Details

sample442.0ms

Algorithm

intervals

Results

180.0ms	44×	body	1280	valid
67.0ms	47×	body	640	valid
26.0ms	137×	body	80	valid
11.0ms	19×	body	320	valid
3.0ms	9×	body	160	valid

simplify34.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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))

rewrite81.0ms

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)))
20.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
18.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1.0 (* (tan x) (tan x)))
113.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(* (tan x) (tan x))
62.0ms	(* (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

prune345.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
16.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- 1.0 (* (tan x) (tan x)))
167.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
76.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify2.2s

Counts

177 → 177

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	249	3696
1	635	3313
2	3108	3118
done	5002	2894

prune372.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:

8.0ms	(pow (sin x) 2)
16.0ms	(pow (sin x) 2)
6.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)

series126.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin x) 2)
37.0ms	(pow (sin x) 2)
32.0ms	(pow (cos x) 2)
32.0ms	(pow (cos x) 2)

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	64	576
1	189	492
2	648	432
3	2390	432
done	5004	432

prune316.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(/ (/ 1 (+ (* (tan x) (tan x)) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

633×	`times-frac`
326×	`add-sqr-sqrt`
273×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-/r/`
49×	`difference-of-squares`
48×	`add-exp-log`
36×	`div-inv`
32×	`div-exp`
20×	`add-cbrt-cube`
19×	`flip3-+` `flip-+`
18×	`pow1` `associate-/r*`
17×	`flip3--` `flip--`
15×	`associate-/l*`
8×	`tan-quot` `cbrt-undiv` `rec-exp` `1-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 404

Calls

4 calls:

14.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))
73.0ms	(/ (/ 1 (+ (* (tan x) (tan x)) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- 1.0 (* (tan x) (tan x)))
50.0ms	(* (tan x) (tan x))
49.0ms	(* (tan x) (tan x))
152.0ms	(/ (/ 1 (+ (* (tan x) (tan x)) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))

simplify1.7s

Counts

416 → 416

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	657	14622
1	2337	12722
done	5000	11697

prune741.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes304.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	1528×	body	1280	valid
888.0ms	1234×	body	640	valid
713.0ms	4305×	body	80	valid
308.0ms	616×	body	320	valid
84.0ms	317×	body	160	valid