Details

sample251.0ms

Algorithm

intervals

Results

157.0ms	100×	body	2560	valid
55.0ms	81×	body	1280	valid
15.0ms	39×	body	640	valid
6.0ms	22×	body	320	valid
5.0ms	256×	pre	80	true
2.0ms	9×	body	160	valid
0.0ms	5×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite22.0ms

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:

2.0ms	(/ 1.0 (tan x))
17.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series147.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 1.0 (tan x))
106.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (50.0ms)

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

prune119.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

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

rewrite29.0ms

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:

3.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
9.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
7.0ms	(* 0.022222222222222223 (pow x 3))

series279.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
57.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
52.0ms	(* 0.0021164021164021165 (pow x 5))
36.0ms	(* 0.022222222222222223 (pow x 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (9.0ms)

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

prune204.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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-+l+` `unpow3`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
19.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
5.0ms	(* 0.0021164021164021165 (pow x 5))
7.0ms	(* 0.022222222222222223 (pow x 3))

series289.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
58.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
54.0ms	(* 0.0021164021164021165 (pow x 5))
39.0ms	(* 0.022222222222222223 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	349	485
1	1525	454
2	5002	454

prune206.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

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)))

rewrite36.0ms

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:

22.0ms	(* (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)))
3.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
3.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series3.8s

Counts

4 → 12

Calls

4 calls:

990.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
903.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
885.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.1s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (44.0ms)

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

prune345.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

regimes70.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	18	7

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.9s	3220×	body	2560	valid
1.7s	2522×	body	1280	valid
464.0ms	1275×	body	640	valid
160.0ms	632×	body	320	valid
146.0ms	8000×	pre	80	true
52.0ms	301×	body	160	valid
4.0ms	50×	body	80	valid