Details

analyze1.4s

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

sample221.0ms

Algorithm

intervals

Results

127.0ms	47×	body	2560	valid
58.0ms	90×	body	1280	valid
15.0ms	56×	body	640	valid
6.0ms	33×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	14×	body	80	valid

simplify473.0ms

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: 27.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.7b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (sin.f64 x))

rewrite22.0ms

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:

8.0ms	(/.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))

series38.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
12.0ms	(-.f64 x (tan.f64 x))
14.0ms	(-.f64 x (sin.f64 x))

simplify69.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (59.0ms)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
0.6b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
0.7b	(-.f64 x (tan.f64 x))
0.7b	(-.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:

7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
30.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series53.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
24.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
9.0ms	(-.f64 x (tan.f64 x))
9.0ms	(-.f64 x (tan.f64 x))

simplify55.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5028	1430

prune80.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	103	4	107

Merged error: 0.0b

Counts

107 → 4

localize10.0ms

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))))
0.7b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (sin.f64 x))

rewrite40.0ms

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:

8.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
13.0ms	(/.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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.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))))
13.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

simplify69.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4944	3904
1	4944	3904

prune131.0ms

Filtered

136 candidates to 238 candidates (-75.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	238	4	242

Merged error: 0.0b

Counts

242 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
0.7b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (sin.f64 x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
100×	`times-frac_binary64`
68×	`cbrt-prod_binary64`
62×	`unpow-prod-down_binary64` `cube-prod_binary64`
50×	`add-cube-cbrt_binary64`
42×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64`
3×	`pow-unpow_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-exp_binary64`

Counts

4 → 186

Calls

4 calls:

11.0ms	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

series48.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
11.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
9.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

simplify46.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5081	3368

prune89.0ms

Filtered

87 candidates to 198 candidates (-127.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	198	4	202

Merged error: 0.0b

Counts

202 → 4

regimes70.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch36.0ms

Steps

Iters	Range		Point
8	0.0007385740607946856	7.846042994431209	0.02800543700756853
9	-0.9472632774743391	-5.5983239675023054e-08	-0.028939001950817302

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	44
1	89	44

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.1s	1657×	body	2560	valid
1.6s	2739×	body	1280	valid
514.0ms	1881×	body	640	valid
176.0ms	913×	body	320	valid
59.0ms	451×	body	160	valid
28.0ms	359×	body	80	valid

Details

analyze1.4s

sample221.0ms

simplify473.0ms

prune4.0ms

localize11.0ms

rewrite22.0ms

series38.0ms

simplify69.0ms

prune89.0ms

localize10.0ms

rewrite48.0ms

series53.0ms

simplify55.0ms

prune80.0ms

localize10.0ms

rewrite40.0ms

series39.0ms

simplify69.0ms

prune131.0ms

localize11.0ms

rewrite40.0ms

series48.0ms

simplify46.0ms

prune89.0ms

regimes70.0ms

bsearch36.0ms

simplify3.0ms

end0.0ms

sample6.7s

Profiling