Details

analyze1.1s (0.2%)

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)

sample124.0ms (0%)

Algorithm

1×

intervals

Results

31.0ms	34×	body	2048	valid
21.0ms	185×	body	128	valid
11.0ms	16×	body	1024	valid
3.0ms	6×	body	4096	valid
3.0ms	20×	body	128	nan
2.0ms	7×	body	512	valid
2.0ms	17×	body	128	invalid
1.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify1.2s (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (750.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune9.0ms (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: 30.0b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite68.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_1101`
10×	`add-log-exp_binary64_1140`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-sqr-sqrt_binary64_1123`
7×	`add-cube-cbrt_binary64_1136`
6×	`distribute-lft-out_binary64_1052`
5×	`pow1_binary64_1162` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
3×	`distribute-rgt-neg-in_binary64_1059` `sqrt-prod_binary64_1117`
2×	`sum-log_binary64_1192` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `neg-sub0_binary64_1096` `associate-/l/_binary64_1048` `associate-+l-_binary64_1036` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `neg-log_binary64_1194` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `cancel-sign-sub-inv_binary64_1067` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 70

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
17.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series865.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
215.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
207.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify258.0ms (0%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (177.0ms)

Iter	Nodes	Cost
0	5668	1826

prune1.4s (0.2%)

Pruning

43 alts after pruning (42 fresh and 1 done)

	Pruned	Kept	Total
New	40	42	82
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	41	43	84

Merged error: 5.1b

Counts

84 → 43

Compiler

Compiled 2991 to 1912 computations (36.1% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite81.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118`
22×	`pow1_binary64_1162`
11×	`pow1/2_binary64_1181`
9×	`flip--_binary64_1076` `flip3--_binary64_1105`
8×	`add-sqr-sqrt_binary64_1123`
7×	`sqrt-prod_binary64_1117`
6×	`*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
5×	`pow-prod-up_binary64_1171`
4×	`frac-times_binary64_1111` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`rem-sqrt-square_binary64_1114` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`pow-plus_binary64_1164` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `pow2_binary64_1182`

Counts

4 → 74

Calls

4 calls:

27.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series486.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
143.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify179.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4951	1719
1	4951	1719

prune1.7s (0.3%)

Pruning

62 alts after pruning (60 fresh and 2 done)

	Pruned	Kept	Total
New	64	22	86
Fresh	3	38	41
Picked	0	1	1
Done	0	1	1
Total	67	62	129

Merged error: 5.1b

Counts

129 → 62

Compiler

Compiled 4720 to 3007 computations (36.3% saved)

localize49.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2) a)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite114.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

28.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2) a)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
13.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series728.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

437.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2) a)
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
101.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
72.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify464.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (241.0ms)

Iter	Nodes	Cost
0	5144	5789

prune4.5s (0.8%)

Pruning

131 alts after pruning (128 fresh and 3 done)

	Pruned	Kept	Total
New	77	86	163
Fresh	17	42	59
Picked	0	1	1
Done	0	2	2
Total	94	131	225

Merged error: 5.1b

Counts

225 → 131

Compiler

Compiled 9101 to 5922 computations (34.9% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite98.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118`
22×	`pow1_binary64_1162`
11×	`pow1/2_binary64_1181`
9×	`flip--_binary64_1076` `flip3--_binary64_1105`
8×	`add-sqr-sqrt_binary64_1123`
7×	`sqrt-prod_binary64_1117`
6×	`*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
5×	`pow-prod-up_binary64_1171`
4×	`frac-times_binary64_1111` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`rem-sqrt-square_binary64_1114` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`pow-plus_binary64_1164` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `pow2_binary64_1182`

Counts

4 → 74

Calls

4 calls:

43.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series370.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
104.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
101.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
57.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify126.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4951	1719
1	4951	1719

prune2.4s (0.4%)

Pruning

145 alts after pruning (141 fresh and 4 done)

	Pruned	Kept	Total
New	68	18	86
Fresh	4	123	127
Picked	0	1	1
Done	0	3	3
Total	72	145	217

Merged error: 5.1b

Counts

217 → 145

Compiler

Compiled 2735 to 1619 computations (40.8% saved)

regimes19.8s (3.3%)

Compiler: Compiled 34157 to 25084 computations (26.6% saved)

bsearch9.4min (94%)

Steps

Iters	Range		Point
7	5.077603163681316e+86	3.0675607530650454e+88	1.0076800180697053e+87
8	1.1967310277021378e-191	8.34259427963184e-189	2.43077786380867e-190
6	-5.59945793777678e+90	-4.402997549349525e+89	-4.787296627726359e+90

Compiler

Compiled 1 to 3 computations (-200% saved)

Details

analyze1.1s (0.2%)

sample124.0ms (0%)

simplify1.2s (0.2%)

prune9.0ms (0%)

localize24.0ms (0%)

rewrite68.0ms (0%)

series865.0ms (0.1%)

simplify258.0ms (0%)

prune1.4s (0.2%)

localize34.0ms (0%)

rewrite81.0ms (0%)

series486.0ms (0.1%)

simplify179.0ms (0%)

prune1.7s (0.3%)

localize49.0ms (0%)

rewrite114.0ms (0%)

series728.0ms (0.1%)

simplify464.0ms (0.1%)

prune4.5s (0.8%)

localize26.0ms (0%)

rewrite98.0ms (0%)

series370.0ms (0.1%)

simplify126.0ms (0%)

prune2.4s (0.4%)

regimes19.8s (3.3%)

bsearch9.4min (94%)

Profiling