Details

analyze462.0ms (7.5%)

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)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	175×	body	128	valid
7.0ms	28×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify228.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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: 33.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

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)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.5%)

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:

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)))

series462.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
128.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5412	2012

prune128.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 6.7b

Counts

84 → 10

Compiler

Compiled 2197 to 1197 computations (45.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_435`
18×	`*-un-lft-identity_binary64_414`
13×	`add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `associate-r_binary64_356`
11×	`times-frac_binary64_420`
9×	`add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`pow1_binary64_472`
4×	`prod-exp_binary64_460` `associate-l_binary64_357`
3×	`flip3-+_binary64_417` `sqrt-prod_binary64_429` `flip-+_binary64_388` `unswap-sqr_binary64_382`
2×	`flip3--_binary64_418` `sqrt-div_binary64_430` `associate-*l/_binary64_359` `distribute-lft-out_binary64_367` `flip--_binary64_389` `cbrt-unprod_binary64_444` `frac-times_binary64_424` `div-exp_binary64_462`
1×	`1-exp_binary64_455` `un-div-inv_binary64_412` `diff-log_binary64_503` `div-inv_binary64_411` `-commutative_binary64_347` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `rec-exp_binary64_461` `pow1/2_binary64_491` `sum-log_binary64_502` `associate-r/_binary64_358` `rem-sqrt-square_binary64_427`

Counts

4 → 79

Calls

4 calls:

14.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 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))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series476.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
132.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4910	2052
1	4910	2052

prune109.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	91	10	101

Merged error: 6.7b

Counts

101 → 10

Compiler

Compiled 2403 to 1379 computations (42.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.2b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.3b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite58.0ms (0.9%)

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:

17.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a 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))))

series979.0ms (15.8%)

Counts

4 → 12

Calls

4 calls:

409.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
319.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
128.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5359	4852

prune207.0ms (3.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	141	11	152

Merged error: 6.6b

Counts

152 → 11

Compiler

Compiled 4703 to 2497 computations (46.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (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:

10.0ms	(/.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)))

series674.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

377.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
120.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5183	2447

prune116.0ms (1.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	93	11	104

Merged error: 6.6b

Counts

104 → 11

Compiler

Compiled 2683 to 1567 computations (41.6% saved)

regimes195.0ms (3.1%)

Compiler: Compiled 726 to 567 computations (21.9% saved)

bsearch111.0ms (1.8%)

Steps

Iters	Range	Point
8	1.8214039147413959e+114	3.0936283487967313e+118	2.1578323955249213e+116
11	2.2854952522798188e-282	3.904822145804709e-260	1.4031237401242977e-270
7	-1.2753667153502532e+154	-8.990067059825001e+151	-1.3091834909018501e+152

Iters

Range

Point

1.8214039147413959e+114

3.0936283487967313e+118

2.1578323955249213e+116

2.2854952522798188e-282

3.904822145804709e-260

1.4031237401242977e-270

-1.2753667153502532e+154

-8.990067059825001e+151

-1.3091834909018501e+152

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	100	92
1	100	92

end0.0ms (0%)

sample1.5s (24.3%)

Algorithm

1×

intervals

Results

303.0ms	1188×	body	2048	valid
279.0ms	5184×	body	128	valid
145.0ms	716×	body	1024	valid
119.0ms	363×	body	4096	valid
54.0ms	367×	body	512	valid
35.0ms	692×	body	128	nan
25.0ms	410×	body	128	invalid
18.0ms	182×	body	256	valid

Compiler

Compiled 362 to 272 computations (24.9% saved)

Details

analyze462.0ms (7.5%)

sample37.0ms (0.6%)

simplify228.0ms (3.7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series462.0ms (7.5%)

simplify71.0ms (1.1%)

prune128.0ms (2.1%)

localize12.0ms (0.2%)

rewrite37.0ms (0.6%)

series476.0ms (7.7%)

simplify70.0ms (1.1%)

prune109.0ms (1.8%)

localize12.0ms (0.2%)

rewrite58.0ms (0.9%)

series979.0ms (15.8%)

simplify67.0ms (1.1%)

prune207.0ms (3.4%)

localize16.0ms (0.3%)

rewrite36.0ms (0.6%)

series674.0ms (10.9%)

simplify70.0ms (1.1%)

prune116.0ms (1.9%)

regimes195.0ms (3.1%)

bsearch111.0ms (1.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (24.3%)

Profiling