Details

sample178.0ms

Algorithm

intervals

Results

89.0ms	118×	body	1280	valid
35.0ms	66×	body	640	valid
12.0ms	256×	pre	80	true
7.0ms	24×	body	320	valid
4.0ms	41×	body	80	valid
1.0ms	7×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5
done	260	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.3b	(tan (+ y z))

rewrite50.0ms

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:

22.0ms	(+ x (- (tan (+ y z)) (tan a)))
18.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series350.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(+ x (- (tan (+ y z)) (tan a)))
139.0ms	(- (tan (+ y z)) (tan a))
59.0ms	(tan (+ y z))

simplify97.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488
done	5001	488

prune242.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `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` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

30.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
149.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
100.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
16.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
425.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
471.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
116.0ms	(* (tan y) (tan z))

simplify89.0ms

Counts

239 → 239

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	704	4490
1	2293	3769
2	5002	3667
done	5002	3667

prune750.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

321×	`*-un-lft-identity`
237×	`add-sqr-sqrt`
180×	`prod-diff`
172×	`times-frac`
146×	`add-cube-cbrt`
92×	`associate-+r+`
58×	`difference-of-squares`
44×	`distribute-lft-out`
30×	`fma-neg` `distribute-lft-out--`
14×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`flip3--` `flip--` `div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`tan-quot` `fma-def` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-*r/` `div-exp` `prod-exp` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 295

Calls

4 calls:

279.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
16.0ms	(/ (* (sin y) (tan z)) (cos y))
189.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
13.0ms	(* (sin y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

448.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
124.0ms	(/ (* (sin y) (tan z)) (cos y))
491.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
89.0ms	(* (sin y) (tan z))

simplify110.0ms

Counts

307 → 307

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	805	7012
1	2633	5836
2	5001	5656
done	5001	5656

prune929.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite362.0ms

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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 104

Calls

4 calls:

34.0ms	(* (+ (tan y) (tan z)) (cos a))
15.0ms	(* (tan y) (tan z))
17.0ms	(* (tan y) (tan z))
293.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series964.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (+ (tan y) (tan z)) (cos a))
107.0ms	(* (tan y) (tan z))
111.0ms	(* (tan y) (tan z))
569.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify85.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	607	1365
1	2835	1198
2	5001	1191
done	5001	1191

prune522.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes313.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	26	20
done	26	20

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.1s	3941×	body	1280	valid
899.0ms	1980×	body	640	valid
377.0ms	8000×	pre	80	true
214.0ms	705×	body	320	valid
123.0ms	1090×	body	80	valid
58.0ms	284×	body	160	valid