Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample226.0ms

Algorithm

intervals

Results

143.0ms	53×	body	2560	valid
46.0ms	86×	body	1280	valid
17.0ms	64×	body	640	valid
5.0ms	25×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	10×	body	80	valid

simplify477.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (sin.f64 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

18.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
6.0ms	(-.f64 x (sin.f64 x))

series43.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
14.0ms	(-.f64 x (tan.f64 x))
15.0ms	(-.f64 x (sin.f64 x))

simplify67.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune89.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

6.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
27.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
11.0ms	(-.f64 x (tan.f64 x))
11.0ms	(-.f64 x (tan.f64 x))
32.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5028	1430

prune84.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Merged error: 0.0b

Counts

107 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

9.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
27.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
11.0ms	(-.f64 x (tan.f64 x))
11.0ms	(-.f64 x (tan.f64 x))
29.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5028	1430

prune88.0ms

Filtered

81 candidates to 103 candidates (-27.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	103	5	108

Merged error: 0.0b

Counts

108 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (sin.f64 x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac_binary64`
200×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
54×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip--_binary64`
6×	`div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 226

Calls

4 calls:

10.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
12.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

series43.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
14.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
11.0ms	(-.f64 x (tan.f64 x))
5.0ms	(-.f64 x (sin.f64 x))

simplify68.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4944	3904
1	4944	3904

prune128.0ms

Filtered

137 candidates to 238 candidates (-73.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	238	5	243

Merged error: 0.0b

Counts

243 → 5

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch37.0ms

Steps

Iters	Range		Point
7	0.003895118747050592	0.1467699116193224	0.026966668772347803
10	-0.37962549694987363	-6.684650092655955e-13	-0.023962012532431926

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	46
1	97	46

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.9s	1579×	body	2560	valid
1.8s	2837×	body	1280	valid
512.0ms	1888×	body	640	valid
161.0ms	889×	body	320	valid
64.0ms	468×	body	160	valid
26.0ms	339×	body	80	valid

Details

analyze1.3s

sample226.0ms

simplify477.0ms

prune4.0ms

localize10.0ms

rewrite31.0ms

series43.0ms

simplify67.0ms

prune89.0ms

localize9.0ms

rewrite44.0ms

series68.0ms

simplify54.0ms

prune84.0ms

localize12.0ms

rewrite48.0ms

series65.0ms

simplify57.0ms

prune88.0ms

localize9.0ms

rewrite42.0ms

series43.0ms

simplify68.0ms

prune128.0ms

regimes47.0ms

bsearch37.0ms

simplify3.0ms

end0.0ms

sample6.6s

Profiling