Details

sample189.0ms

Algorithm

intervals

Results

38.0ms	37×	body	1280	valid
31.0ms	45×	body	640	valid
23.0ms	146×	body	80	valid
8.0ms	15×	body	320	valid
4.0ms	13×	body	160	valid

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	36	15
done	36	15

prune4.0ms

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))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite91.0ms

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:

6.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- 1.0 (* (tan x) (tan x)))
172.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
51.0ms	(* (tan x) (tan x))
67.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

117 → 117

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	138	1632
1	315	1486
2	856	1368
3	2669	1346
done	5000	1342

prune390.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

7.0ms	(pow (cos x) 2)
8.0ms	(pow (cos x) 2)
8.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)

series111.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (cos x) 2)
38.0ms	(pow (cos x) 2)
28.0ms	(pow (sin x) 2)
25.0ms	(pow (sin x) 2)

simplify3.2s

Counts

84 → 84

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	64	576
1	133	492
2	277	432
3	763	432
4	3650	424
done	5000	424

prune413.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))
28.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))
142.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify2.7s

Counts

135 → 135

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	186	2167
1	360	1955
2	887	1806
3	2560	1786
done	5000	1768

prune599.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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 (+ 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
40.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
16.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series283.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1.0 (* (tan x) (tan x)))
151.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
50.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))

simplify3.1s

Counts

124 → 124

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	159	1739
1	375	1505
2	1103	1321
3	3841	1277
done	5000	1273

prune365.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes347.0ms

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	9	17
1	13	17
done	13	17

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.4s	1460×	body	1280	valid
1.4s	1269×	body	640	valid
812.0ms	601×	body	320	valid
791.0ms	4344×	body	80	valid
136.0ms	326×	body	160	valid