Details

sample879.0ms

Algorithm

intervals

Results

434.0ms	86×	body	10240	exit
233.0ms	79×	body	1280	valid
69.0ms	48×	body	640	valid
17.0ms	25×	body	320	valid
17.0ms	90×	body	80	valid
5.0ms	13×	body	160	valid
4.0ms	1×	body	2560	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

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

series229.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(expm1 (sin (expm1 a)))
108.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
3	1219
2	298
1	105
0	61

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.5b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
38.0b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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 (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
17.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series820.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt (expm1 (sin (expm1 a))))
238.0ms	(cbrt (expm1 (sin (expm1 a))))
327.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.3s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	722
1	205
0	97

prune728.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 31.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
38.1b	(fmod (atan2 (* (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`cbrt-prod` `pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1/3`
12×	`exp-prod`
9×	`log-pow`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus`
1×	`log-prod` `exp-sum` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 87

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
18.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
31.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
0.0ms	(fmod (atan2 (* (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series877.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt (expm1 (sin (expm1 a))))
283.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
333.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
7.0ms	(fmod (atan2 (* (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify2.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	869
1	245
0	121

prune1.0s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 31.2b

localize187.0ms

Local error

Found 4 expressions with local error:

3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
38.1b	(fmod (atan2 (* (* (* (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

36×	`exp-prod`
28×	`pow1`
27×	`log-pow`
18×	`pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `log-prod` `pow-plus` `exp-sum` `rem-exp-log`

Counts

4 → 78

Calls

4 calls:

22.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
32.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
21.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
0.0ms	(fmod (atan2 (* (* (* (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series911.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
270.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
306.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
6.0ms	(fmod (atan2 (* (* (* (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify2.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
4	3490
3	958
2	313
1	134
0	73

prune757.0ms

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 31.0b

regimes972.0ms

Accuracy

0% (2.4b remaining)

Error of 34.1b against oracle of 31.8b and baseline of 34.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample21.5s

Algorithm

intervals

Results

11.5s	2633×	body	10240	exit
6.4s	2305×	body	1280	valid
2.0s	1690×	body	640	valid
589.0ms	855×	body	320	valid
444.0ms	2708×	body	80	valid
184.0ms	439×	body	160	valid
8.0ms	3×	body	2560	valid