Details

analyze473.0ms (6.4%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	176×	body	128	valid
7.0ms	30×	body	2048	valid
6.0ms	28×	body	1024	valid
2.0ms	6×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify218.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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

Merged error: 32.0b

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))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
13×	`*-un-lft-identity_binary64_414`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`add-cube-cbrt_binary64_446`
6×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`distribute-lft-out--_binary64_368`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `prod-exp_binary64_460` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `div-sub_binary64_419` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series513.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune116.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 6.3b

Counts

83 → 9

Compiler

Compiled 2061 to 1236 computations (40% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
22×	`times-frac_binary64_420`
21×	`*-un-lft-identity_binary64_414`
17×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
13×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
12×	`add-sqr-sqrt_binary64_435`
11×	`add-cube-cbrt_binary64_446` `associate-/l*_binary64_361`
6×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
5×	`pow1_binary64_472` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`
4×	`flip3-+_binary64_417` `div-inv_binary64_411` `flip-+_binary64_388`
3×	`sqrt-prod_binary64_429`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `pow1/2_binary64_491` `flip--_binary64_389` `associate-/l/_binary64_363` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 102

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.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)))

series910.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

365.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
303.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
116.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4940	3121
1	4940	3121

prune155.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	114	9	123

Merged error: 6.2b

Counts

123 → 9

Compiler

Compiled 3285 to 2026 computations (38.3% saved)

localize12.0ms (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)))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.4%)

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-/r*_binary64_360`
3×	`sqrt-prod_binary64_429` `associate-/l*_binary64_361`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `flip-+_binary64_388` `flip--_binary64_389`
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 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.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)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series625.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4931	1962
1	4931	1962

prune101.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 6.2b

Counts

92 → 9

Compiler

Compiled 2263 to 1412 computations (37.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_414`
18×	`associate-r_binary64_356`
16×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
14×	`add-sqr-sqrt_binary64_435`
13×	`add-cube-cbrt_binary64_446`
12×	`times-frac_binary64_420`
10×	`pow1_binary64_472`
8×	`add-log-exp_binary64_450`
6×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
4×	`distribute-lft-out_binary64_367`
3×	`sqrt-prod_binary64_429` `pow-prod-down_binary64_482`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `cbrt-undiv_binary64_445` `flip-+_binary64_388` `flip--_binary64_389` `div-exp_binary64_462`
1×	`diff-log_binary64_503` `div-inv_binary64_411` `-commutative_binary64_347` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `sub-neg_binary64_407` `associate-l_binary64_357` `pow1/2_binary64_491` `sum-log_binary64_502` `associate-r/_binary64_358` `rem-sqrt-square_binary64_427`

Counts

4 → 76

Calls

4 calls:

14.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
6.0ms	(+.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)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series644.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

351.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
117.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5207	1908

prune100.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	87	10	97

Merged error: 6.2b

Counts

97 → 10

Compiler

Compiled 2167 to 1349 computations (37.7% saved)

regimes692.0ms (9.4%)

Compiler: Compiled 4692 to 3608 computations (23.1% saved)

bsearch115.0ms (1.6%)

Steps

Iters	Range	Point
11	1.533617338164353e+90	3.5739920072306705e+109	6.972667102848289e+99
8	-7.009141771871467e-292	-2.349509325897326e-294	-1.7338129079736815e-293
8	-1.0322269454701605e+98	-2.7621719849249905e+94	-1.0164007120358223e+98

Iters

Range

Point

1.533617338164353e+90

3.5739920072306705e+109

6.972667102848289e+99

-7.009141771871467e-292

-2.349509325897326e-294

-1.7338129079736815e-293

-1.0322269454701605e+98

-2.7621719849249905e+94

-1.0164007120358223e+98

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	82
1	102	82

end0.0ms (0%)

sample2.2s (29.1%)

Algorithm

1×

intervals

Results

312.0ms	1206×	body	2048	valid
274.0ms	5148×	body	128	valid
143.0ms	708×	body	1024	valid
133.0ms	412×	body	4096	valid
58.0ms	358×	body	512	valid
36.0ms	679×	body	128	nan
22.0ms	399×	body	128	invalid
17.0ms	168×	body	256	valid

Compiler

Compiled 1223 to 932 computations (23.8% saved)

Details

analyze473.0ms (6.4%)

sample37.0ms (0.5%)

simplify218.0ms (2.9%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite37.0ms (0.5%)

series513.0ms (6.9%)

simplify97.0ms (1.3%)

prune116.0ms (1.6%)

localize15.0ms (0.2%)

rewrite53.0ms (0.7%)

series910.0ms (12.3%)

simplify86.0ms (1.2%)

prune155.0ms (2.1%)

localize12.0ms (0.2%)

rewrite33.0ms (0.4%)

series625.0ms (8.4%)

simplify67.0ms (0.9%)

prune101.0ms (1.4%)

localize15.0ms (0.2%)

rewrite38.0ms (0.5%)

series644.0ms (8.7%)

simplify70.0ms (0.9%)

prune100.0ms (1.4%)

regimes692.0ms (9.4%)

bsearch115.0ms (1.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (29.1%)

Profiling