Details

sample914.0ms

Algorithm

intervals

Results

357.0ms	70×	body	10240	exit
188.0ms	70×	body	1280	valid
80.0ms	59×	body	640	valid
16.0ms	90×	body	80	valid
12.0ms	20×	body	320	valid
5.0ms	1×	body	5120	valid
5.0ms	16×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.2b	(sin (expm1 a))
38.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
7.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series321.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(expm1 (sin (expm1 a)))
5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
143.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.8s

Counts

51 → 51

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	70	438
1	109	422
2	200	375
3	407	374
4	937	374
5	2449	374
done	5001	374

prune384.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 32.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.1b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite43.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 77

Calls

4 calls:

3.0ms	(cbrt (sin (expm1 a)))
3.0ms	(cbrt (sin (expm1 a)))
32.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series652.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (sin (expm1 a)))
209.0ms	(cbrt (sin (expm1 a)))
229.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify2.7s

Counts

89 → 89

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	97	1079
1	181	979
2	450	738
3	1338	682
done	5001	676

prune601.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 31.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cbrt (sin (expm1 a))))
0.6b	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
38.1b	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod`
44×	`add-sqr-sqrt`
27×	`unpow-prod-down`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`unswap-sqr`
14×	`associate-l`
10×	`add-exp-log`
9×	`associate-r`
6×	`pow1`
5×	`add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp`
2×	`unpow-prod-up` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 107

Calls

4 calls:

2.0ms	(cbrt (cbrt (sin (expm1 a))))
35.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
16.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
0.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series712.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (cbrt (sin (expm1 a))))
241.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
262.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
5.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify2.5s

Counts

119 → 119

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	173	2185
1	389	1595
2	941	1524
3	2731	1487
done	5000	1381

prune1.1s

Pruning

39 alts after pruning (38 fresh and 1 done)

Merged error: 31.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))))
1.0b	(pow (cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (+ 4 1))
38.1b	(fmod (atan2 (expm1 (* (* (pow (cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (+ 4 1)) (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (cbrt (sin (expm1 a))))) 5))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
11×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`pow-pow`
1×	`unpow-prod-up` `pow-to-exp` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (cbrt (cbrt (sin (expm1 a)))))
9.0ms	(cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))))
12.0ms	(pow (cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (+ 4 1))
1.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (+ 4 1)) (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (cbrt (sin (expm1 a))))) 5))) (cbrt (sin (expm1 a))))) (atan a)) a)

series740.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (cbrt (cbrt (sin (expm1 a)))))
226.0ms	(cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))))
297.0ms	(pow (cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (+ 4 1))
11.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (+ 4 1)) (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (cbrt (sin (expm1 a))))) 5))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify4.2s

Counts

74 → 74

Iterations

Useful iterations: 4 (2.2s)

Iter	Nodes	Cost
0	146	1535
1	299	1405
2	596	1272
3	1365	1263
4	4650	1122
done	5000	1122

prune711.0ms

Pruning

54 alts after pruning (53 fresh and 1 done)

Merged error: 30.7b

regimes1.2s

Accuracy

0% (2.7b remaining)

Error of 33.5b against oracle of 30.8b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	16	21
done	16	21

end0.0ms

sample21.6s

Algorithm

intervals

Results

10.9s	2583×	body	10240	exit
6.8s	2312×	body	1280	valid
1.9s	1622×	body	640	valid
944.0ms	2810×	body	80	valid
543.0ms	802×	body	320	valid
154.0ms	446×	body	160	valid
33.0ms	5×	body	5120	valid
9.0ms	3×	body	2560	valid