Details

analyze465.0ms (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)

sample42.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	41×	body	2048	valid
9.0ms	160×	body	128	valid
4.0ms	22×	body	1024	valid
4.0ms	14×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	14×	body	128	invalid
1.0ms	12×	body	128	nan
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify450.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (349.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	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

Error

35.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (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 (+.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))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series622.0ms (7.5%)

Counts

4 → 70

Calls

4 calls:

175.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
163.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
143.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
141.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2065 to 1755 computations (15% saved)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5132	2743

prune165.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	10	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	10	143

Error

5.3b

Counts

143 → 10

Compiler

Compiled 2935 to 1534 computations (47.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.7b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
9.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1107`
53×	`add-sqr-sqrt_binary64_1123`
40×	`*-un-lft-identity_binary64_1101`
28×	`add-cube-cbrt_binary64_1136`
27×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
13×	`associate-/l*_binary64_1046`
12×	`difference-of-squares_binary64_1070`
10×	`associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
9×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
7×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098`
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` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 128

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a 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)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series934.0ms (11.3%)

Counts

4 → 73

Calls

4 calls:

328.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
294.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
163.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
149.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2685 to 2114 computations (21.3% saved)

simplify122.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4944	5665
1	4944	5665

prune270.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	202	9	211

Error

5.2b

Counts

211 → 9

Compiler

Compiled 5696 to 2949 computations (48.2% saved)

localize14.0ms (0.2%)

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))))))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.4%)

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:

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

series774.0ms (9.3%)

Counts

4 → 74

Calls

4 calls:

253.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
189.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
182.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
150.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2686 to 2308 computations (14.1% saved)

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5221	3595

prune192.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	162	9	171

Error

5.2b

Counts

171 → 9

Compiler

Compiled 4184 to 2459 computations (41.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_1107`
82×	`*-un-lft-identity_binary64_1101`
57×	`add-sqr-sqrt_binary64_1123`
56×	`add-cube-cbrt_binary64_1136`
18×	`associate-/r*_binary64_1045`
15×	`add-exp-log_binary64_1139`
13×	`distribute-lft-out_binary64_1052`
9×	`associate-/r/_binary64_1047` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
7×	`div-exp_binary64_1152`
6×	`pow1_binary64_1162`
5×	`flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075`
3×	`sqrt-prod_binary64_1117` `associate-/l*_binary64_1046` `cbrt-undiv_binary64_1135`
2×	`1-exp_binary64_1145` `flip--_binary64_1076` `flip3--_binary64_1105` `rec-exp_binary64_1151` `sqrt-div_binary64_1118`
1×	`inv-pow_binary64_1186` `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` `+-commutative_binary64_1031` `cancel-sign-sub-inv_binary64_1067` `pow-flip_binary64_1175` `pow1/2_binary64_1181`

Counts

4 → 135

Calls

4 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)))

series638.0ms (7.7%)

Counts

4 → 70

Calls

4 calls:

180.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
159.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
156.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
143.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2225 to 1915 computations (13.9% saved)

simplify107.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4942	5229
1	4942	5229

prune223.0ms (2.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	204	10	214

Error

5.2b

Counts

214 → 10

Compiler

Compiled 4990 to 2710 computations (45.7% saved)

regimes753.0ms (9.1%)

Accuracy

Total 1.0b remaining (15.7%)

Threshold costs 0b (0%)

Compiler

Compiled 3968 to 3066 computations (22.7% saved)

bsearch91.0ms (1.1%)

Steps

Iters	Range	Point
7	4.439910738019466e+106	5.798110015544735e+108	4.1520730840908697e+108
5	3.2347926633587567e-304	7.235591602889142e-304	3.4760502493091374e-304
9	-2.6814749618107856e+120	-3.441340305064103e+113	-5.188391915920029e+118

Iters

Range

Point

4.439910738019466e+106

5.798110015544735e+108

4.1520730840908697e+108

3.2347926633587567e-304

7.235591602889142e-304

3.4760502493091374e-304

-2.6814749618107856e+120

-3.441340305064103e+113

-5.188391915920029e+118

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	121	91
1	121	91

end0.0ms (0%)

sample2.1s (25.3%)

Algorithm

1×

intervals

Results

310.0ms	1194×	body	2048	valid
276.0ms	5113×	body	128	valid
146.0ms	729×	body	1024	valid
125.0ms	393×	body	4096	valid
57.0ms	387×	body	512	valid
35.0ms	693×	body	128	nan
21.0ms	406×	body	128	invalid
18.0ms	184×	body	256	valid

Compiler

Compiled 1103 to 843 computations (23.6% saved)

Details

analyze465.0ms (5.6%)

sample42.0ms (0.5%)

simplify450.0ms (5.4%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite31.0ms (0.4%)

series622.0ms (7.5%)

simplify72.0ms (0.9%)

prune165.0ms (2%)

localize13.0ms (0.2%)

rewrite51.0ms (0.6%)

series934.0ms (11.3%)

simplify122.0ms (1.5%)

prune270.0ms (3.3%)

localize14.0ms (0.2%)

rewrite35.0ms (0.4%)

series774.0ms (9.3%)

simplify58.0ms (0.7%)

prune192.0ms (2.3%)

localize13.0ms (0.2%)

rewrite43.0ms (0.5%)

series638.0ms (7.7%)

simplify107.0ms (1.3%)

prune223.0ms (2.7%)

regimes753.0ms (9.1%)

bsearch91.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.1s (25.3%)

Profiling