
18.0ms	(/ (- 1.0 (cos x)) (* x x))

series97.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
77.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.5s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4103
2	936
1	290
0	116

prune317.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma -1/24 (* x x) 1/2)
0.2b	(* 1/720 (* x x))
12.1b	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

0.0ms	(fma -1/24 (* x x) 1/2)
17.0ms	(* 1/720 (* x x))
1.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))

series144.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma -1/24 (* x x) 1/2)
30.0ms	(* 1/720 (* x x))
57.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))

simplify1.6s

Counts

50 → 50

Iterations

Iter	Nodes
done	5031
3	1679
2	393
1	141
0	68

prune301.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

12.1b	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
12.5b	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
12.5b	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
12.5b	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
1.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
1.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
1.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
154.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
185.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
218.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
3	1431
2	431
1	166
0	77

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

12.1b	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
12.1b	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
12.5b	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
12.5b	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

0.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
0.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
1.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
1.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
83.0ms	(fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2))
229.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))
251.0ms	(cbrt (fma (* x x) (* 1/720 (* x x)) (fma -1/24 (* x x) 1/2)))

simplify1.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	1431
2	431
1	166
0	77

prune294.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes175.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 31.9b

bsearch130.0ms

Steps

Iters	Range		Point
8	0.02586244036059231	44.35744796693956	0.02880979041531034
10	-733100.9210806559	-4.034181863829644e-08	-0.03224345637809938

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1592×	body	2560	valid
525.0ms	2285×	body	80	valid
524.0ms	1470×	body	640	valid
397.0ms	1217×	body	1280	valid
193.0ms	945×	body	320	valid
61.0ms	491×	body	160	valid