Details

sample404.0ms

Algorithm

intervals

Results

196.0ms	77×	body	10240	exit
130.0ms	71×	body	1280	valid
43.0ms	57×	body	640	valid
11.0ms	34×	body	320	valid
8.0ms	84×	body	80	valid
2.0ms	10×	body	160	valid

simplify1.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
40.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

2.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series68.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (expm1 a))
2.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify973.0ms

Counts

40 → 40

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	101	293
6	176	293
7	436	293
8	1564	293
done	5001	293

prune156.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 33.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series38.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
30.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.3s

Counts

52 → 52

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	47	614
1	58	559
2	74	490
3	96	490
4	140	490
5	259	490
6	562	490
7	1737	490
done	5000	488

prune177.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
40.5b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
14.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series496.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (sin (expm1 a)))
157.0ms	(cbrt (sin (expm1 a)))
176.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify3.5s

Counts

81 → 81

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	63	945
1	99	864
2	272	648
3	957	601
4	4373	592
done	5000	576

prune313.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 33.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a)))))
0.8b	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
40.5b	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
43×	`add-sqr-sqrt`
27×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unswap-sqr`
13×	`associate-l`
10×	`add-exp-log`
9×	`associate-r`
6×	`pow1`
5×	`add-cbrt-cube` `sqr-pow`
4×	`add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
29.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a)))))
5.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
0.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series545.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (sin (expm1 a)))
177.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a)))))
203.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
3.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.4s

Counts

105 → 105

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	121	1694
1	245	1414
2	673	1318
3	2368	1186
done	5000	1175

prune381.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 32.8b

regimes451.0ms

Accuracy

0% (2.2b remaining)

Error of 34.0b against oracle of 31.8b and baseline of 34.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	20	34
done	20	34

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.2s	2484×	body	10240	exit
4.0s	2365×	body	1280	valid
1.1s	1664×	body	640	valid
270.0ms	2737×	body	80	valid
259.0ms	813×	body	320	valid
90.0ms	418×	body	160	valid
9.0ms	2×	body	5120	valid
2.0ms	1×	body	2560	valid