Details

sample287.0ms

Algorithm

intervals

Results

138.0ms	57×	body	2560	valid
78.0ms	85×	body	1280	valid
31.0ms	66×	body	640	valid
10.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid
1.0ms	6×	body	80	valid

simplify45.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 54

Calls

2 calls:

51.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

series134.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- 1.0 (cos x)) (sin x))
51.0ms	(- 1.0 (cos x))

simplify3.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	1811
2	583
1	242
0	108

prune682.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ (* (* x x) 1/24) 1/2))
0.0b	(* (pow x 5) 1/240)
0.2b	(* (* x x) 1/24)

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-exp-log`
12×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`prod-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+`

Counts

3 → 69

Calls

3 calls:

133.0ms	(* x (+ (* (* x x) 1/24) 1/2))
27.0ms	(* (pow x 5) 1/240)
24.0ms	(* (* x x) 1/24)

series288.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(* x (+ (* (* x x) 1/24) 1/2))
87.0ms	(* (pow x 5) 1/240)
64.0ms	(* (* x x) 1/24)

simplify2.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1184
1	357
0	123

prune783.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (pow x 5) 1/240)
0.1b	(* x (* (* x x) 1/24))
0.2b	(* (* x x) 1/24)

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
19×	`add-cbrt-cube`
17×	`pow1`
14×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`associate-l`
10×	`cbrt-unprod`
9×	`pow-prod-down`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
4×	`unpow-prod-down` `unswap-sqr`
3×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

3 → 68

Calls

3 calls:

35.0ms	(* (pow x 5) 1/240)
76.0ms	(* x (* (* x x) 1/24))
36.0ms	(* (* x x) 1/24)

series261.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(* (pow x 5) 1/240)
87.0ms	(* x (* (* x x) 1/24))
60.0ms	(* (* x x) 1/24)

simplify5.9s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	2843
2	730
1	247
0	104

prune696.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b	(/ (sin x) (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 162

Calls

3 calls:

48.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
44.0ms	(/ (sin x) (- 1.0 (cos x)))
21.0ms	(- 1.0 (cos x))

series233.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
90.0ms	(/ (sin x) (- 1.0 (cos x)))
47.0ms	(- 1.0 (cos x))

simplify7.3s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
3	4852
2	1451
1	582
0	242

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes449.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.1b

bsearch2.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	47
1	47
0	36

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.7s	1603×	body	2560	valid
2.8s	2740×	body	1280	valid
1.3s	1901×	body	640	valid
285.0ms	934×	body	320	valid
147.0ms	465×	body	160	valid
40.0ms	356×	body	80	valid
9.0ms	1×	body	5120	valid