Details

sample839.0ms

Algorithm

intervals

Results

445.0ms	92×	body	10240	exit
217.0ms	77×	body	1280	valid
63.0ms	58×	body	640	valid
17.0ms	79×	body	80	valid
17.0ms	27×	body	320	valid
6.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize95.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-log1p` `expm1-udef`

Counts

4 → 40

Calls

4 calls:

1.0ms	(expm1 a)
0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series180.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(expm1 a)
3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
146.0ms	(expm1 (sin (expm1 a)))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	64	414
1	109	395
2	300	350
3	1172	350
done	5000	348

prune402.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
40.6b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `log1p-expm1-u` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube`
3×	`log-prod`
1×	`expm1-log1p` `rem-log-exp` `rem-exp-log` `expm1-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series212.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(expm1 (sin (expm1 a)))
56.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.0s

Counts

62 → 62

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	73	666
1	113	592
2	250	528
3	710	528
4	3142	528
done	5000	528

prune445.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 33.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.4b	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
40.6b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `log-pow`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `sqrt-pow1`
6×	`add-exp-log` `sqrt-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow1/2` `rem-log-exp`
1×	`rem-exp-log`

Counts

4 → 66

Calls

4 calls:

2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
16.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
1.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series364.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
156.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
141.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
4.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify2.2s

Counts

78 → 78

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	63	1203
1	76	1041
2	97	940
3	161	940
4	262	940
5	583	940
6	2149	940
done	5000	875

prune652.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 33.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series167.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	30	673
1	42	669
2	94	555
3	257	552
4	1337	552
done	5000	552

prune346.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 33.4b

regimes609.0ms

Accuracy

0% (1.5b remaining)

Error of 33.7b against oracle of 32.1b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
done	12	24

end0.0ms

sample22.9s

Algorithm

intervals

Results

11.3s	2598×	body	10240	exit
6.8s	2318×	body	1280	valid
2.5s	1655×	body	640	valid
995.0ms	2773×	body	80	valid
522.0ms	834×	body	320	valid
238.0ms	414×	body	160	valid
16.0ms	2×	body	5120	valid
15.0ms	4×	body	2560	valid