Details

sample136.0ms

Algorithm

intervals

Results

49.0ms	127×	body	1280	valid
19.0ms	256×	pre	80	true
16.0ms	67×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	29×	body	80	valid
1.0ms	7×	body	160	valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.8b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
4.3b	(tan (+ y z))

rewrite21.0ms

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:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series110.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ x (- (tan (+ y z)) (tan a)))
35.0ms	(- (tan (+ y z)) (tan a))
27.0ms	(tan (+ y z))

simplify1.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (132.0ms)

Iter	Nodes	Cost
0	92	627
1	199	590
2	430	572
3	1025	570
4	3627	570
done	5001	570

prune94.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.1b

Counts

52 → 6

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
14.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
16.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series316.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (tan y) (tan z))
139.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
130.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
23.0ms	(* (tan y) (tan z))

simplify1.3s

Counts

79 → 79

Iterations

Useful iterations: 3 (397.0ms)

Iter	Nodes	Cost
0	155	1433
1	368	1362
2	930	1302
3	2312	1291
done	5001	1291

prune163.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	73	12	85

Merged error: 0.1b

Counts

85 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*l/`
18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`tan-quot` `*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `frac-add` `-commutative` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

9.0ms	(* (+ (tan y) (tan z)) (cos a))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
16.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (+ (tan y) (tan z)) (cos a))
23.0ms	(* (tan y) (tan z))
23.0ms	(* (tan y) (tan z))
161.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify965.0ms

Counts

108 → 108

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	201	2138
1	603	2041
2	2241	1664
done	5000	1653

prune185.0ms

Filtered

84 candidates to 108 candidates (-28.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	108	12	120

Merged error: 0.1b

Counts

120 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
0.2b	(* (+ (tan y) (tan z)) (cos a))
0.2b	(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
0.2b	(* (tan y) (tan z))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

16.0ms	(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
9.0ms	(* (+ (tan y) (tan z)) (cos a))
22.0ms	(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
6.0ms	(* (tan y) (tan z))

series370.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
37.0ms	(* (+ (tan y) (tan z)) (cos a))
170.0ms	(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
23.0ms	(* (tan y) (tan z))

simplify2.0s

Counts

119 → 119

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	213	3148
1	515	2901
2	1467	2729
done	5000	2588

prune136.0ms

Filtered

85 candidates to 119 candidates (-40.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	121	10	131

Merged error: 0.1b

Counts

131 → 10

regimes938.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	29
1	27	27
done	27	27

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	3963×	body	1280	valid
560.0ms	8000×	pre	80	true
485.0ms	2013×	body	640	valid
110.0ms	666×	body	320	valid
58.0ms	1056×	body	80	valid
35.0ms	302×	body	160	valid

Details

sample136.0ms

simplify78.0ms

prune5.0ms

localize15.0ms

rewrite21.0ms

series110.0ms

simplify1.5s

prune94.0ms

localize16.0ms

rewrite43.0ms

series316.0ms

simplify1.3s

prune163.0ms

localize21.0ms

rewrite40.0ms

series247.0ms

simplify965.0ms

prune185.0ms

localize21.0ms

rewrite56.0ms

series370.0ms

simplify2.0s

prune136.0ms

regimes938.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.4s

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