Details

sample400.0ms

Algorithm

intervals

Results

193.0ms	77×	body	10240	exit
129.0ms	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)

rewrite4.0ms

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:

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)

series164.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sin (expm1 a))
99.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	202	375
3	414	374
4	944	374
5	2449	374
done	5000	374

prune189.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 33.9b

localize16.0ms

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` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 48

Calls

4 calls:

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

simplify1.2s

Counts

60 → 60

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	55	692
1	66	629
2	82	560
3	105	560
4	150	560
5	270	560
6	590	560
7	1791	560
done	5000	558

prune202.0ms

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)

rewrite21.0ms

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:

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)

series430.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (sin (expm1 a)))
138.0ms	(cbrt (sin (expm1 a)))
149.0ms	(* (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)

simplify1.6s

Counts

89 → 89

Iterations

Useful iterations: done (1.6s)

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

prune352.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 33.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
0.8b	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
40.5b	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
43×	`add-sqr-sqrt`
27×	`unpow-prod-down`
18×	`*-un-lft-identity`
16×	`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 → 104

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
31.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
8.0ms	(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)

series470.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (sin (expm1 a)))
155.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
176.0ms	(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)

simplify1.7s

Counts

116 → 116

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	172	2130
1	388	1541
2	968	1456
3	2961	1299
done	5001	1289

prune465.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 32.8b

regimes439.0ms

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	19	36
1	25	36
done	25	36

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.2s	2484×	body	10240	exit
4.0s	2365×	body	1280	valid
1.2s	1664×	body	640	valid
266.0ms	2737×	body	80	valid
265.0ms	813×	body	320	valid
85.0ms	418×	body	160	valid
9.0ms	2×	body	5120	valid
2.0ms	1×	body	2560	valid