Details

sample1.1s

Algorithm

intervals

Results

450.0ms	90×	body	10240	exit
285.0ms	62×	body	1280	valid
122.0ms	67×	body	640	valid
97.0ms	25×	body	320	valid
19.0ms	86×	body	80	valid
6.0ms	16×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
39.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
59.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series134.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(expm1 (sin (expm1 a)))
111.0ms	(sin (expm1 a))
21.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

30 → 30

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	28	238
1	31	238
2	35	206
3	44	206
4	56	206
5	80	206
6	137	206
7	342	206
8	1219	206
done	5000	206

prune169.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 33.4b

localize31.0ms

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))))
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite22.0ms

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)))
16.0ms	(* (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)

series801.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt (sin (expm1 a)))
254.0ms	(cbrt (sin (expm1 a)))
289.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
4.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify6.0s

Counts

81 → 81

Iterations

Useful iterations: done (6.0s)

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

prune600.0ms

Pruning

29 alts after pruning (27 fresh and 2 done)

Merged error: 32.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.6b	(* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
39.3b	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite65.0ms

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:

3.0ms	(cbrt (sin (expm1 a)))
49.0ms	(* (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)

series894.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt (sin (expm1 a)))
303.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a)))))
308.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
7.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 5) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify2.9s

Counts

105 → 105

Iterations

Useful iterations: done (2.9s)

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

prune891.0ms

Pruning

40 alts after pruning (39 fresh and 1 done)

Merged error: 32.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
0.8b	(cbrt (cbrt (cbrt (sin (expm1 a)))))
0.8b	(cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2))
39.3b	(fmod (atan2 (expm1 (* (* (* (cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2)) (pow (cbrt (cbrt (sin (expm1 a)))) 5)) (cbrt (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`cbrt-prod`
18×	`unpow-prod-down`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-pow` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `unpow2`

Counts

4 → 70

Calls

4 calls:

10.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
5.0ms	(cbrt (cbrt (cbrt (sin (expm1 a)))))
10.0ms	(cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2)) (pow (cbrt (cbrt (sin (expm1 a)))) 5)) (cbrt (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series898.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
242.0ms	(cbrt (cbrt (cbrt (sin (expm1 a)))))
310.0ms	(cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2))
8.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2)) (pow (cbrt (cbrt (sin (expm1 a)))) 5)) (cbrt (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify3.7s

Counts

82 → 82

Iterations

Useful iterations: 3 (349.0ms)

Iter	Nodes	Cost
0	126	1268
1	225	1168
2	389	1066
3	917	1060
4	3946	1060
done	5001	1060

prune636.0ms

Pruning

48 alts after pruning (48 fresh and 0 done)

Merged error: 31.7b

regimes995.0ms

Accuracy

0% (2.4b remaining)

Error of 33.5b against oracle of 31.1b and baseline of 33.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	108
1	26	108
done	26	108

end0.0ms

sample21.5s

Algorithm

intervals

Results

11.2s	2518×	body	10240	exit
6.4s	2220×	body	1280	valid
2.1s	1694×	body	640	valid
580.0ms	846×	body	320	valid
561.0ms	2815×	body	80	valid
145.0ms	422×	body	160	valid
18.0ms	3×	body	5120	valid