Details

sample201.0ms

Algorithm

intervals

Results

104.0ms	130×	body	1280	valid
30.0ms	58×	body	640	valid
13.0ms	256×	pre	80	true
7.0ms	22×	body	320	valid
4.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify125.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	33	9
4	38	9
5	45	9
6	51	9
7	61	9
8	74	9
9	86	9
10	95	9
done	95	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
6.2b	(tan (+ y z))

rewrite74.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-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:

31.0ms	(+ x (- (tan (+ y z)) (tan a)))
31.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series564.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms	(+ x (- (tan (+ y z)) (tan a)))
229.0ms	(- (tan (+ y z)) (tan a))
106.0ms	(tan (+ y z))

simplify3.5s

Counts

81 → 81

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	644	882
3	2382	793
done	5000	773

prune298.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b	(* (tan y) (tan z))

rewrite486.0ms

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` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

18.0ms	(+ (tan y) (tan z))
277.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
142.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
24.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (tan y) (tan z))
628.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
710.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
159.0ms	(* (tan y) (tan z))

simplify1.8s

Counts

219 → 219

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	296	6641
1	659	5549
2	1645	5029
done	5000	4398

prune981.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1))
0.1b	(+ (tan y) (tan z))
0.1b	(+ x (+ (- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a)) 0))
0.1b	(- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a))

rewrite923.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
48×	`prod-diff`
22×	`distribute-lft-out`
17×	`add-log-exp`
16×	`fma-neg`
6×	`add-exp-log` `fma-def` `sum-log` `add-cbrt-cube`
5×	`tan-quot` `div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`flip3-+` `associate-/r*` `flip-+` `associate-/l/`
2×	`+-commutative` `diff-log` `frac-add` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `associate-+l-` `associate-+r-` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--`

Counts

4 → 159

Calls

4 calls:

41.0ms	(/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1))
9.0ms	(+ (tan y) (tan z))
756.0ms	(+ x (+ (- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a)) 0))
109.0ms	(- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a))

series1.8s

Counts

4 → 12

Calls

4 calls:

345.0ms	(/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1))
133.0ms	(+ (tan y) (tan z))
559.0ms	(+ x (+ (- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a)) 0))
756.0ms	(- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a))

simplify3.7s

Counts

171 → 171

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	228	4803
1	526	4043
2	1393	3665
3	4830	3232
done	5000	3230

prune652.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan z)) (cbrt (tan z)))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

27.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
4.0ms	(cbrt (tan z))
4.0ms	(cbrt (tan z))
4.0ms	(cbrt (tan z))

series763.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
207.0ms	(cbrt (tan z))
168.0ms	(cbrt (tan z))
186.0ms	(cbrt (tan z))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	90	824
1	178	736
2	391	692
3	820	651
4	1925	646
done	5000	614

prune381.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes247.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	27
1	23	27
done	23	27

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.5s	3904×	body	1280	valid
972.0ms	2002×	body	640	valid
407.0ms	8000×	pre	80	true
229.0ms	717×	body	320	valid
123.0ms	1120×	body	80	valid
62.0ms	257×	body	160	valid