Details

analyze462.0ms (6.8%)

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)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	36×	body	2048	valid
8.0ms	156×	body	128	valid
6.0ms	30×	body	1024	valid
6.0ms	18×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	16×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify422.0ms (6.3%)

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

Merged error: 35.3b

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)
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.4%)

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:

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)))

series236.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
67.0ms	(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)))))
34.0ms	(-.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

prune121.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 4.9b

Counts

85 → 8

Compiler

Compiled 2137 to 1160 computations (45.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.1b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.2b	(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_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:

14.0ms	(/.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))))))
10.0ms	(-.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))))

series522.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
174.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
64.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5011	5032

prune211.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	149	7	156

Merged error: 4.9b

Counts

156 → 7

Compiler

Compiled 4790 to 2553 computations (46.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1464`
28×	`*-un-lft-identity_binary64_1442`
18×	`times-frac_binary64_1448` `add-cube-cbrt_binary64_1477`
11×	`sqrt-prod_binary64_1458`
10×	`difference-of-squares_binary64_1411`
8×	`add-log-exp_binary64_1481`
7×	`cancel-sign-sub-inv_binary64_1408`
6×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
4×	`flip3--_binary64_1446` `flip--_binary64_1417`
3×	`associate-/l*_binary64_1387`
2×	`associate-/r/_binary64_1388` `sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

4 → 88

Calls

4 calls:

8.0ms	(/.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)))

series347.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
65.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4882	2580
1	4882	2580

prune128.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	100	7	107

Merged error: 4.9b

Counts

107 → 7

Compiler

Compiled 2935 to 1747 computations (40.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(/.f64 1 (.f64 (/.f64 1 c) (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) 4)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-exp-log_binary64_1480`
42×	`div-exp_binary64_1493`
24×	`prod-exp_binary64_1491`
22×	`add-cbrt-cube_binary64_1478`
15×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
14×	`add-sqr-sqrt_binary64_1464`
11×	`*-un-lft-identity_binary64_1442`
9×	`cbrt-undiv_binary64_1476` `add-cube-cbrt_binary64_1477`
8×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
7×	`cancel-sign-sub-inv_binary64_1408` `sqrt-prod_binary64_1458`
4×	`cbrt-unprod_binary64_1475`
3×	`times-frac_binary64_1448` `associate-/r/_binary64_1388` `associate-/l*_binary64_1387` `flip3--_binary64_1446` `flip--_binary64_1417`
2×	`sub-neg_binary64_1435` `sqrt-div_binary64_1459` `pow-flip_binary64_1516` `diff-log_binary64_1534` `difference-of-squares_binary64_1411`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `inv-pow_binary64_1527` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `frac-2neg_binary64_1453` `frac-times_binary64_1452` `pow1/2_binary64_1522` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/.f64 1 (.f64 (/.f64 1 c) (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) 4)))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series502.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

339.0ms	(/.f64 1 (.f64 (/.f64 1 c) (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) 4)))
66.0ms	(-.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))))
36.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4935	2558
1	4935	2558

prune134.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	114	7	121

Merged error: 4.9b

Counts

121 → 7

Compiler

Compiled 2782 to 1729 computations (37.9% saved)

regimes812.0ms (12%)

Compiler: Compiled 3926 to 3030 computations (22.8% saved)

bsearch123.0ms (1.8%)

Steps

Iters	Range	Point
10	2.111580858145245e+148	6.118292371914786e+159	2.1353619288367854e+148
7	6.41317177798842e-285	1.0212591469716465e-282	5.126982040291221e-283
10	-8.988626090881866e+157	-1.220652379953807e+147	-1.4220016328491612e+151

Iters

Range

Point

2.111580858145245e+148

6.118292371914786e+159

2.1353619288367854e+148

6.41317177798842e-285

1.0212591469716465e-282

5.126982040291221e-283

-8.988626090881866e+157

-1.220652379953807e+147

-1.4220016328491612e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	98	89
1	98	89

end0.0ms (0%)

sample2.1s (31.4%)

Algorithm

1×

intervals

Results

288.0ms	1100×	body	2048	valid
283.0ms	5210×	body	128	valid
158.0ms	751×	body	1024	valid
129.0ms	395×	body	4096	valid
56.0ms	359×	body	512	valid
32.0ms	633×	body	128	nan
22.0ms	409×	body	128	invalid
19.0ms	185×	body	256	valid

Compiler

Compiled 1078 to 821 computations (23.8% saved)

Details

analyze462.0ms (6.8%)

sample43.0ms (0.6%)

simplify422.0ms (6.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite29.0ms (0.4%)

series236.0ms (3.5%)

simplify89.0ms (1.3%)

prune121.0ms (1.8%)

localize12.0ms (0.2%)

rewrite55.0ms (0.8%)

series522.0ms (7.7%)

simplify105.0ms (1.6%)

prune211.0ms (3.1%)

localize15.0ms (0.2%)

rewrite33.0ms (0.5%)

series347.0ms (5.1%)

simplify80.0ms (1.2%)

prune128.0ms (1.9%)

localize17.0ms (0.3%)

rewrite39.0ms (0.6%)

series502.0ms (7.4%)

simplify71.0ms (1.1%)

prune134.0ms (2%)

regimes812.0ms (12%)

bsearch123.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (31.4%)

Profiling