Details

sample236.0ms

Algorithm

intervals

Results

66.0ms	25×	body	320	valid
43.0ms	45×	body	1280	valid
26.0ms	34×	body	640	valid
17.0ms	136×	body	80	valid
7.0ms	256×	pre	80	true
5.0ms	16×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	9	11
1	14	11
2	20	10
3	23	10
4	24	10
done	24	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (* e (sin v)) (fma (cos v) e 1.0))
0.1b	(* e (sin v))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 43

Calls

2 calls:

12.0ms	(/ (* e (sin v)) (fma (cos v) e 1.0))
14.0ms	(* e (sin v))

series372.0ms

Counts

2 → 6

Calls

2 calls:

214.0ms	(/ (* e (sin v)) (fma (cos v) e 1.0))
157.0ms	(* e (sin v))

simplify2.2s

Counts

49 → 49

Iterations

Useful iterations: 3 (917.0ms)

Iter	Nodes	Cost
0	93	565
1	217	549
2	708	469
3	2925	465
done	5000	465

prune216.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma (cos v) e 1.0) (sin v))
0.2b	(/ e (/ (fma (cos v) e 1.0) (sin v)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
9×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

2 → 101

Calls

2 calls:

11.0ms	(/ (fma (cos v) e 1.0) (sin v))
21.0ms	(/ e (/ (fma (cos v) e 1.0) (sin v)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(/ (fma (cos v) e 1.0) (sin v))
114.0ms	(/ e (/ (fma (cos v) e 1.0) (sin v)))

simplify2.4s

Counts

107 → 107

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	197	1980
1	426	1894
2	1315	1785
3	4104	1777
done	5000	1777

prune450.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (fma (cos v) e 1.0) (sin v))
0.3b	(/ (sqrt e) (/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt e)))
0.4b	(/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt e))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

1566×	`times-frac`
737×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
564×	`sqrt-prod`
91×	`associate-/r*`
59×	`div-inv`
22×	`associate-/l*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `associate-/l/`

Counts

3 → 742

Calls

3 calls:

7.0ms	(/ (fma (cos v) e 1.0) (sin v))
52.0ms	(/ (sqrt e) (/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt e)))
16.0ms	(/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt e))

series476.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(/ (fma (cos v) e 1.0) (sin v))
182.0ms	(/ (sqrt e) (/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt e)))
184.0ms	(/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt e))

simplify2.0s

Counts

751 → 751

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	942	22838
1	2109	21047
done	5001	19694

prune2.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (cos v) e 1.0) (sin v))
0.3b	(/ (* (sqrt e) (sqrt (sqrt e))) (/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt (sqrt e))))
0.4b	(/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt (sqrt e)))
0.4b	(* (sqrt e) (sqrt (sqrt e)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

733×	`times-frac`
382×	`sqrt-prod`
349×	`add-sqr-sqrt`
335×	`add-cube-cbrt` `*-un-lft-identity`
133×	`associate-/r*`
34×	`add-exp-log` `add-cbrt-cube`
33×	`div-inv`
17×	`associate-/l*`
16×	`cbrt-undiv` `div-exp`
15×	`pow1`
11×	`sqrt-pow1`
9×	`associate-r`
7×	`pow1/2`
6×	`associate-l` `pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`pow3`
1×	`sqrt-unprod` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 498

Calls

4 calls:

11.0ms	(/ (fma (cos v) e 1.0) (sin v))
61.0ms	(/ (* (sqrt e) (sqrt (sqrt e))) (/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt (sqrt e))))
17.0ms	(/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt (sqrt e)))
19.0ms	(* (sqrt e) (sqrt (sqrt e)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (fma (cos v) e 1.0) (sin v))
163.0ms	(/ (* (sqrt e) (sqrt (sqrt e))) (/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt (sqrt e))))
246.0ms	(/ (/ (fma (cos v) e 1.0) (sin v)) (sqrt (sqrt e)))
263.0ms	(* (sqrt e) (sqrt (sqrt e)))

simplify1.2s

Counts

510 → 510

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	703	13172
1	1713	11984
done	5001	11129

prune2.1s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
done	9	10

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	1474×	body	1280	valid
1.1s	1283×	body	640	valid
1.1s	4298×	body	80	valid
262.0ms	8000×	pre	80	true
206.0ms	631×	body	320	valid
70.0ms	314×	body	160	valid