Details

sample214.0ms

Algorithm

intervals

Results

138.0ms	100×	body	2560	valid
51.0ms	90×	body	1280	valid
7.0ms	27×	body	640	valid
3.0ms	20×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	17×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4
done	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
4.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

6.0ms	(/ 1.0 (tan x))
28.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ 1.0 (tan x))
100.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify49.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326
done	5001	326

prune108.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
21.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
13.0ms	(* 0.0021164021164021165 (pow x 5))
12.0ms	(* 0.022222222222222223 (pow x 3))

series272.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
59.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
46.0ms	(* 0.0021164021164021165 (pow x 5))
38.0ms	(* 0.022222222222222223 (pow x 3))

simplify52.0ms

Counts

92 → 92

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	355	465
1	1532	436
2	5001	436
done	5001	436

prune190.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

52.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
8.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
932.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
912.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
905.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify55.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	480	1634
1	1767	1548
2	5001	1352
done	5001	1352

prune402.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-div`
16×	`cbrt-prod`
9×	`flip3-+` `flip-+`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `associate-l/`

Counts

4 → 59

Calls

4 calls:

6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
22.0ms	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
10.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series4.3s

Counts

4 → 12

Calls

4 calls:

905.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.1s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.2s	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.1s	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify55.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	589	1393
1	1963	1320
2	5001	1211
done	5001	1211

prune368.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 0.1b

regimes100.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	18	7
done	18	7

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.4s	3254×	body	2560	valid
1.4s	2479×	body	1280	valid
346.0ms	1261×	body	640	valid
110.0ms	635×	body	320	valid
93.0ms	8000×	pre	80	true
40.0ms	325×	body	160	valid
3.0ms	46×	body	80	valid