Details

sample638.0ms

Algorithm

intervals

Results

399.0ms	28×	body	320	valid
136.0ms	116×	body	1280	valid
49.0ms	59×	body	640	valid
16.0ms	256×	pre	80	true
7.0ms	42×	body	80	valid
4.0ms	11×	body	160	valid

simplify131.0ms

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: 13.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
3.4b	(tan (+ y z))

rewrite53.0ms

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:

17.0ms	(- (tan (+ y z)) (tan a))
23.0ms	(+ x (- (tan (+ y z)) (tan a)))
12.0ms	(tan (+ y z))

series510.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms	(- (tan (+ y z)) (tan a))
199.0ms	(+ x (- (tan (+ y z)) (tan a)))
101.0ms	(tan (+ y z))

simplify3.0s

Counts

51 → 51

Iterations

Useful iterations: 3 (259.0ms)

Iter	Nodes	Cost
0	91	627
1	196	590
2	453	572
3	1241	570
4	4651	570
done	5000	570

prune228.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite440.0ms

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:

49.0ms	(/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y))))
114.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
229.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
42.0ms	(* (tan z) (tan y))

series1.8s

Counts

4 → 12

Calls

4 calls:

372.0ms	(/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y))))
625.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
603.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
154.0ms	(* (tan z) (tan y))

simplify2.5s

Counts

102 → 102

Iterations

Useful iterations: 3 (1.1s)

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

prune658.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan z) (tan y))
0.2b	(* (tan z) (tan y))
0.3b	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
0.3b	(pow (* (tan z) (tan y)) 3)

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
44×	`tan-quot`
23×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
14×	`associate-r/` `associate-l/`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative`
2×	`pow-pow` `pow-plus` `pow-exp` `rem-cube-cbrt` `unswap-sqr`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

17.0ms	(* (tan z) (tan y))
27.0ms	(* (tan z) (tan y))
125.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
26.0ms	(pow (* (tan z) (tan y)) 3)

series654.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (tan z) (tan y))
147.0ms	(* (tan z) (tan y))
162.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
214.0ms	(pow (* (tan z) (tan y)) 3)

simplify1.1s

Counts

128 → 128

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	156	1401
1	418	1107
2	1812	1041
done	5000	1037

prune602.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (+ (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))
2.3b	(exp (+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))))

rewrite903.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

102.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
169.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
16.0ms	(* (tan z) (tan y))
612.0ms	(exp (+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))))

series1.9s

Counts

4 → 12

Calls

4 calls:

626.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
491.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
124.0ms	(* (tan z) (tan y))
629.0ms	(exp (+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))))

simplify1.5s

Counts

83 → 83

Iterations

Useful iterations: 3 (664.0ms)

Iter	Nodes	Cost
0	144	1677
1	332	1612
2	903	1517
3	2678	1506
done	5000	1506

prune401.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes338.0ms

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: 1 (3.0ms)

Iter	Nodes	Cost
0	22	44
1	31	40
done	31	40

end0.0ms

sample10.2s

Algorithm

intervals

Results

5.7s	3866×	body	1280	valid
1.8s	1994×	body	640	valid
1.3s	689×	body	320	valid
557.0ms	8000×	pre	80	true
271.0ms	1177×	body	80	valid
89.0ms	274×	body	160	valid