Details

analyze100.0ms (1.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms	68×	body	2048	valid
7.0ms	145×	body	128	valid
5.0ms	24×	body	1024	valid
2.0ms	15×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

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

12.7b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1442`
14×	`add-sqr-sqrt_binary64_1464`
12×	`sqrt-prod_binary64_1458`
7×	`cancel-sign-sub-inv_binary64_1408`
5×	`add-cube-cbrt_binary64_1477`
4×	`add-log-exp_binary64_1481` `difference-of-squares_binary64_1411`
3×	`distribute-lft-out_binary64_1393` `pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
2×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-exp-log_binary64_1480`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

2 → 41

Calls

2 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series113.0ms (2%)

Counts

2 → 6

Calls

2 calls:

64.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
49.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4848	861
1	4848	861

prune61.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	5	48

Error

12.2b

Counts

48 → 5

Compiler

Compiled 819 to 750 computations (8.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.8b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`*-un-lft-identity_binary64_1442`
83×	`add-sqr-sqrt_binary64_1464`
53×	`times-frac_binary64_1448`
33×	`distribute-lft-out_binary64_1393`
26×	`add-cube-cbrt_binary64_1477`
20×	`sqrt-prod_binary64_1458`
16×	`difference-of-squares_binary64_1411`
13×	`cancel-sign-sub-inv_binary64_1408`
8×	`add-log-exp_binary64_1481` `distribute-lft-out--_binary64_1394`
6×	`associate-/r_binary64_1386` `add-cbrt-cube_binary64_1478` `associate-/l_binary64_1387` `add-exp-log_binary64_1480`
5×	`pow1_binary64_1503`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-/l/_binary64_1389` `div-inv_binary64_1439` `associate-/r/_binary64_1388` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `div-sub_binary64_1447` `div-exp_binary64_1493`

Counts

4 → 122

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series296.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
51.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
51.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
35.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4977	3694
1	4977	3694

prune257.0ms (4.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Error

12.1b

Counts

139 → 4

Compiler

Compiled 3650 to 3285 computations (10% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.8b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite105.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

347×	`times-frac_binary64_1448`
344×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
128×	`distribute-lft-out_binary64_1393`
120×	`add-cube-cbrt_binary64_1477`
64×	`sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411`
48×	`associate-/r*_binary64_1386`
32×	`distribute-lft-out--_binary64_1394`
17×	`add-exp-log_binary64_1480`
13×	`cancel-sign-sub-inv_binary64_1408`
11×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
9×	`associate-/l*_binary64_1387`
8×	`add-log-exp_binary64_1481` `div-exp_binary64_1493`
7×	`div-inv_binary64_1439`
6×	`flip3--_binary64_1446` `flip--_binary64_1417`
5×	`pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476`
2×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`inv-pow_binary64_1527` `sum-log_binary64_1533` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `pow-flip_binary64_1516` `diff-log_binary64_1534`

Counts

4 → 297

Calls

4 calls:

28.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
18.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series390.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
143.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
61.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
34.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify157.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4937	12224
1	4937	12224

prune1.0s (17.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	309	4	313

Error

12.1b

Counts

313 → 4

Compiler

Compiled 10203 to 9252 computations (9.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.5b	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
1.8b	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

rewrite65.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`sqrt-prod_binary64_1458`
80×	`add-sqr-sqrt_binary64_1464`
56×	`*-un-lft-identity_binary64_1442`
51×	`times-frac_binary64_1448`
48×	`cancel-sign-sub-inv_binary64_1408`
44×	`add-cube-cbrt_binary64_1477`
17×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
12×	`difference-of-squares_binary64_1411`
11×	`associate-r_binary64_1382`
8×	`pow1_binary64_1503`
6×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
5×	`div-inv_binary64_1439` `associate-l_binary64_1383`
4×	`rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-times_binary64_1452` `distribute-lft-out--_binary64_1394`
3×	`sub-neg_binary64_1435` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `sqrt-div_binary64_1459` `distribute-lft-out_binary64_1393` `pow1/2_binary64_1522` `associate-l/_binary64_1385`
1×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `diff-log_binary64_1534` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

4 → 155

Calls

4 calls:

25.0ms	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

series329.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
67.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
48.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
48.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5051	4538

prune498.0ms (8.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	167	4	171

Error

12.1b

Counts

171 → 4

Compiler

Compiled 6393 to 5772 computations (9.7% saved)

regimes260.0ms (4.5%)

Accuracy

Total 0.0b remaining (0.2%)

Threshold costs 0.0b (0.2%)

Compiler

Compiled 2950 to 2796 computations (5.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	51
1	34	51

end0.0ms (0%)

sample1.7s (30.1%)

Algorithm

1×

intervals

Results

575.0ms	2157×	body	2048	valid
204.0ms	1006×	body	1024	valid
187.0ms	4083×	body	128	valid
77.0ms	513×	body	512	valid
22.0ms	241×	body	256	valid

Compiler

Compiled 455 to 431 computations (5.3% saved)

Details

analyze100.0ms (1.7%)

sample37.0ms (0.6%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite22.0ms (0.4%)

series113.0ms (2%)

simplify61.0ms (1.1%)

prune61.0ms (1.1%)

localize13.0ms (0.2%)

rewrite52.0ms (0.9%)

series296.0ms (5.1%)

simplify93.0ms (1.6%)

prune257.0ms (4.4%)

localize12.0ms (0.2%)

rewrite105.0ms (1.8%)

series390.0ms (6.7%)

simplify157.0ms (2.7%)

prune1.0s (17.4%)

localize16.0ms (0.3%)

rewrite65.0ms (1.1%)

series329.0ms (5.7%)

simplify83.0ms (1.4%)

prune498.0ms (8.6%)

regimes260.0ms (4.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.7s (30.1%)

Profiling