Details

analyze662.0ms (6.7%)

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)

sample45.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	168×	body	128	valid
9.0ms	34×	body	2048	valid
7.0ms	11×	body	4096	valid
5.0ms	27×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	15×	body	128	nan
1.0ms	8×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify300.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune5.0ms (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

Merged error: 34.7b

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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series706.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
161.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
90.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5031	1979

prune146.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 6.3b

Counts

87 → 10

Compiler

Compiled 2210 to 1329 computations (39.9% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.1b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite109.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`times-frac_binary64_425`
21×	`*-un-lft-identity_binary64_419`
17×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`add-sqr-sqrt_binary64_441`
11×	`add-cube-cbrt_binary64_454` `associate-/l*_binary64_364`
6×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
5×	`distribute-lft-out_binary64_370` `associate-/r*_binary64_363` `pow1_binary64_480`
4×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393`
3×	`sqrt-prod_binary64_435`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`pow1/2_binary64_499` `sum-log_binary64_510` `flip3--_binary64_423` `sqrt-pow1_binary64_437` `flip--_binary64_394` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `associate-/l/_binary64_366`

Counts

4 → 102

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
25.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.2s (12.3%)

Counts

4 → 12

Calls

4 calls:

533.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
359.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
172.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
152.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5005	3121

prune200.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	115	9	124

Merged error: 6.3b

Counts

124 → 9

Compiler

Compiled 3305 to 2038 computations (38.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_419`
15×	`add-sqr-sqrt_binary64_441`
14×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`distribute-lft-out_binary64_370` `pow1_binary64_480`
4×	`associate-/r*_binary64_363`
3×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 72

Calls

4 calls:

13.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series852.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

442.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
173.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
144.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
93.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5099	1969

prune123.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 6.3b

Counts

93 → 9

Compiler

Compiled 2301 to 1435 computations (37.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite64.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
14×	`add-cube-cbrt_binary64_454`
13×	`associate-r_binary64_359`
10×	`times-frac_binary64_425`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458`
7×	`pow1_binary64_480`
6×	`associate-l_binary64_360`
5×	`flip3--_binary64_423` `flip--_binary64_394` `sqrt-prod_binary64_435`
4×	`difference-of-squares_binary64_388` `cancel-sign-sub-inv_binary64_385`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out--_binary64_371` `diff-log_binary64_511`
1×	`pow-prod-down_binary64_490` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r/_binary64_361` `-commutative_binary64_350` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 83

Calls

4 calls:

27.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series798.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
246.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
139.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
105.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4939	2239
1	4939	2239

prune110.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 6.3b

Counts

104 → 9

Compiler

Compiled 2216 to 1298 computations (41.4% saved)

regimes1.0s (10.4%)

Compiler: Compiled 4244 to 3268 computations (23% saved)

bsearch132.0ms (1.3%)

Steps

Iters	Range	Point
7	3.2655091505015865e+113	5.382552162036069e+115	5.059898287600192e+114
10	1.487630782429774e-293	4.053235089317713e-282	1.5108660979098973e-293
8	-7.53749972592922e+156	-1.2615238965052474e+154	-1.2977258341580385e+154

Iters

Range

Point

3.2655091505015865e+113

5.382552162036069e+115

5.059898287600192e+114

1.487630782429774e-293

4.053235089317713e-282

1.5108660979098973e-293

-7.53749972592922e+156

-1.2615238965052474e+154

-1.2977258341580385e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	88
1	113	88

end0.0ms (0%)

sample2.9s (29.2%)

Algorithm

1×

intervals

Results

432.0ms	1159×	body	2048	valid
382.0ms	5143×	body	128	valid
221.0ms	793×	body	1024	valid
172.0ms	377×	body	4096	valid
75.0ms	336×	body	512	valid
47.0ms	670×	body	128	nan
28.0ms	385×	body	128	invalid
28.0ms	192×	body	256	valid

Compiler

Compiled 1115 to 850 computations (23.8% saved)

Details

analyze662.0ms (6.7%)

sample45.0ms (0.5%)

simplify300.0ms (3%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite51.0ms (0.5%)

series706.0ms (7.1%)

simplify87.0ms (0.9%)

prune146.0ms (1.5%)

localize30.0ms (0.3%)

rewrite109.0ms (1.1%)

series1.2s (12.3%)

simplify89.0ms (0.9%)

prune200.0ms (2%)

localize19.0ms (0.2%)

rewrite43.0ms (0.4%)

series852.0ms (8.6%)

simplify71.0ms (0.7%)

prune123.0ms (1.2%)

localize18.0ms (0.2%)

rewrite64.0ms (0.6%)

series798.0ms (8.1%)

simplify81.0ms (0.8%)

prune110.0ms (1.1%)

regimes1.0s (10.4%)

bsearch132.0ms (1.3%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.9s (29.2%)

Profiling