Details

sample225.0ms

Algorithm

intervals

Results

125.0ms	118×	body	1280	valid
44.0ms	72×	body	640	valid
12.0ms	256×	pre	80	true
9.0ms	23×	body	320	valid
4.0ms	31×	body	80	valid
3.0ms	12×	body	160	valid

simplify135.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.7b	(tan (+ y z))

rewrite58.0ms

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:

30.0ms	(+ x (- (tan (+ y z)) (tan a)))
17.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series469.0ms

Counts

3 → 9

Calls

3 calls:

223.0ms	(+ x (- (tan (+ y z)) (tan a)))
183.0ms	(- (tan (+ y z)) (tan a))
63.0ms	(tan (+ y z))

simplify2.9s

Counts

51 → 51

Iterations

Useful iterations: 3 (263.0ms)

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

prune240.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite447.0ms

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:

65.0ms	(/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y))))
109.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
242.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
25.0ms	(* (tan z) (tan y))

series1.7s

Counts

4 → 12

Calls

4 calls:

303.0ms	(/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y))))
680.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
600.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
155.0ms	(* (tan z) (tan y))

simplify2.4s

Counts

102 → 102

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	189	2099
1	450	1986
2	1233	1912
3	3498	1900
done	5001	1900

prune503.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

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:

101.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
25.0ms	(* (tan z) (tan y))
16.0ms	(* (tan z) (tan y))
16.0ms	(* (tan z) (tan y))

series606.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
110.0ms	(* (tan z) (tan y))
180.0ms	(* (tan z) (tan y))
141.0ms	(* (tan z) (tan y))

simplify3.0s

Counts

124 → 124

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	116	1312
1	305	1231
2	1029	1047
3	3751	1017
done	5000	1017

prune401.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
29×	`prod-exp` `cbrt-unprod`
16×	`tan-quot`
13×	`pow1` `add-sqr-sqrt`
12×	`cbrt-undiv` `div-exp` `associate-l`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`frac-times` `associate-r/` `associate-r*`
5×	`pow-prod-down` `associate-*l/`
4×	`add-log-exp`
3×	`*-commutative`
2×	`times-frac` `associate-/r/` `cos-mult` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l/` `sin-mult` `associate-/l`

Counts

4 → 109

Calls

4 calls:

79.0ms	(* (/ (* (sin y) (sin z)) (* (cos z) (cos y))) (* (tan z) (tan y)))
15.0ms	(* (tan z) (tan y))
16.0ms	(* (tan z) (tan y))
20.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (/ (* (sin y) (sin z)) (* (cos z) (cos y))) (* (tan z) (tan y)))
104.0ms	(* (tan z) (tan y))
105.0ms	(* (tan z) (tan y))
113.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: 2 (344.0ms)

Iter	Nodes	Cost
0	169	2077
1	480	1969
2	2248	1484
done	5000	1484

prune510.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes237.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	44
1	34	44
done	34	44

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.2s	3881×	body	1280	valid
1.6s	2035×	body	640	valid
882.0ms	8000×	pre	80	true
545.0ms	1101×	body	80	valid
279.0ms	685×	body	320	valid
79.0ms	298×	body	160	valid