Details

sample200.0ms

Algorithm

intervals

Results

75.0ms	86×	body	1280	valid
73.0ms	42×	body	2560	valid
26.0ms	68×	body	640	valid
8.0ms	34×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	8×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series426.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- 1.0 (cos x)) (sin x))
374.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
3	2334
2	774
1	308
0	134

prune435.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))
1.2b	(- 1.0 (cos x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 177

Calls

3 calls:

28.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
23.0ms	(/ (sin x) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series159.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
65.0ms	(/ (sin x) (- 1.0 (cos x)))
41.0ms	(- 1.0 (cos x))

simplify3.0s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
3	4657
2	1573
1	650
0	269

prune688.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (/ 1 (sin x)) (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
38×	`add-cube-cbrt`
27×	`prod-diff`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-l`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-/r` `sub-neg` `flip3--` `fma-neg` `log1p-expm1-u` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`clear-num` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 126

Calls

3 calls:

5.0ms	(/ 1 (sin x))
40.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series100.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ 1 (sin x))
55.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
3	3495
2	1255
1	537
0	204

prune585.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`add-cbrt-cube` `prod-diff` `add-exp-log`
8×	`associate-/l/`
6×	`fma-def`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `pow1` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `times-frac` `fma-neg`
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 → 93

Calls

4 calls:

33.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
10.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
16.0ms	(- 1.0 (cos x))

series132.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
13.0ms	(+ 1.0 (cos x))
13.0ms	(+ 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1521
1	418
0	153

prune558.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

regimes354.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.3b

bsearch154.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.027845000675864373
10	-17239113253358.373	-4.96108325192681e-05	-0.027638311984739105

simplify12.0ms

Iterations

Iter	Nodes
done	34
1	34
0	30

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.3s	1660×	body	2560	valid
2.2s	2710×	body	1280	valid
915.0ms	1881×	body	640	valid
353.0ms	940×	body	320	valid
124.0ms	474×	body	160	valid
73.0ms	332×	body	80	valid
15.0ms	3×	body	5120	valid