Details

sample235.0ms

Algorithm

intervals

Results

99.0ms	42×	body	2560	valid
72.0ms	83×	body	1280	valid
32.0ms	66×	body	640	valid
13.0ms	37×	body	320	valid
4.0ms	17×	body	160	valid
1.0ms	11×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 1.0 (cos x))

rewrite41.0ms

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:

30.0ms	(/ (- 1.0 (cos x)) (sin x))
8.0ms	(- 1.0 (cos x))

series115.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (- 1.0 (cos x)) (sin x))
45.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

74 → 74

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune284.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite112.0ms

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:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
29.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
8.0ms	(- 1.0 (cos x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
58.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
66.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
39.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

144 → 144

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	195	1743
1	370	1509
2	856	1372
3	2563	1333
done	5000	1322

prune528.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.4b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`exp-prod`
31×	`log-pow`
30×	`add-cube-cbrt`
28×	`log-prod`
24×	`times-frac`
20×	`exp-sum`
9×	`prod-diff`
7×	`pow1`
6×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`exp-diff` `rem-log-exp`
1×	`sub-neg` `diff-log` `div-inv` `rem-exp-log`

Counts

4 → 109

Calls

4 calls:

7.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
46.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
21.0ms	(- 1.0 (cos x))

series202.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (log (- 1.0 (cos x))))
95.0ms	(log (- 1.0 (cos x)))
49.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
35.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

121 → 121

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	226	1503
1	363	1123
2	728	988
3	1883	949
done	5001	921

prune538.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
111×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

32.0ms	(* (cos x) (+ 1.0 (cos x)))
14.0ms	(+ 1.0 (cos x))
7.0ms	(pow (cos x) 3)
57.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (+ 1.0 (cos x)))
12.0ms	(+ 1.0 (cos x))
48.0ms	(pow (cos x) 3)
75.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.2s

Counts

271 → 271

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	273	7533
1	612	4117
2	1963	3101
done	5001	2379

prune476.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

regimes329.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.5b

bsearch139.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	0.020771119462007017
9	-7465.585501010854	-0.008005822963963436	-0.023647737046597096

simplify13.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	37	61
1	42	61
done	42	61

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.5s	1652×	body	2560	valid
2.4s	2679×	body	1280	valid
988.0ms	1931×	body	640	valid
381.0ms	933×	body	320	valid
202.0ms	433×	body	160	valid
83.0ms	368×	body	80	valid
22.0ms	4×	body	5120	valid