Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample124.0ms

Algorithm

intervals

Results

48.0ms	52×	body	1280	valid
28.0ms	45×	body	640	valid
19.0ms	132×	body	80	valid
7.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid
3.0ms	19×	body	80	invalid
0.0ms	3×	body	80	nan

simplify556.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4685	21
1	4685	21

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.1b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
8.6b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.9b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))
29.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series103.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 x (tan.f64 B))
11.0ms	(/.f64 F (sin.f64 B))
37.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
25.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify48.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5053	1634

prune199.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	9	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 0.0b

Counts

129 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.9b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
11.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series101.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 x (tan.f64 B))
33.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
29.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify77.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4931	2549
1	4931	2549

prune194.0ms

Filtered

115 candidates to 150 candidates (-30.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	150	9	159

Merged error: 0.0b

Counts

159 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
1.0b	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
9.7b	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
11.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

53×	`unpow-prod-down_binary64`
49×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
33×	`times-frac_binary64`
19×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
12×	`pow1_binary64`
11×	`sqr-pow_binary64` `associate-/l*_binary64`
9×	`pow-exp_binary64`
7×	`pow-unpow_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-to-exp_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 144

Calls

4 calls:

13.0ms	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
6.0ms	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
10.0ms	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

series192.0ms

Counts

4 → 10

Calls

4 calls:

85.0ms	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
0.0ms	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
53.0ms	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
55.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

simplify64.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4909	3340
1	4909	3340

prune267.0ms

Filtered

116 candidates to 154 candidates (-32.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	154	9	163

Merged error: 0.0b

Counts

163 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
8.6b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.9b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
26×	`associate-l_binary64`
25×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
10×	`associate-r_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
7×	`pow1_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`associate-l/_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 119

Calls

4 calls:

6.0ms	(/.f64 F (sin.f64 B))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
14.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series76.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 F (sin.f64 B))
18.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
34.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify56.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4938	1703
1	4938	1703

prune130.0ms

Filtered

102 candidates to 131 candidates (-28.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	131	9	140

Merged error: 0.0b

Counts

140 → 9

regimes224.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.4b

bsearch155.0ms

Steps

Iters	Range		Point
11	2843332931705721.0	1.3747690356736337e+41	46213591011832264.0
6	-4.700695915016074e+101	-5.160568024256584e+100	-5.94905980657102e+100

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	135	68
1	135	68

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1661×	body	1280	valid
801.0ms	1341×	body	640	valid
545.0ms	3965×	body	80	valid
281.0ms	668×	body	320	valid
104.0ms	365×	body	160	valid
91.0ms	654×	body	80	invalid
11.0ms	116×	body	80	nan

Details

analyze1.7s

sample124.0ms

simplify556.0ms

prune15.0ms

localize21.0ms

rewrite53.0ms

series103.0ms

simplify48.0ms

prune199.0ms

localize18.0ms

rewrite44.0ms

series101.0ms

simplify77.0ms

prune194.0ms

localize28.0ms

rewrite44.0ms

series192.0ms

simplify64.0ms

prune267.0ms

localize19.0ms

rewrite40.0ms

series76.0ms

simplify56.0ms

prune130.0ms

regimes224.0ms

bsearch155.0ms

simplify3.0ms

end0.0ms

sample3.6s

Profiling