Details

analyze669.0ms (7.3%)

Algorithm

1×

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample51.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	41×	body	2048	valid
10.0ms	159×	body	128	valid
9.0ms	23×	body	4096	valid
4.0ms	21×	body	1024	valid
2.0ms	10×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	9×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify554.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (428.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

37.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162`
4×	`associate-/l*_binary64_1046`
3×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 72

Calls

4 calls:

9.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)

series306.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
86.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
85.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
44.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify144.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune162.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

5.9b

Counts

85 → 8

Compiler

Compiled 2115 to 1145 computations (45.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.5b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.5b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite93.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1107`
59×	`add-sqr-sqrt_binary64_1123`
44×	`*-un-lft-identity_binary64_1101`
30×	`add-cube-cbrt_binary64_1136`
27×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
14×	`difference-of-squares_binary64_1070`
13×	`sqrt-prod_binary64_1117` `associate-/l*_binary64_1046`
10×	`associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
9×	`associate-/r*_binary64_1045`
7×	`distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105`
6×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `div-inv_binary64_1098` `cancel-sign-sub-inv_binary64_1067`
5×	`pow1_binary64_1162`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-div_binary64_1118`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `associate-/l/_binary64_1048` `pow1/2_binary64_1181`

Counts

4 → 136

Calls

4 calls:

24.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
14.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series746.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

275.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
268.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
119.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
83.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify173.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5011	5032

prune576.0ms (6.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	149	7	156

Error

5.9b

Counts

156 → 7

Compiler

Compiled 4759 to 2523 computations (47% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1123`
28×	`*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
11×	`sqrt-prod_binary64_1117`
10×	`difference-of-squares_binary64_1070`
8×	`add-log-exp_binary64_1140`
7×	`cancel-sign-sub-inv_binary64_1067`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162` `distribute-lft-out--_binary64_1053`
4×	`flip--_binary64_1076` `flip3--_binary64_1105`
3×	`associate-/l*_binary64_1046`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `associate-/r/_binary64_1047` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

4 → 88

Calls

4 calls:

11.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series508.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
101.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
99.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
36.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4882	2580
1	4882	2580

prune171.0ms (1.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	100	7	107

Error

5.9b

Counts

107 → 7

Compiler

Compiled 2900 to 1713 computations (40.9% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
6×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
2×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 54

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series255.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
75.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
58.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
36.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4915	1236
1	4915	1236

prune126.0ms (1.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	66	7	73

Error

5.9b

Counts

73 → 7

Compiler

Compiled 2448 to 1315 computations (46.3% saved)

regimes1.0s (11.3%)

Accuracy

Total 1.3b remaining (20.2%)

Threshold costs 0b (0%)

Compiler

Compiled 3918 to 2946 computations (24.8% saved)

bsearch210.0ms (2.3%)

Steps

Iters	Range	Point
10	5.190475798884544e+30	1.3615842048100228e+49	1.3266789206923356e+49
10	1.5765947289601362e-267	1.201235150462888e-255	3.53250645588002e-262
10	-4.745339480181553e+165	-1.1523709868748084e+152	-1.6066190304518379e+153

Iters

Range

Point

5.190475798884544e+30

1.3615842048100228e+49

1.3266789206923356e+49

1.5765947289601362e-267

1.201235150462888e-255

3.53250645588002e-262

-4.745339480181553e+165

-1.1523709868748084e+152

-1.6066190304518379e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	121	91
1	121	91

end0.0ms (0%)

sample3.0s (32.3%)

Algorithm

1×

intervals

Results

419.0ms	1169×	body	2048	valid
365.0ms	5144×	body	128	valid
199.0ms	736×	body	1024	valid
177.0ms	405×	body	4096	valid
74.0ms	362×	body	512	valid
47.0ms	660×	body	128	nan
31.0ms	393×	body	128	invalid
25.0ms	184×	body	256	valid

Compiler

Compiled 1077 to 801 computations (25.6% saved)

Details

analyze669.0ms (7.3%)

sample51.0ms (0.6%)

simplify554.0ms (6%)

prune7.0ms (0.1%)

localize23.0ms (0.2%)

rewrite41.0ms (0.4%)

series306.0ms (3.3%)

simplify144.0ms (1.6%)

prune162.0ms (1.8%)

localize19.0ms (0.2%)

rewrite93.0ms (1%)

series746.0ms (8.1%)

simplify173.0ms (1.9%)

prune576.0ms (6.3%)

localize27.0ms (0.3%)

rewrite43.0ms (0.5%)

series508.0ms (5.5%)

simplify120.0ms (1.3%)

prune171.0ms (1.9%)

localize28.0ms (0.3%)

rewrite29.0ms (0.3%)

series255.0ms (2.8%)

simplify83.0ms (0.9%)

prune126.0ms (1.4%)

regimes1.0s (11.3%)

bsearch210.0ms (2.3%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.0s (32.3%)

Profiling