Details

analyze830.0ms (12.2%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
6.0ms	24×	body	2048	valid
5.0ms	27×	body	1024	valid
5.0ms	10×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	28×	body	128	nan
1.0ms	11×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify333.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (327.0ms)

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

Error

30.9b

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)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite28.0ms (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-/l*_binary64_364`
3×	`sqrt-prod_binary64_435` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
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:

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)))

series246.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
72.0ms	(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)))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune116.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

5.2b

Counts

85 → 7

Compiler

Compiled 2102 to 1132 computations (46.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.8b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
9.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_425`
59×	`add-sqr-sqrt_binary64_441`
44×	`*-un-lft-identity_binary64_419`
30×	`add-cube-cbrt_binary64_454`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`difference-of-squares_binary64_388`
13×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
10×	`associate-/r/_binary64_365` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`associate-/r*_binary64_363`
7×	`flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
6×	`add-log-exp_binary64_458` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
5×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`sub-neg_binary64_412` `pow1/2_binary64_499` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`

Counts

4 → 136

Calls

4 calls:

15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.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)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series528.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
167.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
71.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5011	5032

prune211.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	147	8	155

Error

5.1b

Counts

155 → 8

Compiler

Compiled 4797 to 2552 computations (46.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.8b	(/.f64 (.f64 4 (/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))) a)
9.4b	(/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_441`
23×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
17×	`*-un-lft-identity_binary64_419`
11×	`add-cube-cbrt_binary64_454`
9×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
8×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385`
5×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow1_binary64_480`
3×	`flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/r/_binary64_365` `frac-2neg_binary64_430` `associate-/l*_binary64_364`
1×	`sub-neg_binary64_412` `pow1/2_binary64_499` `associate-*r/_binary64_361` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`

Counts

4 → 90

Calls

4 calls:

13.0ms	(/.f64 (.f64 4 (/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))) a)
10.0ms	(/.f64 (.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))))

series488.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
164.0ms	(/.f64 (.f64 4 (/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))) a)
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
58.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4950	2566
1	4950	2566

prune117.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	102	8	110

Error

5.1b

Counts

110 → 8

Compiler

Compiled 2886 to 1582 computations (45.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_425`
82×	`*-un-lft-identity_binary64_419`
57×	`add-sqr-sqrt_binary64_441`
56×	`add-cube-cbrt_binary64_454`
18×	`associate-/r*_binary64_363`
15×	`add-exp-log_binary64_457`
13×	`distribute-lft-out_binary64_370`
9×	`associate-/r/_binary64_365` `add-cbrt-cube_binary64_455`
8×	`add-log-exp_binary64_458`
7×	`div-exp_binary64_470`
6×	`pow1_binary64_480`
5×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393`
3×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364` `cbrt-undiv_binary64_453`
2×	`sqrt-div_binary64_436` `1-exp_binary64_463` `flip3--_binary64_423` `rec-exp_binary64_469` `flip--_binary64_394`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `inv-pow_binary64_504` `pow1/2_binary64_499` `sum-log_binary64_510` `frac-2neg_binary64_430` `pow-flip_binary64_493` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 135

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 a (+.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	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series246.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4904	4499
1	4904	4499

prune180.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	147	8	155

Error

5.1b

Counts

155 → 8

Compiler

Compiled 4125 to 2264 computations (45.1% saved)

regimes605.0ms (8.9%)

Accuracy

Total 1.1b remaining (16.6%)

Threshold costs 0b (0%)

Compiler

Compiled 4402 to 3234 computations (26.5% saved)

bsearch113.0ms (1.7%)

Steps

Iters	Range	Point
9	1.3757201747748946e+122	4.2744175307429915e+127	4.506449921036379e+122
8	-5.094737738097033e-276	-1.1972161547110289e-278	-1.2572184622052755e-278
9	-8.994821103457546e+83	-5.5446932295606685e+78	-6.936942472764157e+83

Iters

Range

Point

1.3757201747748946e+122

4.2744175307429915e+127

4.506449921036379e+122

-5.094737738097033e-276

-1.1972161547110289e-278

-1.2572184622052755e-278

-8.994821103457546e+83

-5.5446932295606685e+78

-6.936942472764157e+83

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	98	89
1	98	89

end0.0ms (0%)

sample2.2s (31.7%)

Algorithm

1×

intervals

Results

294.0ms	5280×	body	128	valid
284.0ms	1081×	body	2048	valid
150.0ms	716×	body	1024	valid
130.0ms	395×	body	4096	valid
54.0ms	341×	body	512	valid
38.0ms	656×	body	128	nan
23.0ms	419×	body	128	invalid
19.0ms	187×	body	256	valid

Compiler

Compiled 1197 to 872 computations (27.2% saved)

Details

analyze830.0ms (12.2%)

sample41.0ms (0.6%)

simplify333.0ms (4.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite28.0ms (0.4%)

series246.0ms (3.6%)

simplify89.0ms (1.3%)

prune116.0ms (1.7%)

localize12.0ms (0.2%)

rewrite55.0ms (0.8%)

series528.0ms (7.8%)

simplify111.0ms (1.6%)

prune211.0ms (3.1%)

localize14.0ms (0.2%)

rewrite44.0ms (0.6%)

series488.0ms (7.2%)

simplify66.0ms (1%)

prune117.0ms (1.7%)

localize15.0ms (0.2%)

rewrite40.0ms (0.6%)

series246.0ms (3.6%)

simplify87.0ms (1.3%)

prune180.0ms (2.7%)

regimes605.0ms (8.9%)

bsearch113.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (31.7%)

Profiling