Details

sample169.0ms

Algorithm

intervals

Results

88.0ms	119×	body	1280	valid
38.0ms	72×	body	640	valid
11.0ms	256×	pre	80	true
6.0ms	22×	body	320	valid
3.0ms	39×	body	80	valid
1.0ms	4×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

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))
3.1b	(tan (+ y z))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `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 → 42

Calls

3 calls:

8.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series285.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(+ x (- (tan (+ y z)) (tan a)))
113.0ms	(- (tan (+ y z)) (tan a))
50.0ms	(tan (+ y z))

simplify1.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	91	627
1	197	590
2	430	572
3	1029	570
4	3630	570
done	5000	570

prune153.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`tan-quot`
6×	`pow1` `distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
75.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
44.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
341.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
380.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
95.0ms	(* (tan y) (tan z))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: 3 (637.0ms)

Iter	Nodes	Cost
0	188	2099
1	448	1986
2	1177	1912
3	3310	1900
done	5001	1900

prune358.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
44×	`tan-quot`
22×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
16×	`add-sqr-sqrt`
14×	`associate-r/` `associate-l/`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`pow-sqr` `*-commutative` `pow-prod-up` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-plus`
1×	`pow2` `swap-sqr`

Counts

4 → 112

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
21.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (tan y) (tan z))
90.0ms	(* (tan y) (tan z))
90.0ms	(* (tan y) (tan z))
114.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify1.0s

Counts

124 → 124

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	115	1312
1	308	1231
2	1143	1047
done	5000	1027

prune398.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (sin z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(* (/ (* (tan y) (sin z)) (cos z)) (* (tan y) (tan z)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
17×	`tan-quot`
16×	`associate-l`
15×	`pow1`
14×	`prod-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
7×	`frac-times` `associate-*r/`
6×	`pow-prod-down` `associate-*l/`
4×	`cbrt-undiv` `div-exp` `*-commutative` `add-log-exp`
3×	`times-frac` `unswap-sqr`
1×	`div-inv`

Counts

4 → 98

Calls

4 calls:

7.0ms	(* (tan y) (sin z))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
20.0ms	(* (/ (* (tan y) (sin z)) (cos z)) (* (tan y) (tan z)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (tan y) (sin z))
92.0ms	(* (tan y) (tan z))
91.0ms	(* (tan y) (tan z))
169.0ms	(* (/ (* (tan y) (sin z)) (cos z)) (* (tan y) (tan z)))

simplify861.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	151	1398
1	424	1358
2	1715	1102
done	5000	1102

prune455.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

-9.7% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	41
1	37	41
done	37	41

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.0s	3862×	body	1280	valid
877.0ms	2021×	body	640	valid
322.0ms	8000×	pre	80	true
211.0ms	712×	body	320	valid
98.0ms	1118×	body	80	valid
58.0ms	287×	body	160	valid