Details

sample631.0ms

Algorithm

intervals

Results

204.0ms	154×	body	80	valid
138.0ms	55×	body	1280	valid
44.0ms	53×	body	640	valid
13.0ms	21×	body	320	valid
5.0ms	10×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	10	12
1	31	12
2	61	11
3	63	11
done	63	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

23.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
7.0ms	(/ 1.0 (tan B))
22.0ms	(* x (/ 1.0 (tan B)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
70.0ms	(/ 1.0 (tan B))
240.0ms	(* x (/ 1.0 (tan B)))

simplify6.1s

Counts

129 → 129

Iterations

Useful iterations: done (6.1s)

Iter	Nodes	Cost
0	188	1244
1	2335	1176
done	5000	1075

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ x (tan B))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ x (tan B))

series357.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
158.0ms	(/ x (tan B))

simplify4.0s

Counts

78 → 78

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	136	724
1	723	697
done	5001	635

prune451.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`tan-quot` `cbrt-div` `associate-/r/` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

7.0ms	(cbrt (/ 1.0 (tan B)))
7.0ms	(cbrt (/ 1.0 (tan B)))
7.0ms	(cbrt (/ 1.0 (tan B)))
80.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))

series1.0s

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt (/ 1.0 (tan B)))
221.0ms	(cbrt (/ 1.0 (tan B)))
209.0ms	(cbrt (/ 1.0 (tan B)))
347.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))

simplify11.9s

Counts

170 → 170

Iterations

Useful iterations: done (11.9s)

Iter	Nodes	Cost
0	185	2379
1	2887	2212
done	5000	2124

prune877.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

109×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`tan-quot` `add-exp-log` `associate-/r/`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

3.0ms	(cbrt (/ 1.0 (sin B)))
4.0ms	(cbrt (/ 1.0 (tan B)))
6.0ms	(cbrt (/ 1.0 (tan B)))
59.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))

series1.1s

Counts

4 → 12

Calls

4 calls:

220.0ms	(cbrt (/ 1.0 (sin B)))
283.0ms	(cbrt (/ 1.0 (tan B)))
268.0ms	(cbrt (/ 1.0 (tan B)))
303.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))

simplify11.1s

Counts

169 → 169

Iterations

Useful iterations: done (11.1s)

Iter	Nodes	Cost
0	235	2369
1	3036	2201
done	5000	2113

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	13
1	14	11
done	14	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.5s	1706×	body	1280	valid
1.4s	4938×	body	80	valid
1.0s	1451×	body	640	valid
702.0ms	334×	body	160	valid
489.0ms	726×	body	320	valid