Details

sample196.0ms

Algorithm

intervals

Results

79.0ms	38×	body	2560	valid
63.0ms	91×	body	1280	valid
28.0ms	72×	body	640	valid
6.0ms	25×	body	320	valid
4.0ms	19×	body	160	valid
1.0ms	11×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

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

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite37.0ms

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--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

26.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(- 1.0 (cos x))

series118.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(- 1.0 (cos x))

simplify564.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune357.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.6b	(- 1.0 (cos x))

rewrite73.0ms

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`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 159

Calls

3 calls:

33.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
21.0ms	(/ (sin x) (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series168.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
58.0ms	(/ (sin x) (- 1.0 (cos x)))
37.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

168 → 168

Iterations

Iter	Nodes
done	5004
2	2765
1	583
0	239

prune430.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ (cos x) 1.0)
1.6b	(- 1.0 (cos x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-/l/`
6×	`add-cube-cbrt`
5×	`flip3-+` `flip-+`
4×	`frac-times` `pow1` `flip3--` `flip--`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `+-commutative` `sum-log` `div-exp` `associate-l/` `associate-r/` `distribute-lft-out`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

39.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
10.0ms	(+ 1.0 (cos x))
10.0ms	(+ (cos x) 1.0)
9.0ms	(- 1.0 (cos x))

series162.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
16.0ms	(+ 1.0 (cos x))
12.0ms	(+ (cos x) 1.0)
21.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	1869
1	379
0	137

prune456.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ 1.0 (cos x)) (- 1.0 (cos x)))
0.4b	(+ 1.0 (cos x))
0.4b	(+ (cos x) 1.0)
1.6b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-log-exp`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`flip3-+` `associate-r` `flip-+`
4×	`frac-times` `flip3--` `associate-l` `flip--`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

48.0ms	(* (+ 1.0 (cos x)) (- 1.0 (cos x)))
5.0ms	(+ 1.0 (cos x))
5.0ms	(+ (cos x) 1.0)
10.0ms	(- 1.0 (cos x))

series126.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (+ 1.0 (cos x)) (- 1.0 (cos x)))
11.0ms	(+ 1.0 (cos x))
13.0ms	(+ (cos x) 1.0)
37.0ms	(- 1.0 (cos x))

simplify724.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1464
1	304
0	115

prune404.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes232.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch95.0ms

Steps

Iters	Range		Point
8	0.00104763160503943	5.1212688054922095	0.022437772981647713
9	-205.8624528279525	-0.0007095347148853646	-0.0218703537251575

simplify5.0ms

Iterations

Iter	Nodes
done	45
2	45
1	44
0	31

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.6s	1504×	body	2560	valid
3.0s	2754×	body	1280	valid
930.0ms	1935×	body	640	valid
795.0ms	977×	body	320	valid
164.0ms	490×	body	160	valid
40.0ms	339×	body	80	valid
9.0ms	1×	body	5120	valid