Details

sample424.0ms

Algorithm

intervals

Results

281.0ms	103×	body	2560	valid
84.0ms	79×	body	1280	valid
25.0ms	42×	body	640	valid
6.0ms	17×	body	320	valid
6.0ms	256×	pre	80	true
3.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	8
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite38.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `tan-quot` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

9.0ms	(/ 1.0 (tan x))
26.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series523.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ 1.0 (tan x))
480.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	3982
2	685
1	242
0	115

prune191.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

8.0ms	(+ (* x 0.3333333333333333) (* (pow x 3) 0.022222222222222223))
33.0ms	(+ (+ (* x 0.3333333333333333) (* (pow x 3) 0.022222222222222223)) (* 0.0021164021164021165 (pow x 5)))
17.0ms	(* 0.0021164021164021165 (pow x 5))
15.0ms	(* (pow x 3) 0.022222222222222223)

series304.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* x 0.3333333333333333) (* (pow x 3) 0.022222222222222223))
71.0ms	(+ (+ (* x 0.3333333333333333) (* (pow x 3) 0.022222222222222223)) (* 0.0021164021164021165 (pow x 5)))
73.0ms	(* 0.0021164021164021165 (pow x 5))
58.0ms	(* (pow x 3) 0.022222222222222223)

simplify632.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1458
1	361
0	139

prune384.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

116.0ms	(* (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))) (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))))
22.0ms	(cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))
14.0ms	(cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))
13.0ms	(cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))

series1.5s

Counts

4 → 12

Calls

4 calls:

389.0ms	(* (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))) (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))))
348.0ms	(cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))
356.0ms	(cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))
366.0ms	(cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))

simplify765.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	2259
1	527
0	196

prune751.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333)))
0.7b	(cbrt (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333))))
0.7b	(cbrt (* (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))) (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))))
0.9b	(pow (cbrt (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333)))) (+ 3 1))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
22×	`cbrt-prod`
13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`unpow-prod-down`
8×	`flip3-+` `flip-+`
5×	`pow1` `add-exp-log`
4×	`frac-times` `pow-unpow` `add-cbrt-cube` `pow1/3` `add-log-exp`
2×	`pow-pow` `associate-l/` `associate-r/`
1×	`pow-to-exp` `unpow-prod-up` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

23.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333)))
26.0ms	(cbrt (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333))))
45.0ms	(cbrt (* (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))) (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))))
38.0ms	(pow (cbrt (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333)))) (+ 3 1))

series1.7s

Counts

4 → 12

Calls

4 calls:

361.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333)))
405.0ms	(cbrt (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333))))
454.0ms	(cbrt (* (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165))) (cbrt (+ (+ (* x 0.3333333333333333) (* 0.022222222222222223 (pow x 3))) (* (pow x 5) 0.0021164021164021165)))))
448.0ms	(pow (cbrt (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* (pow x 5) 0.0021164021164021165)) (* x 0.3333333333333333)))) (+ 3 1))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	3805
1	924
0	345

prune805.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.1b

regimes144.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample12.7s

Algorithm

intervals

Results

7.2s	3279×	body	2560	valid
3.2s	2515×	body	1280	valid
1.1s	1225×	body	640	valid
586.0ms	632×	body	320	valid
290.0ms	8000×	pre	80	true
66.0ms	300×	body	160	valid
6.0ms	49×	body	80	valid