Details

analyze109.0ms (0.7%)

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)

sample71.0ms (0.5%)

Algorithm

1×

intervals

Results

28.0ms	70×	body	2048	valid
18.0ms	36×	body	1024	valid
10.0ms	131×	body	128	valid
3.0ms	16×	body	512	valid
0.0ms	3×	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%)

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

15.9b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite109.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

15.9b

Rules

21×	`*-un-lft-identity_binary64_1442`
20×	`add-sqr-sqrt_binary64_1464`
12×	`add-cube-cbrt_binary64_1477`
9×	`times-frac_binary64_1448`
8×	`sqrt-prod_binary64_1458`
7×	`cancel-sign-sub-inv_binary64_1408`
4×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `difference-of-squares_binary64_1411`
3×	`distribute-lft-out--_binary64_1394` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`pow1_binary64_1503` `distribute-lft-out_binary64_1393`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

2 → 52

Calls

2 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 990 to 900 computations (9.1% saved)

series128.0ms (0.9%)

Error

15.9b

Counts

2 → 6

Calls

2 calls:

78.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
40.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 198 to 193 computations (2.5% saved)

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5003	962

prune87.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Error

15.4b

Counts

59 → 4

Compiler

Compiled 983 to 896 computations (8.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.9b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite311.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

34×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
28×	`times-frac_binary64_1448`
27×	`add-cube-cbrt_binary64_1477`
13×	`cancel-sign-sub-inv_binary64_1408`
8×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
4×	`pow1_binary64_1503` `distribute-lft-out_binary64_1393`
3×	`div-inv_binary64_1439`
2×	`difference-of-squares_binary64_1411` `sqrt-prod_binary64_1458` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394` `sum-log_binary64_1533` `flip3-+_binary64_1445` `flip-+_binary64_1416` `+-commutative_binary64_1372`

Counts

4 → 95

Calls

4 calls:

12.0ms	(+.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	(/.f64 1/2 (hypot.f64 1 x))
6.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 2505 to 2244 computations (10.4% saved)

series202.0ms (1.4%)

Error

15.4b

Counts

4 → 12

Calls

4 calls:

73.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
50.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
33.0ms	(/.f64 1/2 (hypot.f64 1 x))
33.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 684 to 637 computations (6.9% saved)

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4940	1445
1	4940	1445

prune210.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Error

15.2b

Counts

111 → 4

Compiler

Compiled 2534 to 2271 computations (10.4% saved)

localize16.0ms (0.1%)

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 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.9b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite1.1s (7.8%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

130×	`add-sqr-sqrt_binary64_1464`
89×	`*-un-lft-identity_binary64_1442`
88×	`times-frac_binary64_1448`
50×	`add-cube-cbrt_binary64_1477`
38×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
36×	`difference-of-squares_binary64_1411`
32×	`cancel-sign-sub-inv_binary64_1408`
15×	`distribute-lft-out_binary64_1393`
10×	`associate-/l*_binary64_1387`
9×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481` `sqr-pow_binary64_1414`
6×	`distribute-lft-out--_binary64_1394`
5×	`pow1_binary64_1503` `div-inv_binary64_1439`
4×	`associate-/r*_binary64_1386`
3×	`pow-unpow_binary64_1519`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `unpow3_binary64_1508` `cube-mult_binary64_1472` `div-exp_binary64_1493` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416` `sqrt-prod_binary64_1458`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `cube-div_binary64_1471` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 181

Calls

4 calls:

46.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
15.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
12.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 8870 to 7902 computations (10.9% saved)

series634.0ms (4.4%)

Error

15.2b

Counts

4 → 12

Calls

4 calls:

340.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
121.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
77.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
69.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 1332 to 1213 computations (8.9% saved)

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5253	5997

prune780.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	191	6	197

Error

15.2b

Counts

197 → 6

Compiler

Compiled 8721 to 7747 computations (11.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))
0.0b	(/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6)
0.8b	(-.f64 1/512 (pow.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)) 3))

rewrite2.5s (17%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

161×	`times-frac_binary64_1448`
136×	`add-sqr-sqrt_binary64_1464`
109×	`*-un-lft-identity_binary64_1442`
107×	`add-cube-cbrt_binary64_1477`
102×	`unpow-prod-down_binary64_1521`
89×	`cube-prod_binary64_1470`
86×	`cancel-sign-sub-inv_binary64_1408`
24×	`associate-/r*_binary64_1386`
19×	`sqr-pow_binary64_1414`
17×	`add-exp-log_binary64_1480`
15×	`unpow3_binary64_1508` `cube-mult_binary64_1472`
12×	`difference-of-squares_binary64_1411`
8×	`add-cbrt-cube_binary64_1478`
7×	`div-exp_binary64_1493`
6×	`add-log-exp_binary64_1481` `associate-/l*_binary64_1387`
5×	`pow1_binary64_1503` `div-inv_binary64_1439`
4×	`pow-exp_binary64_1510`
3×	`pow-unpow_binary64_1519` `pow-to-exp_binary64_1511`
2×	`cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394` `pow-pow_binary64_1514`

Counts

4 → 268

Calls

4 calls:

37.0ms	(-.f64 1/512 (pow.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)) 3))
11.0ms	(/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))
10.0ms	(/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))
8.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6)

Compiler

Compiled 17638 to 15767 computations (10.6% saved)

series477.0ms (3.3%)

Error

15.2b

Counts

4 → 12

Calls

4 calls:

167.0ms	(-.f64 1/512 (pow.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)) 3))
101.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6)
87.0ms	(/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))
80.0ms	(/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))

Compiler

Compiled 1944 to 1753 computations (9.8% saved)

simplify162.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4922	5126
1	4922	5126

prune2.5s (17.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	278	2	280
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	281	5	286

Error

15.2b

Counts

286 → 5

Compiler

Compiled 16728 to 14912 computations (10.9% saved)

regimes1.1s (7.6%)

Accuracy

Total 0.3b remaining (1.8%)

Threshold costs 0.3b (1.8%)

Compiler

Compiled 12666 to 11693 computations (7.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	54
1	70	54

end0.0ms (0%)

sample3.6s (24.6%)

Algorithm

1×

intervals

Results

620.0ms	2114×	body	2048	valid
221.0ms	994×	body	1024	valid
210.0ms	4123×	body	128	valid
81.0ms	524×	body	512	valid
23.0ms	245×	body	256	valid

Compiler

Compiled 1845 to 1704 computations (7.6% saved)

Details

analyze109.0ms (0.7%)

sample71.0ms (0.5%)

simplify8.0ms (0.1%)

prune4.0ms (0%)

localize6.0ms (0%)

rewrite109.0ms (0.7%)

series128.0ms (0.9%)

simplify119.0ms (0.8%)

prune87.0ms (0.6%)

localize11.0ms (0.1%)

rewrite311.0ms (2.1%)

series202.0ms (1.4%)

simplify77.0ms (0.5%)

prune210.0ms (1.5%)

localize16.0ms (0.1%)

rewrite1.1s (7.8%)

series634.0ms (4.4%)

simplify125.0ms (0.9%)

prune780.0ms (5.4%)

localize30.0ms (0.2%)

rewrite2.5s (17%)

series477.0ms (3.3%)

simplify162.0ms (1.1%)

prune2.5s (17.5%)

regimes1.1s (7.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.6s (24.6%)

Profiling