Details

analyze459.0ms (4.3%)

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)

sample43.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	167×	body	128	valid
8.0ms	35×	body	2048	valid
5.0ms	16×	body	4096	valid
3.0ms	18×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	7×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify419.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (326.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune9.0ms (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

36.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1070`
15×	`add-sqr-sqrt_binary64_1092`
14×	`add-cube-cbrt_binary64_1105`
12×	`times-frac_binary64_1076`
8×	`add-log-exp_binary64_1109`
6×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108`
5×	`distribute-lft-out_binary64_1021` `pow1_binary64_1131`
4×	`associate-/l*_binary64_1015`
3×	`sqrt-prod_binary64_1086` `associate-/r*_binary64_1014`
2×	`sqrt-div_binary64_1087` `flip--_binary64_1045` `flip-+_binary64_1044` `flip3--_binary64_1074` `associate-/l/_binary64_1017` `flip3-+_binary64_1073`
1×	`cancel-sign-sub-inv_binary64_1036` `frac-2neg_binary64_1081` `cbrt-undiv_binary64_1104` `pow1/2_binary64_1150` `clear-num_binary64_1069` `+-commutative_binary64_1000` `div-exp_binary64_1121` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088` `sub-neg_binary64_1063` `diff-log_binary64_1162` `sum-log_binary64_1161` `div-inv_binary64_1067`

Counts

4 → 72

Calls

8 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series563.0ms (5.3%)

Counts

4 → 63

Calls

4 calls:

193.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
152.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
106.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 1784 to 1524 computations (14.6% saved)

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4975	2734
1	4975	2734

prune206.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

7.3b

Counts

136 → 10

Compiler

Compiled 2862 to 1551 computations (45.8% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 -1/2 (/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) a))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1076`
59×	`add-sqr-sqrt_binary64_1092`
44×	`*-un-lft-identity_binary64_1070`
30×	`add-cube-cbrt_binary64_1105`
27×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108`
14×	`difference-of-squares_binary64_1039`
13×	`sqrt-prod_binary64_1086` `associate-/l*_binary64_1015`
10×	`associate-/r/_binary64_1016` `cbrt-undiv_binary64_1104` `div-exp_binary64_1121`
9×	`associate-/r*_binary64_1014`
7×	`flip--_binary64_1045` `flip3--_binary64_1074` `distribute-lft-out--_binary64_1022`
6×	`cancel-sign-sub-inv_binary64_1036` `cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `add-log-exp_binary64_1109` `div-inv_binary64_1067`
5×	`pow1_binary64_1131`
2×	`sqrt-div_binary64_1087` `frac-2neg_binary64_1081` `clear-num_binary64_1069`
1×	`pow1/2_binary64_1150` `associate-/l/_binary64_1017` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088` `sub-neg_binary64_1063` `diff-log_binary64_1162`

Counts

4 → 136

Calls

8 calls:

15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
7.0ms	(-.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))))
0.0ms	(.f64 -1/2 (/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) a))

series953.0ms (8.9%)

Counts

4 → 75

Calls

4 calls:

325.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
272.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
200.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
155.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3010 to 2350 computations (21.9% saved)

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4974	6566
1	4974	6566

prune294.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Error

7.3b

Counts

221 → 8

Compiler

Compiled 6282 to 3307 computations (47.4% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
0.0b	(.f64 -1/2 (.f64 4 (.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))))
0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1092`
28×	`*-un-lft-identity_binary64_1070`
18×	`times-frac_binary64_1076` `add-cube-cbrt_binary64_1105`
11×	`sqrt-prod_binary64_1086`
10×	`difference-of-squares_binary64_1039`
8×	`add-log-exp_binary64_1109`
7×	`cancel-sign-sub-inv_binary64_1036`
6×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `associate-/r*_binary64_1014`
5×	`distribute-lft-out--_binary64_1022` `pow1_binary64_1131`
4×	`flip--_binary64_1045` `flip3--_binary64_1074`
3×	`associate-/l*_binary64_1015`
2×	`sqrt-div_binary64_1087` `associate-/r/_binary64_1016` `sub-neg_binary64_1063` `diff-log_binary64_1162`
1×	`frac-2neg_binary64_1081` `cbrt-undiv_binary64_1104` `pow1/2_binary64_1150` `clear-num_binary64_1069` `div-exp_binary64_1121` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088` `div-inv_binary64_1067`

Counts

4 → 88

Calls

8 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
9.0ms	(-.f64 b (sqrt.f64 (-.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))))
0.0ms	(.f64 -1/2 (.f64 4 (.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))))

series756.0ms (7.1%)

