Details

analyze453.0ms (9%)

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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	36×	body	2048	valid
8.0ms	156×	body	128	valid
7.0ms	30×	body	1024	valid
5.0ms	18×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	16×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify393.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (298.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

Merged error: 35.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.3%)

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)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_414`
15×	`add-sqr-sqrt_binary64_435`
14×	`add-cube-cbrt_binary64_446`
12×	`times-frac_binary64_420`
8×	`add-log-exp_binary64_450`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
5×	`pow1_binary64_472` `distribute-lft-out_binary64_367`
4×	`associate-/l*_binary64_361`
3×	`sqrt-prod_binary64_429` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `flip-+_binary64_388` `flip--_binary64_389` `associate-/l/_binary64_363`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `frac-2neg_binary64_425` `pow1/2_binary64_491` `sum-log_binary64_502` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 71

Calls

4 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)))

series235.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
38.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4944	2018
1	4944	2018

prune116.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 4.9b

Counts

84 → 8

Compiler

Compiled 2121 to 1151 computations (45.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.1b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_420`
57×	`add-sqr-sqrt_binary64_435`
42×	`*-un-lft-identity_binary64_414`
28×	`add-cube-cbrt_binary64_446`
27×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
14×	`difference-of-squares_binary64_383`
13×	`associate-/l*_binary64_361`
10×	`associate-/r/_binary64_362` `cbrt-undiv_binary64_445` `sqrt-prod_binary64_429` `div-exp_binary64_462`
9×	`associate-/r*_binary64_360`
7×	`flip3--_binary64_418` `distribute-lft-out--_binary64_368` `flip--_binary64_389`
6×	`div-inv_binary64_411` `prod-exp_binary64_460` `add-log-exp_binary64_450` `cbrt-unprod_binary64_444`
5×	`pow1_binary64_472`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`

Counts

4 → 130

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))))))
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))))

series515.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
168.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
63.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5244	4840

prune209.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	143	7	150

Merged error: 4.9b

Counts

150 → 7

Compiler

Compiled 4591 to 2426 computations (47.2% saved)

localize13.0ms (0.3%)

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))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_435`
26×	`*-un-lft-identity_binary64_414`
18×	`times-frac_binary64_420`
16×	`add-cube-cbrt_binary64_446`
10×	`difference-of-squares_binary64_383`
8×	`sqrt-prod_binary64_429` `add-log-exp_binary64_450`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `associate-/r*_binary64_360`
5×	`distribute-lft-out--_binary64_368` `pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`associate-/l*_binary64_361`
2×	`associate-/r/_binary64_362` `sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `frac-2neg_binary64_425` `pow1/2_binary64_491` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/.f64 c (-.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)))

series334.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
62.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	2450
1	4894	2450

prune119.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 4.9b

Counts

100 → 7

Compiler

Compiled 2774 to 1645 computations (40.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_420`
121×	`add-sqr-sqrt_binary64_435`
94×	`*-un-lft-identity_binary64_414`
68×	`add-cube-cbrt_binary64_446`
26×	`difference-of-squares_binary64_383`
22×	`associate-/r*_binary64_360`
16×	`sqrt-prod_binary64_429`
13×	`distribute-lft-out--_binary64_368`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
5×	`pow1_binary64_472` `div-inv_binary64_411`
3×	`flip3--_binary64_418` `cbrt-undiv_binary64_445` `flip--_binary64_389` `associate-/l*_binary64_361` `div-exp_binary64_462`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`associate-/r/_binary64_362` `clear-num_binary64_413` `sqrt-pow1_binary64_431` `frac-2neg_binary64_425` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 146

Calls

4 calls:

12.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
7.0ms	(-.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)))

series274.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
68.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
35.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4956	5651
1	4956	5651

prune215.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	158	7	165

Merged error: 4.9b

Counts

165 → 7

Compiler

Compiled 5181 to 3002 computations (42.1% saved)

regimes160.0ms (3.2%)

Compiler: Compiled 324 to 300 computations (7.4% saved)

bsearch108.0ms (2.1%)

Steps

Iters	Range	Point
10	2.111580858145245e+148	6.118292371914786e+159	2.1353619288367854e+148
7	6.41317177798842e-285	1.0212591469716465e-282	5.126982040291221e-283
10	-8.988626090881866e+157	-1.220652379953807e+147	-1.4220016328491612e+151

Iters

Range

Point

2.111580858145245e+148

6.118292371914786e+159

2.1353619288367854e+148

6.41317177798842e-285

1.0212591469716465e-282

5.126982040291221e-283

-8.988626090881866e+157

-1.220652379953807e+147

-1.4220016328491612e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	95
1	105	95

end0.0ms (0%)

sample1.3s (26.6%)

Algorithm

1×

intervals

Results

270.0ms	1100×	body	2048	valid
265.0ms	5210×	body	128	valid
144.0ms	751×	body	1024	valid
118.0ms	395×	body	4096	valid
50.0ms	359×	body	512	valid
30.0ms	633×	body	128	nan
21.0ms	185×	body	256	valid
20.0ms	409×	body	128	invalid

Compiler

Compiled 230 to 185 computations (19.6% saved)

Details

analyze453.0ms (9%)

sample41.0ms (0.8%)

simplify393.0ms (7.8%)

prune4.0ms (0.1%)

localize14.0ms (0.3%)

rewrite29.0ms (0.6%)

series235.0ms (4.7%)

simplify68.0ms (1.4%)

prune116.0ms (2.3%)

localize15.0ms (0.3%)

rewrite52.0ms (1%)

series515.0ms (10.2%)

simplify72.0ms (1.4%)

prune209.0ms (4.1%)

localize13.0ms (0.3%)

rewrite32.0ms (0.6%)

series334.0ms (6.6%)

simplify86.0ms (1.7%)

prune119.0ms (2.4%)

localize15.0ms (0.3%)

rewrite45.0ms (0.9%)

series274.0ms (5.4%)

simplify84.0ms (1.7%)

prune215.0ms (4.3%)

regimes160.0ms (3.2%)

bsearch108.0ms (2.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (26.6%)

Profiling