Details

sample333.0ms

Algorithm

intervals

Results

191.0ms	124×	body	1280	valid
49.0ms	58×	body	640	valid
18.0ms	256×	pre	80	true
15.0ms	26×	body	320	valid
6.0ms	37×	body	80	valid
5.0ms	11×	body	160	valid

simplify7.0s

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	39	9
5	89	9
6	193	9
7	451	9
8	1380	9
9	4837	9
done	5001	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
4.6b	(tan (+ y z))

rewrite61.0ms

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:

18.0ms	(+ x (- (tan (+ y z)) (tan a)))
32.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(tan (+ y z))

series519.0ms

Counts

3 → 9

Calls

3 calls:

191.0ms	(+ x (- (tan (+ y z)) (tan a)))
216.0ms	(- (tan (+ y z)) (tan a))
111.0ms	(tan (+ y z))

simplify998.0ms

Counts

81 → 81

Iterations

Useful iterations: done (996.0ms)

Iter	Nodes	Cost
0	128	1195
1	283	1011
2	1003	882
done	5000	795

prune496.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite537.0ms

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:

298.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
19.0ms	(+ (tan y) (tan z))
161.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
36.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

630.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
192.0ms	(+ (tan y) (tan z))
583.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
152.0ms	(* (tan y) (tan z))

simplify2.6s

Counts

219 → 219

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	296	6641
1	701	5567
2	2715	5029
done	5001	4679

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

18×	`tan-quot`
14×	`*-un-lft-identity`
13×	`add-log-exp`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`frac-sub`
6×	`pow1` `add-exp-log` `fma-def` `prod-diff` `add-cbrt-cube`
5×	`associate-+r+`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u`
3×	`associate-r` `associate-l` `frac-add` `sum-log`
2×	`+-commutative` `sub-neg` `diff-log` `associate-*r/` `distribute-lft-out`
1×	`associate-+r-` `flip3--` `fma-neg` `pow-prod-down` `prod-exp` `un-div-inv` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

74.0ms	(+ x (- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a)))
9.0ms	(+ (tan y) (tan z))
60.0ms	(- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a))
48.0ms	(* (tan y) (tan z))

series1.7s

Counts

4 → 12

Calls

4 calls:

607.0ms	(+ x (- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a)))
183.0ms	(+ (tan y) (tan z))
707.0ms	(- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a))
193.0ms	(* (tan y) (tan z))

simplify2.7s

Counts

103 → 103

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	211	2052
1	564	1889
2	2716	1715
done	5003	1704

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.4b	(pow (* (tan y) (tan z)) 3)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
44×	`tan-quot`
23×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
14×	`associate-r/` `associate-l/`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative`
2×	`pow-pow` `pow-plus` `pow-exp` `rem-cube-cbrt` `unswap-sqr`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

16.0ms	(* (tan y) (tan z))
30.0ms	(* (tan y) (tan z))
128.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
27.0ms	(pow (* (tan y) (tan z)) 3)

series745.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (tan y) (tan z))
142.0ms	(* (tan y) (tan z))
216.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
245.0ms	(pow (* (tan y) (tan z)) 3)

simplify2.3s

Counts

136 → 136

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	161	1465
1	559	1191
2	3820	1100
done	5000	1092

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes599.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	19	30
1	27	28
2	35	28
3	39	28
done	39	28

end0.0ms

sample9.1s

Algorithm

intervals

Results

5.3s	3938×	body	1280	valid
1.3s	1960×	body	640	valid
844.0ms	8000×	pre	80	true
725.0ms	673×	body	320	valid
177.0ms	1130×	body	80	valid
114.0ms	299×	body	160	valid