Details

analyze824.0ms (8.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
0	3	3
1	3	3

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)

sample44.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	167×	body	128	valid
9.0ms	34×	body	2048	valid
5.0ms	27×	body	1024	valid
5.0ms	16×	body	4096	valid
2.0ms	9×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify337.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (332.0ms)

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

32.8b

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)
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite141.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

32.6b

Rules

24×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
12×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`pow1_binary64_821` `distribute-lft-out_binary64_711`
4×	`associate-/l*_binary64_705`
3×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l/_binary64_707`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `sum-log_binary64_851` `+-commutative_binary64_690` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(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	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series708.0ms (7.4%)

Error

4.8b

Counts

4 → 74

Calls

4 calls:

194.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
161.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
145.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
141.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 3330 to 2521 computations (24.3% saved)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5025	3006

prune159.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	9	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	9	147

Error

4.7b

Counts

147 → 9

Compiler

Compiled 3120 to 1667 computations (46.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.3b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite139.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

21×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
13×	`add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `associate-r_binary64_700`
11×	`times-frac_binary64_766`
9×	`add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`pow1_binary64_821`
4×	`prod-exp_binary64_809` `associate-l_binary64_701`
3×	`sqrt-prod_binary64_776` `flip3-+_binary64_763` `flip-+_binary64_734` `unswap-sqr_binary64_728`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `div-exp_binary64_811` `cbrt-unprod_binary64_793` `frac-times_binary64_770` `associate-*l/_binary64_703` `distribute-lft-out_binary64_711`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `1-exp_binary64_804` `rec-exp_binary64_810` `cbrt-undiv_binary64_794` `un-div-inv_binary64_758` `associate-r/_binary64_702` `div-inv_binary64_757` `-commutative_binary64_691` `sum-log_binary64_851` `+-commutative_binary64_690` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726`

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 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)))

Compiler

Compiled 2417 to 1345 computations (44.4% saved)

series703.0ms (7.4%)

Error

4.7b

Counts

4 → 74

Calls

4 calls:

204.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
147.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
143.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
143.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3600 to 2800 computations (22.2% saved)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4960	3046
1	4960	3046

prune158.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	154	9	163

Error

4.7b

Counts

163 → 9

Compiler

Compiled 3398 to 1944 computations (42.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite112.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

10×	`*-un-lft-identity_binary64_760`
8×	`add-log-exp_binary64_799` `add-sqr-sqrt_binary64_782`
6×	`pow1_binary64_821` `add-cube-cbrt_binary64_795` `sqrt-prod_binary64_776`
4×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `sqrt-div_binary64_777`
2×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773` `sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `+-commutative_binary64_690`

Counts

4 → 54

Calls

4 calls:

6.0ms	(+.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2320 to 1211 computations (47.8% saved)

series704.0ms (7.4%)

Error

4.7b

Counts

4 → 74

Calls

4 calls:

157.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
154.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
153.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 6352 to 4298 computations (32.3% saved)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4969	2448
1	4969	2448

prune191.0ms (2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	127	10	137

Error

4.6b

Counts

137 → 10

Compiler

Compiled 4547 to 2436 computations (46.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) a) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.6b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
14.4b	(/.f64 (.f64 4 (.f64 a c)) a)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite258.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

68×	`add-sqr-sqrt_binary64_782`
66×	`times-frac_binary64_766`
49×	`*-un-lft-identity_binary64_760`
31×	`add-cube-cbrt_binary64_795`
27×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
18×	`difference-of-squares_binary64_729`
15×	`sqrt-prod_binary64_776`
10×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
9×	`div-inv_binary64_757` `associate-/r*_binary64_704` `distribute-lft-out--_binary64_712`
8×	`associate-/l*_binary64_705`
6×	`add-log-exp_binary64_799` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `cancel-sign-sub-inv_binary64_726`
5×	`pow1_binary64_821`
3×	`flip3--_binary64_764` `flip--_binary64_735`
2×	`sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r/_binary64_706`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `diff-log_binary64_852` `sub-neg_binary64_753` `associate-/l/_binary64_707`

Counts

4 → 134

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) a) (-.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)))))
6.0ms	(/.f64 (.f64 4 (.f64 a c)) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4903 to 2490 computations (49.2% saved)

series726.0ms (7.6%)

Error

4.6b

Counts

4 → 63

Calls

4 calls:

324.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) a) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
156.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
147.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
33.0ms	(/.f64 (.f64 4 (.f64 a c)) a)

Compiler

Compiled 3805 to 2726 computations (28.4% saved)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5148	5277

prune251.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	198	9	207

Error

4.6b

Counts

207 → 9

Compiler

Compiled 5362 to 2846 computations (46.9% saved)

regimes975.0ms (10.2%)

Accuracy

Total 1.0b remaining (14.6%)

Threshold costs 1.0b (14.6%)

Compiler

Compiled 6424 to 4742 computations (26.2% saved)

bsearch115.0ms (1.2%)

Steps

Iters	Range	Point
8	1.5905874592677548e+138	3.700038265310273e+141	2.675726436471294e+140
10	4.187536786763886e-285	1.4677073935158917e-272	9.402708844729834e-273
9	-6.267505861007114e+103	-9.12455274129916e+97	-2.6495164398004875e+103

Iters

Range

Point

1.5905874592677548e+138

3.700038265310273e+141

2.675726436471294e+140

4.187536786763886e-285

1.4677073935158917e-272

9.402708844729834e-273

-6.267505861007114e+103

-9.12455274129916e+97

-2.6495164398004875e+103

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	89
1	94	89

end0.0ms (0%)

sample2.6s (27.7%)

Algorithm

1×

intervals

Results

305.0ms	1145×	body	2048	valid
283.0ms	5146×	body	128	valid
161.0ms	724×	body	1024	valid
151.0ms	445×	body	4096	valid
55.0ms	361×	body	512	valid
34.0ms	660×	body	128	nan
19.0ms	358×	body	128	invalid
18.0ms	179×	body	256	valid

Compiler

Compiled 1716 to 1260 computations (26.6% saved)

Details

analyze824.0ms (8.6%)

sample44.0ms (0.5%)

simplify337.0ms (3.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite141.0ms (1.5%)

series708.0ms (7.4%)

simplify70.0ms (0.7%)

prune159.0ms (1.7%)

localize15.0ms (0.2%)

rewrite139.0ms (1.5%)

series703.0ms (7.4%)

simplify68.0ms (0.7%)

prune158.0ms (1.7%)

localize13.0ms (0.1%)

rewrite112.0ms (1.2%)

series704.0ms (7.4%)

simplify64.0ms (0.7%)

prune191.0ms (2%)

localize12.0ms (0.1%)

rewrite258.0ms (2.7%)

series726.0ms (7.6%)

simplify94.0ms (1%)

prune251.0ms (2.6%)

regimes975.0ms (10.2%)

bsearch115.0ms (1.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.6s (27.7%)

Profiling