Counts

4 → 80

Calls

4 calls:

271.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
190.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
151.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
142.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2861 to 2446 computations (14.5% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4954	3941
1	4954	3941

prune214.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	168	8	176

Error

7.3b

Counts

176 → 8

Compiler

Compiled 4427 to 2629 computations (40.6% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.1b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.1b	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_1076`
82×	`*-un-lft-identity_binary64_1070`
57×	`add-sqr-sqrt_binary64_1092`
56×	`add-cube-cbrt_binary64_1105`
18×	`associate-/r*_binary64_1014`
15×	`add-exp-log_binary64_1108`
13×	`distribute-lft-out_binary64_1021`
9×	`add-cbrt-cube_binary64_1106` `associate-/r/_binary64_1016`
8×	`add-log-exp_binary64_1109`
7×	`div-exp_binary64_1121`
6×	`pow1_binary64_1131`
5×	`flip-+_binary64_1044` `flip3-+_binary64_1073` `div-inv_binary64_1067`
3×	`sqrt-prod_binary64_1086` `cbrt-undiv_binary64_1104` `associate-/l*_binary64_1015`
2×	`sqrt-div_binary64_1087` `flip--_binary64_1045` `flip3--_binary64_1074` `rec-exp_binary64_1120` `1-exp_binary64_1114`
1×	`cancel-sign-sub-inv_binary64_1036` `inv-pow_binary64_1155` `frac-2neg_binary64_1081` `pow1/2_binary64_1150` `clear-num_binary64_1069` `+-commutative_binary64_1000` `rem-sqrt-square_binary64_1083` `pow-flip_binary64_1144` `sqrt-pow1_binary64_1088` `sub-neg_binary64_1063` `diff-log_binary64_1162` `sum-log_binary64_1161`

Counts

4 → 135

Calls

8 calls:

12.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series562.0ms (5.3%)

Counts

4 → 63

Calls

4 calls:

200.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
147.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
103.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 1924 to 1664 computations (13.5% saved)

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4912	5220
1	4912	5220

prune225.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	197	9	206

Error

7.3b

Counts

206 → 9

Compiler

Compiled 4923 to 2723 computations (44.7% saved)

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	1070	1593
1	1070	1593

regimes476.0ms (4.5%)

Accuracy

Total 1.4b remaining (22.4%)

Threshold costs 0b (0%)

Compiler

Compiled 3144 to 2388 computations (24% saved)

bsearch104.0ms (1%)

Steps

Iters	Range	Point
10	3.8530791125633152e+65	1.6148340927808046e+81	1.1102892118009466e+81
8	7.407819669024023e-264	1.1267988616538363e-260	6.382555368342549e-262
8	-2.896882628819812e+127	-9.970494331055357e+124	-3.675391325498039e+126

Iters

Range

Point

3.8530791125633152e+65

1.6148340927808046e+81

1.1102892118009466e+81

7.407819669024023e-264

1.1267988616538363e-260

6.382555368342549e-262

-2.896882628819812e+127

-9.970494331055357e+124

-3.675391325498039e+126

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	117	91
1	117	91

end0.0ms (0%)

sample4.8s (44.7%)

Algorithm

1×

intervals

Results

472.0ms	1148×	body	2048	valid
268.0ms	5152×	body	128	valid
143.0ms	731×	body	1024	valid
116.0ms	381×	body	4096	valid
62.0ms	407×	body	512	valid
35.0ms	689×	body	128	nan
20.0ms	181×	body	256	valid
18.0ms	363×	body	128	invalid

Compiler

Compiled 3320 to 2499 computations (24.7% saved)

Pareto

-0.09669508024149041

Details

analyze459.0ms (4.3%)

sample43.0ms (0.4%)

simplify419.0ms (3.9%)

prune9.0ms (0.1%)

localize11.0ms (0.1%)

rewrite29.0ms (0.3%)

series563.0ms (5.3%)

simplify82.0ms (0.8%)

prune206.0ms (1.9%)

localize13.0ms (0.1%)

rewrite59.0ms (0.6%)

series953.0ms (8.9%)

simplify93.0ms (0.9%)

prune294.0ms (2.8%)

localize14.0ms (0.1%)

rewrite36.0ms (0.3%)

series756.0ms (7.1%)

simplify79.0ms (0.7%)

prune214.0ms (2%)

localize13.0ms (0.1%)

rewrite42.0ms (0.4%)

series562.0ms (5.3%)

simplify107.0ms (1%)

prune225.0ms (2.1%)

simplify47.0ms (0.4%)

regimes476.0ms (4.5%)

bsearch104.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.8s (44.7%)

Profiling