Details

sample329.0ms

Algorithm

intervals

Results

199.0ms	127×	body	1280	valid
50.0ms	69×	body	640	valid
18.0ms	256×	pre	80	true
13.0ms	26×	body	320	valid
4.0ms	25×	body	80	valid
3.0ms	9×	body	160	valid

simplify118.0ms

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: 12.2b

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))
3.6b	(tan (+ y z))

rewrite47.0ms

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	(+ x (- (tan (+ y z)) (tan a)))
23.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series396.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(+ x (- (tan (+ y z)) (tan a)))
186.0ms	(- (tan (+ y z)) (tan a))
59.0ms	(tan (+ y z))

simplify3.2s

Counts

51 → 51

Iterations

Useful iterations: 3 (275.0ms)

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

prune190.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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

rewrite149.0ms

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:

34.0ms	(* (+ (tan y) (tan z)) (cos a))
67.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
28.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (+ (tan y) (tan z)) (cos a))
736.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
154.0ms	(* (tan y) (tan z))
138.0ms	(* (tan y) (tan z))

simplify1.7s

Counts

108 → 108

Iterations

Useful iterations: done (1.7s)

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

prune606.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan y)) (cbrt (tan y)))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

24.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
4.0ms	(cbrt (tan y))
4.0ms	(cbrt (tan y))
3.0ms	(cbrt (tan y))

series700.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
160.0ms	(cbrt (tan y))
164.0ms	(cbrt (tan y))
145.0ms	(cbrt (tan y))

simplify2.0s

Counts

91 → 91

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	86	784
1	170	704
2	374	660
3	753	621
4	1812	616
done	5000	586

prune632.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan y))
0.3b	(* (tan z) (tan z))
4.9b	(/ (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (- (tan y) (tan z)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

15.0ms	(* (tan y) (tan z))
26.0ms	(* (tan y) (tan y))
19.0ms	(* (tan z) (tan z))
122.0ms	(/ (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (- (tan y) (tan z)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (tan y) (tan z))
44.0ms	(* (tan y) (tan y))
41.0ms	(* (tan z) (tan z))
452.0ms	(/ (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (- (tan y) (tan z)))

simplify1.6s

Counts

128 → 128

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	205	1691
1	502	1539
2	1883	1365
done	5002	1329

prune775.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes925.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	46
1	31	46
done	31	46

end0.0ms

sample10.8s

Algorithm

intervals

Results

5.7s	3854×	body	1280	valid
2.8s	1964×	body	640	valid
1.0s	8000×	pre	80	true
404.0ms	697×	body	320	valid
218.0ms	1161×	body	80	valid
108.0ms	324×	body	160	valid