Details

sample214.0ms

Algorithm

intervals

Results

85.0ms	98×	body	1280	valid
80.0ms	45×	body	2560	valid
21.0ms	59×	body	640	valid
8.0ms	29×	body	320	valid
4.0ms	16×	body	160	valid
1.0ms	9×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite59.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

49.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series81.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- 1.0 (cos x)) (sin x))
23.0ms	(- 1.0 (cos x))

simplify1.0s

Counts

74 → 74

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	134	964
1	309	834
2	1215	733
done	5001	692

prune302.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

40.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
11.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
20.0ms	(exp (log (- 1.0 (cos x))))
116.0ms	(log (- 1.0 (cos x)))
35.0ms	(- 1.0 (cos x))

simplify935.0ms

Counts

130 → 130

Iterations

Useful iterations: done (930.0ms)

Iter	Nodes	Cost
0	200	1750
1	374	1389
2	1294	1247
done	5001	1206

prune417.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (- 1.0 (cos x)) (sin x))
87.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
40.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

144 → 144

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	195	1743
1	392	1512
2	1407	1374
done	5000	1335

prune515.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (exp (log 1)) (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 237

Calls

3 calls:

54.0ms	(/ (exp (log 1)) (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
14.0ms	(- 1.0 (cos x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (exp (log 1)) (/ (sin x) (- 1.0 (cos x))))
72.0ms	(/ (sin x) (- 1.0 (cos x)))
36.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

246 → 246

Iterations

Useful iterations: 2 (866.0ms)

Iter	Nodes	Cost
0	363	5108
1	916	3819
2	4620	3641
done	5000	3641

prune803.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

regimes214.0ms

Accuracy

98.5% (0.4b remaining)

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

bsearch113.0ms

Steps

Iters	Range		Point
9	0.00015484893005477947	28918.939680702064	0.01743449574326637
10	-2676750800.736259	-2.9526231381329305e-09	-0.02270927157581989

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	42
1	30	42
done	30	42

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.2s	1567×	body	2560	valid
2.9s	2839×	body	1280	valid
1.0s	1853×	body	640	valid
736.0ms	943×	body	320	valid
177.0ms	440×	body	160	valid
47.0ms	357×	body	80	valid
5.0ms	1×	body	5120	valid