Details

sample168.0ms

Algorithm

intervals

Results

64.0ms	40×	body	640	valid
25.0ms	41×	body	1280	valid
14.0ms	145×	body	80	valid
6.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	37	15
done	37	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series233.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1.0 (* (tan x) (tan x)))
107.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

117 → 117

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	138	1632
1	351	1506
2	1543	1368
done	5000	1360

prune388.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

16.0ms	(* (tan x) (tan x))
22.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
83.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))
199.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify883.0ms

Counts

118 → 118

Iterations

Useful iterations: done (878.0ms)

Iter	Nodes	Cost
0	118	1623
1	295	1455
2	1236	1306
done	5000	1295

prune397.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (- 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`pow1` `add-exp-log` `associate-l`
20×	`times-frac`
15×	`add-cbrt-cube`
10×	`associate-r`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`frac-times` `associate-*r/` `div-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down` `associate-l/` `associate-/r` `-commutative` `associate-/l`
2×	`cbrt-undiv` `pow2` `distribute-rgt-in` `sub-neg` `rec-exp` `flip3--` `distribute-lft-in` `flip3-+` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

23.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
73.0ms	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (- 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series384.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
174.0ms	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (- 1.0 (* (tan x) (tan x))))
63.0ms	(* (tan x) (tan x))
65.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

147 → 147

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	176	2160
1	474	1973
2	3125	1692
done	5001	1666

prune417.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
0.2b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (sin x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

18.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
59.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
21.0ms	(* (sin x) (tan x))
26.0ms	(* (tan x) (tan x))

series364.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
172.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
67.0ms	(* (sin x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	172	1940
1	443	1852
2	2065	1714
done	5004	1705

prune436.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
done	13	18

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.3s	1540×	body	1280	valid
842.0ms	1265×	body	640	valid
788.0ms	4278×	body	80	valid
248.0ms	610×	body	320	valid
216.0ms	307×	body	160	valid