Details

analyze809.0ms (11.8%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
6.0ms	24×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	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)

simplify349.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (344.0ms)

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))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1442`
15×	`add-sqr-sqrt_binary64_1464`
14×	`add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
8×	`add-log-exp_binary64_1481`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`distribute-lft-out_binary64_1393` `pow1_binary64_1503`
4×	`associate-/l*_binary64_1387`
3×	`associate-/r*_binary64_1386` `sqrt-prod_binary64_1458`
2×	`associate-/l/_binary64_1389` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

4 → 72

Calls

4 calls:

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

series234.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune121.0ms (1.8%)

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)

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 (.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))))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1448`
59×	`add-sqr-sqrt_binary64_1464`
44×	`*-un-lft-identity_binary64_1442`
30×	`add-cube-cbrt_binary64_1477`
27×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
14×	`difference-of-squares_binary64_1411`
13×	`associate-/l*_binary64_1387` `sqrt-prod_binary64_1458`
10×	`cbrt-undiv_binary64_1476` `associate-/r/_binary64_1388` `div-exp_binary64_1493`
9×	`associate-/r*_binary64_1386`
7×	`flip3--_binary64_1446` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394`
6×	`cancel-sign-sub-inv_binary64_1408` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `add-log-exp_binary64_1481` `prod-exp_binary64_1491`
5×	`pow1_binary64_1503`
2×	`clear-num_binary64_1441` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 136

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))))))
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))))

series519.0ms (7.6%)

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))))))
169.0ms	(/.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)))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify116.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5011	5032

prune220.0ms (3.2%)

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)

localize13.0ms (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_1464`
23×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
17×	`*-un-lft-identity_binary64_1442`
11×	`add-cube-cbrt_binary64_1477`
9×	`associate-/r*_binary64_1386` `times-frac_binary64_1448` `sqrt-prod_binary64_1458`
8×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
6×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481` `difference-of-squares_binary64_1411`
5×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `pow1_binary64_1503`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394`
2×	`div-inv_binary64_1439` `associate-/r/_binary64_1388` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `associate-*r/_binary64_1384` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `diff-log_binary64_1534` `pow1/2_binary64_1522`

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))))

series500.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
168.0ms	(/.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))))
61.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4950	2566
1	4950	2566

prune125.0ms (1.8%)

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)

localize13.0ms (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))))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_1448`
82×	`*-un-lft-identity_binary64_1442`
57×	`add-sqr-sqrt_binary64_1464`
56×	`add-cube-cbrt_binary64_1477`
18×	`associate-/r*_binary64_1386`
15×	`add-exp-log_binary64_1480`
13×	`distribute-lft-out_binary64_1393`
9×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
8×	`add-log-exp_binary64_1481`
7×	`div-exp_binary64_1493`
6×	`pow1_binary64_1503`
5×	`div-inv_binary64_1439` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`cbrt-undiv_binary64_1476` `associate-/l*_binary64_1387` `sqrt-prod_binary64_1458`
2×	`1-exp_binary64_1486` `flip3--_binary64_1446` `rec-exp_binary64_1492` `sqrt-div_binary64_1459` `flip--_binary64_1417`
1×	`sqrt-pow1_binary64_1460` `inv-pow_binary64_1527` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 135

Calls

4 calls:

13.0ms	(/.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)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series266.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
74.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4904	4499
1	4904	4499

prune175.0ms (2.6%)

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)

regimes665.0ms (9.7%)

Accuracy

Total 1.2b remaining (16.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4402 to 3234 computations (26.5% saved)

bsearch114.0ms (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	121	91
1	121	91

end0.0ms (0%)

sample2.1s (30.6%)

Algorithm

1×

intervals

Results

274.0ms	1081×	body	2048	valid
267.0ms	5280×	body	128	valid
140.0ms	716×	body	1024	valid
120.0ms	395×	body	4096	valid
51.0ms	341×	body	512	valid
34.0ms	656×	body	128	nan
21.0ms	419×	body	128	invalid
18.0ms	187×	body	256	valid

Compiler

Compiled 1198 to 873 computations (27.1% saved)

Details

analyze809.0ms (11.8%)

sample38.0ms (0.6%)

simplify349.0ms (5.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite33.0ms (0.5%)

series234.0ms (3.4%)

simplify96.0ms (1.4%)

prune121.0ms (1.8%)

localize14.0ms (0.2%)

rewrite56.0ms (0.8%)

series519.0ms (7.6%)

simplify116.0ms (1.7%)

prune220.0ms (3.2%)

localize13.0ms (0.2%)

rewrite44.0ms (0.6%)

series500.0ms (7.3%)

simplify71.0ms (1%)

prune125.0ms (1.8%)

localize13.0ms (0.2%)

rewrite43.0ms (0.6%)

series266.0ms (3.9%)

simplify84.0ms (1.2%)

prune175.0ms (2.6%)

regimes665.0ms (9.7%)

bsearch114.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (30.6%)

Profiling