Details

sample306.0ms

Algorithm

intervals

Results

174.0ms	98×	body	2560	valid
60.0ms	75×	body	1280	valid
28.0ms	256×	pre	80	true
17.0ms	41×	body	640	valid
7.0ms	27×	body	320	valid
3.0ms	14×	body	160	valid
0.0ms	1×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
done	11	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.5b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite90.0ms

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:

30.0ms	(/ 1.0 (tan x))
58.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series209.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ 1.0 (tan x))
161.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify2.8s

Counts

56 → 56

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	115	619
1	234	592
2	497	566
3	1071	564
4	2824	562
done	5000	561

prune212.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

23.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
14.0ms	(* 0.022222222222222223 (pow x 3))
17.0ms	(* 0.0021164021164021165 (pow x 5))

series206.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
47.0ms	(* 0.022222222222222223 (pow x 3))
80.0ms	(* 0.0021164021164021165 (pow x 5))

simplify4.3s

Counts

78 → 78

Iterations

Useful iterations: 2 (233.0ms)

Iter	Nodes	Cost
0	123	847
1	300	764
2	963	708
3	4972	708
done	5001	708

prune282.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.0021164021164021165 (pow x 5))
1.8b	(log (exp (* 0.0021164021164021165 (pow x 5))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

52.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
29.0ms	(* 0.022222222222222223 (pow x 3))
26.0ms	(* 0.0021164021164021165 (pow x 5))
7.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
68.0ms	(* 0.022222222222222223 (pow x 3))
100.0ms	(* 0.0021164021164021165 (pow x 5))
94.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

simplify4.4s

Counts

95 → 95

Iterations

Useful iterations: 2 (236.0ms)

Iter	Nodes	Cost
0	143	1042
1	321	888
2	991	820
3	4967	820
done	5001	820

prune344.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
0.6b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
0.6b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
0.6b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

rewrite605.0ms

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:

536.0ms	(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
18.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
30.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
17.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
401.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
387.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
391.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

simplify1.2s

Counts

99 → 99

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	196	4286
1	494	4021
2	1615	3786
done	5000	3270

prune436.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 0.2b

regimes152.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	17
1	20	17
done	20	17

end0.0ms

sample13.3s

Algorithm

intervals

Results

8.5s	3276×	body	2560	valid
3.4s	2506×	body	1280	valid
722.0ms	1203×	body	640	valid
209.0ms	645×	body	320	valid
155.0ms	8000×	pre	80	true
78.0ms	325×	body	160	valid
5.0ms	45×	body	80	valid