Details

sample359.0ms

Algorithm

intervals

Results

170.0ms	128×	body	1280	valid
107.0ms	68×	body	640	valid
18.0ms	256×	pre	80	true
13.0ms	23×	body	320	valid
5.0ms	29×	body	80	valid
2.0ms	8×	body	160	valid

simplify136.0ms

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: 13.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.1b	(tan (+ y z))

rewrite64.0ms

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:

16.0ms	(+ x (- (tan (+ y z)) (tan a)))
26.0ms	(- (tan (+ y z)) (tan a))
20.0ms	(tan (+ y z))

series482.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(+ x (- (tan (+ y z)) (tan a)))
198.0ms	(- (tan (+ y z)) (tan a))
98.0ms	(tan (+ y z))

simplify3.1s

Counts

51 → 51

Iterations

Useful iterations: 3 (324.0ms)

Iter	Nodes	Cost
0	91	627
1	196	590
2	453	572
3	1243	570
4	4659	570
done	5000	570

prune254.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))

rewrite172.0ms

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:

45.0ms	(* (+ (tan y) (tan z)) (cos a))
70.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
22.0ms	(* (tan y) (tan z))
31.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (+ (tan y) (tan z)) (cos a))
774.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
135.0ms	(* (tan y) (tan z))
138.0ms	(* (tan y) (tan z))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	195	2138
1	579	2041
2	2282	1664
done	5000	1625

prune815.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

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:

32.0ms	(* (tan y) (tan z))
22.0ms	(* (tan y) (tan z))
16.0ms	(* (tan y) (tan z))
99.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (tan y) (tan z))
137.0ms	(* (tan y) (tan z))
160.0ms	(* (tan y) (tan z))
236.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify2.5s

Counts

124 → 124

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	115	1312
1	307	1231
2	1045	1047
3	3794	1017
done	5000	1017

prune740.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

24×	`tan-quot`
17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`frac-times` `associate-*l/`
6×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`unswap-sqr`

Counts

4 → 88

Calls

4 calls:

62.0ms	(* (* (tan y) (tan z)) (tan z))
31.0ms	(* (tan y) (tan z))
33.0ms	(* (tan y) (tan z))
16.0ms	(* (tan y) (tan z))

series530.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (* (tan y) (tan z)) (tan z))
140.0ms	(* (tan y) (tan z))
125.0ms	(* (tan y) (tan z))
136.0ms	(* (tan y) (tan z))

simplify2.2s

Counts

100 → 100

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	94	943
1	241	925
2	720	811
3	1765	804
done	5000	798

prune586.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes1.4s

Accuracy

0% (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	22	43
1	32	43
done	32	43

end0.0ms

sample10.2s

Algorithm

intervals

Results

5.3s	3921×	body	1280	valid
2.1s	1982×	body	640	valid
1.1s	698×	body	320	valid
878.0ms	8000×	pre	80	true
240.0ms	1132×	body	80	valid
88.0ms	267×	body	160	valid