Details

analyze457.0ms (5.6%)

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)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	38×	body	2048	valid
9.0ms	175×	body	128	valid
5.0ms	24×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	4×	body	4096	valid
1.0ms	18×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify236.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

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

Merged error: 34.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
6×	`difference-of-squares_binary64_1070` `sqrt-prod_binary64_1117` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
5×	`pow1_binary64_1162`
4×	`flip--_binary64_1076` `flip3--_binary64_1105` `cancel-sign-sub-inv_binary64_1067`
3×	`distribute-lft-out--_binary64_1053`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series554.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
130.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
68.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune126.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 5.7b

Counts

87 → 7

Compiler

Compiled 2119 to 1154 computations (45.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.1b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1101`
14×	`add-sqr-sqrt_binary64_1123`
11×	`add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
9×	`add-exp-log_binary64_1139` `sqrt-prod_binary64_1117` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `cancel-sign-sub-inv_binary64_1067`
6×	`associate-/l*_binary64_1046`
5×	`pow1_binary64_1162`
4×	`flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `sqrt-div_binary64_1118`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `associate-/l/_binary64_1048` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`sub-div_binary64_1108` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `distribute-rgt-out--_binary64_1055` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `frac-sub_binary64_1110` `associate-/r*_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 80

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
9.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series646.0ms (8%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
183.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4939	2187
1	4939	2187

prune119.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Merged error: 5.7b

Counts

99 → 8

Compiler

Compiled 2604 to 1495 computations (42.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite121.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_1107`
439×	`add-sqr-sqrt_binary64_1123`
364×	`*-un-lft-identity_binary64_1101`
290×	`add-cube-cbrt_binary64_1136`
74×	`difference-of-squares_binary64_1070`
71×	`associate-/r*_binary64_1045`
40×	`sqrt-prod_binary64_1117`
37×	`distribute-lft-out--_binary64_1053`
25×	`add-exp-log_binary64_1139`
17×	`div-inv_binary64_1098`
15×	`div-exp_binary64_1152`
13×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
6×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135`
5×	`associate-/r/_binary64_1047`
4×	`cancel-sign-sub-inv_binary64_1067`
3×	`1-exp_binary64_1145` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l*_binary64_1046` `rec-exp_binary64_1151`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `sqrt-div_binary64_1118`
1×	`inv-pow_binary64_1186` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `pow-flip_binary64_1175` `pow1/2_binary64_1181`

Counts

4 → 356

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series574.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify187.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5062	16295

prune709.0ms (8.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	367	9	376

Merged error: 5.6b

Counts

376 → 9

Compiler

Compiled 12756 to 7096 computations (44.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
10.7b	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) 2)) (/.f64 b (.f64 a 2)))
24.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136` `cancel-sign-sub-inv_binary64_1067`
6×	`cbrt-prod_binary64_1132`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137` `cbrt-div_binary64_1133`
3×	`times-frac_binary64_1107` `frac-sub_binary64_1110`
2×	`diff-log_binary64_1193` `pow1/3_binary64_1183` `frac-times_binary64_1111` `sub-neg_binary64_1094`
1×	`sub-div_binary64_1108` `associate-r/_binary64_1043` `div-inv_binary64_1098` `associate-l/_binary64_1044`

Counts

4 → 60

Calls

4 calls:

16.0ms	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) 2)) (/.f64 b (.f64 a 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series822.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

409.0ms	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) 2)) (/.f64 b (.f64 a 2)))
179.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
167.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4964	2148
1	4964	2148

prune121.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 5.6b

Counts

81 → 9

Compiler

Compiled 2939 to 1665 computations (43.3% saved)

regimes892.0ms (11%)

Compiler: Compiled 4068 to 3056 computations (24.9% saved)

bsearch62.0ms (0.8%)

Steps

Iters	Range		Point
8	3.000591128364517e-86	3.8061952448547226e-83	2.6283193000196084e-84
8	-4.420005681040467e+157	-5.368815422905672e+153	-6.135258149216111e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample2.0s (25.1%)

Algorithm

1×

intervals

Results

270.0ms	1126×	body	2048	valid
267.0ms	5180×	body	128	valid
140.0ms	730×	body	1024	valid
137.0ms	446×	body	4096	valid
49.0ms	351×	body	512	valid
32.0ms	681×	body	128	nan
20.0ms	400×	body	128	invalid
16.0ms	167×	body	256	valid

Compiler

Compiled 1093 to 812 computations (25.7% saved)

Details

analyze457.0ms (5.6%)

sample37.0ms (0.5%)

simplify236.0ms (2.9%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite41.0ms (0.5%)

series554.0ms (6.8%)

simplify75.0ms (0.9%)

prune126.0ms (1.6%)

localize13.0ms (0.2%)

rewrite47.0ms (0.6%)

series646.0ms (8%)

simplify68.0ms (0.8%)

prune119.0ms (1.5%)

localize13.0ms (0.2%)

rewrite121.0ms (1.5%)

series574.0ms (7.1%)

simplify187.0ms (2.3%)

prune709.0ms (8.7%)

localize18.0ms (0.2%)

rewrite39.0ms (0.5%)

series822.0ms (10.1%)

simplify83.0ms (1%)

prune121.0ms (1.5%)

regimes892.0ms (11%)

bsearch62.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.0s (25.1%)

Profiling