Details

sample509.0ms

Algorithm

intervals

Results

319.0ms	129×	body	1280	valid
79.0ms	56×	body	640	valid
33.0ms	256×	pre	80	true
19.0ms	21×	body	320	valid
12.0ms	39×	body	80	valid
6.0ms	11×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
34	2015
33	1949
32	1871
31	1805
30	1727
29	1661
28	1583
27	1517
26	1439
25	1373
24	1295
23	1229
22	1151
21	1085
20	1007
19	941
18	863
17	797
16	719
15	653
14	575
13	510
12	430
11	354
10	254
9	186
8	103
7	71
6	61
5	46
4	35
3	29
2	22
1	15
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.2b	(tan (+ y z))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`tan-sum` `associate-+r+` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 45

Calls

3 calls:

22.0ms	(+ x (- (tan (+ y z)) (tan a)))
33.0ms	(- (tan (+ y z)) (tan a))
9.0ms	(tan (+ y z))

series515.0ms

Counts

3 → 9

Calls

3 calls:

222.0ms	(+ x (- (tan (+ y z)) (tan a)))
181.0ms	(- (tan (+ y z)) (tan a))
111.0ms	(tan (+ y z))

simplify2.6s

Counts

54 → 54

Iterations

Iter	Nodes
4	6132
3	1497
2	470
1	198
0	94

prune535.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite268.0ms

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-cbrt-cube` `add-exp-log`
7×	`tan-quot`
6×	`pow1` `distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`associate-+r+` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-/r/` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `frac-2neg` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

45.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
112.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
82.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms	(* (tan y) (tan z))

series1.8s

Counts

4 → 12

Calls

4 calls:

365.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
633.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
661.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
171.0ms	(* (tan y) (tan z))

simplify1.8s

Counts

106 → 106

Iterations

Iter	Nodes
3	4224
2	1247
1	455
0	193

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`times-frac` `insert-posit16`
3×	`associate-/r` `associate-r` `associate-l*` `tan-quot`
2×	`cbrt-undiv` `associate-+r+` `sum-log` `sub-neg` `diff-log` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `clear-num` `associate-+r-` `frac-2neg` `flip3-+` `flip3--` `pow-prod-down` `-commutative` `frac-sub` `flip-+` `div-inv` `flip--` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 78

Calls

4 calls:

220.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
29.0ms	(/ (* (tan y) (sin z)) (cos z))
130.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
12.0ms	(* (tan y) (sin z))

series1.5s

Counts

4 → 12

Calls

4 calls:

541.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
166.0ms	(/ (* (tan y) (sin z)) (cos z))
642.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
127.0ms	(* (tan y) (sin z))

simplify2.8s

Counts

90 → 90

Iterations

Iter	Nodes
3	4489
2	1154
1	401
0	170

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan z) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan y))
5.3b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

42×	`tan-quot`
22×	`add-sqr-sqrt`
20×	`pow1`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`frac-times` `add-cbrt-cube` `add-exp-log`
12×	`associate-*r/` `frac-sub`
11×	`associate-*l/` `associate-/r/` `associate-/l/`
9×	`associate-r` `associate-l`
8×	`flip3--` `flip--`
6×	`swap-sqr`
4×	`times-frac` `prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-prod-down` `*-commutative` `unswap-sqr`
2×	`pow2` `cbrt-undiv` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-sub` `div-inv`

Counts

4 → 127

Calls

4 calls:

29.0ms	(* (tan z) (tan z))
16.0ms	(* (tan y) (tan z))
14.0ms	(* (tan y) (tan y))
105.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

series805.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (tan z) (tan z))
145.0ms	(* (tan y) (tan z))
50.0ms	(* (tan y) (tan y))
540.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

simplify952.0ms

Counts

139 → 139

Iterations

Iter	Nodes
2	2681
1	655
0	232

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes855.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	21
1	21
0	18

end0.0ms

sample16.0s

Algorithm

intervals

Results

10.2s	3872×	body	1280	valid
2.9s	1966×	body	640	valid
1.1s	8000×	pre	80	true
737.0ms	722×	body	320	valid
380.0ms	1170×	body	80	valid
159.0ms	270×	body	160	valid