Details

sample329.0ms

Algorithm

intervals

Results

188.0ms	113×	body	1280	valid
49.0ms	61×	body	640	valid
19.0ms	256×	pre	80	true
15.0ms	28×	body	320	valid
7.0ms	43×	body	80	valid
5.0ms	11×	body	160	valid

simplify6.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	4724
8	1354
7	446
6	193
5	89
4	39
3	33
2	22
1	15
0	9

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.7b	(tan (+ y z))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
2×	`tan-sum` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

14.0ms	(+ x (- (tan (+ y z)) (tan a)))
17.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(tan (+ y z))

series508.0ms

Counts

3 → 9

Calls

3 calls:

232.0ms	(+ x (- (tan (+ y z)) (tan a)))
192.0ms	(- (tan (+ y z)) (tan a))
84.0ms	(tan (+ y z))

simplify745.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1003
1	284
0	128

prune555.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan z) (tan y))
0.1b	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
0.2b	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
0.2b	(* (tan z) (tan y))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sum-log` `associate-r` `associate-l`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

14.0ms	(+ (tan z) (tan y))
164.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
109.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
17.0ms	(* (tan z) (tan y))

series1.6s

Counts

4 → 12

Calls

4 calls:

192.0ms	(+ (tan z) (tan y))
593.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
720.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
132.0ms	(* (tan z) (tan y))

simplify2.6s

Counts

219 → 219

Iterations

Iter	Nodes
done	5000
2	2655
1	701
0	298

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
59.8b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `tan-quot`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
1.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt (tan a))
183.0ms	(cbrt (tan a))
198.0ms	(cbrt (tan a))
303.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify3.5s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	3181
3	775
2	239
1	107
0	55

prune766.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
59.6b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (log1p (expm1 (cbrt (tan a)))) (cbrt (tan a)))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `tan-quot`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (tan a))
1.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
0.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (log1p (expm1 (cbrt (tan a)))) (cbrt (tan a)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

235.0ms	(cbrt (tan a))
179.0ms	(cbrt (tan a))
208.0ms	(cbrt (tan a))
940.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (log1p (expm1 (cbrt (tan a)))) (cbrt (tan a)))))

simplify895.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
3	942
2	226
1	100
0	53

prune748.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes654.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample9.8s

Algorithm

intervals

Results

6.4s	3894×	body	1280	valid
1.5s	1975×	body	640	valid
563.0ms	8000×	pre	80	true
340.0ms	717×	body	320	valid
194.0ms	1082×	body	80	valid
143.0ms	332×	body	160	valid