Details

sample820.0ms

Algorithm

intervals

Results

330.0ms	70×	body	10240	exit
222.0ms	70×	body	1280	valid
81.0ms	90×	body	80	valid
78.0ms	59×	body	640	valid
13.0ms	20×	body	320	valid
8.0ms	1×	body	5120	valid
6.0ms	16×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune6.0ms

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

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

Counts

4 → 28

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
6.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series175.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(expm1 (sin (expm1 a)))
3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
97.0ms	(sin (expm1 a))
73.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify66.0ms

Counts: 40 → 40

prune479.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.3b

localize91.0ms

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (expm1 (sin (expm1 a))))
2.0ms	(cbrt (expm1 (sin (expm1 a))))
4.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series573.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (expm1 (sin (expm1 a))))
164.0ms	(cbrt (expm1 (sin (expm1 a))))
141.0ms	(cbrt (expm1 (sin (expm1 a))))
6.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify58.0ms

Counts: 52 → 52

prune524.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.6b	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
38.1b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
20×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`pow1/3` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down`
1×	`pow3` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 64

Calls

4 calls:

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

series441.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (expm1 (sin (expm1 a))))
161.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
128.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify86.0ms

Counts: 76 → 76

prune648.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 31.8b

localize141.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
38.1b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
38.1b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
38.1b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
1×	`pow1/3`

Counts

4 → 35

Calls

4 calls:

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

series223.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify81.0ms

Counts: 47 → 47

prune388.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 31.6b

regimes1.1s

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.6b and baseline of 33.5b

bsearch0.0ms

simplify120.0ms

end0.0ms

sample22.1s

Algorithm

intervals

Results

11.3s	2583×	body	10240	exit
6.3s	2312×	body	1280	valid
2.3s	1622×	body	640	valid
592.0ms	802×	body	320	valid
581.0ms	446×	body	160	valid
541.0ms	2810×	body	80	valid
27.0ms	5×	body	5120	valid
9.0ms	3×	body	2560	valid