Details

sample522.0ms

Algorithm

intervals

Results

117.0ms	54×	body	2560	valid
73.0ms	83×	body	1280	valid
18.0ms	58×	body	640	valid
7.0ms	32×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	11×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series161.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ (- x (sin x)) (- x (tan x)))
53.0ms	(- x (tan x))
38.0ms	(- x (sin x))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune210.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (tan x))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

15.0ms	(/ (sin x) (- x (tan x)))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))
84.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sin x) (- x (tan x)))
46.0ms	(- x (tan x))
50.0ms	(- x (tan x))
166.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune255.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- x (tan x))
0.8b	(- x (tan x))
0.8b	(- x (tan x))
0.8b	(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/` `associate-*l/`
9×	`frac-sub`
8×	`frac-times`
5×	`sub-div`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

6.0ms	(- x (tan x))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))
22.0ms	(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

series342.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- x (tan x))
54.0ms	(- x (tan x))
47.0ms	(- x (tan x))
194.0ms	(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	335	863
1	1141	768
2	4949	748
3	5001	740

prune225.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

26.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series147.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (- x (sin x)) (- x (tan x)))
50.0ms	(- x (tan x))
28.0ms	(- x (sin x))

simplify152.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune180.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch86.0ms

Steps

Iters	Range		Point
11	1.661404138935296e-22	2.5556453819330236	0.026711642772946572
9	-0.04331797882383785	-2.2082264187638084e-10	-0.026797644779880028

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.3s	1576×	body	2560	valid
1.8s	2801×	body	1280	valid
643.0ms	1898×	body	640	valid
218.0ms	930×	body	320	valid
69.0ms	466×	body	160	valid
29.0ms	329×	body	80	valid