Details

analyze97.0ms (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)

sample43.0ms (0.8%)

Algorithm

1×

intervals

Results

20.0ms	64×	body	2048	valid
7.0ms	39×	body	1024	valid
5.0ms	130×	body	128	valid
2.0ms	13×	body	512	valid
1.0ms	10×	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

16.6b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(hypot.f64 1 x)
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite121.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

Rules

26×	`*-un-lft-identity_binary64_1442`
24×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477`
12×	`sqrt-prod_binary64_1458`
9×	`times-frac_binary64_1448`
7×	`cancel-sign-sub-inv_binary64_1408`
6×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`pow1_binary64_1503`
4×	`difference-of-squares_binary64_1411`
3×	`distribute-lft-out_binary64_1393` `distribute-lft-out--_binary64_1394` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

4 → 75

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

Compiler

Compiled 1401 to 1270 computations (9.4% saved)

series170.0ms (3%)

Error

16.6b

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
57.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
29.0ms	(/.f64 1/2 (hypot.f64 1 x))
8.0ms	(hypot.f64 1 x)

Compiler

Compiled 396 to 385 computations (2.8% saved)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4821	1307
1	4821	1307

prune96.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	2	88

Error

16.1b

Counts

88 → 2

Compiler

Compiled 1363 to 1237 computations (9.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(hypot.f64 1 x)
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite113.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

18×	`add-sqr-sqrt_binary64_1464`
16×	`*-un-lft-identity_binary64_1442`
13×	`cancel-sign-sub-inv_binary64_1408`
12×	`add-cube-cbrt_binary64_1477`
10×	`times-frac_binary64_1448`
6×	`add-log-exp_binary64_1481`
5×	`pow1_binary64_1503`
4×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-prod_binary64_1458`
2×	`difference-of-squares_binary64_1411` `sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `div-inv_binary64_1439` `distribute-lft-out--_binary64_1394` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out_binary64_1393` `rem-sqrt-square_binary64_1455`

Counts

4 → 57

Calls

4 calls:

7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.0ms	(hypot.f64 1 x)
1.0ms	(hypot.f64 1 x)

Compiler

Compiled 1507 to 1347 computations (10.6% saved)

series136.0ms (2.4%)

Error

16.1b

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
47.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
10.0ms	(hypot.f64 1 x)
9.0ms	(hypot.f64 1 x)

Compiler

Compiled 684 to 637 computations (6.9% saved)

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5253	791

prune98.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	69	2	71

Error

16.1b

Counts

71 → 2

Compiler

Compiled 1546 to 1384 computations (10.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite146.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

21×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
15×	`add-cube-cbrt_binary64_1477`
13×	`cancel-sign-sub-inv_binary64_1408`
10×	`times-frac_binary64_1448`
8×	`sqrt-prod_binary64_1458` `log-pow_binary64_1531`
7×	`exp-prod_binary64_1494`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`log-prod_binary64_1528`
2×	`difference-of-squares_binary64_1411` `sqrt-div_binary64_1459` `distribute-lft-out_binary64_1393`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `div-inv_binary64_1439` `distribute-lft-out--_binary64_1394` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `rem-log-exp_binary64_1483`

Counts

4 → 69

Calls

4 calls:

8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.0ms	(hypot.f64 1 x)

Compiler

Compiled 2007 to 1814 computations (9.6% saved)

series279.0ms (5%)

Error

16.1b

Counts

4 → 12

Calls

4 calls:

153.0ms	(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
53.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
49.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
10.0ms	(hypot.f64 1 x)

Compiler

Compiled 774 to 727 computations (6.1% saved)

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4840	1056
1	4840	1056

prune124.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	81	2	83

Error

16.1b

Counts

83 → 2

Compiler

Compiled 1976 to 1784 computations (9.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
31.3b	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))

rewrite378.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

56×	`add-sqr-sqrt_binary64_1464`
46×	`cancel-sign-sub-inv_binary64_1408`
42×	`*-un-lft-identity_binary64_1442`
39×	`times-frac_binary64_1448`
36×	`add-cube-cbrt_binary64_1477`
35×	`unpow-prod-down_binary64_1521`
28×	`sqrt-prod_binary64_1458`
10×	`add-log-exp_binary64_1481`
9×	`difference-of-squares_binary64_1411`
6×	`pow1_binary64_1503`
5×	`add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `div-inv_binary64_1439`
3×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `sqr-pow_binary64_1414` `distribute-lft-out--_binary64_1394` `pow-unpow_binary64_1519` `pow-pow_binary64_1514`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `sqrt-pow2_binary64_1461`

Counts

4 → 124

Calls

4 calls:

12.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
5.0ms	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)

Compiler

Compiled 5020 to 4546 computations (9.4% saved)

series346.0ms (6.2%)

Error

16.1b

Counts

4 → 12

Calls

4 calls:

118.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
109.0ms	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
52.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
47.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 1152 to 1069 computations (7.2% saved)

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5054	1858

prune319.0ms (5.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	135	3	138

Error

16.1b

Counts

138 → 3

Compiler

Compiled 4504 to 4054 computations (10% saved)

regimes500.0ms (8.9%)

Accuracy

Total 0.0b remaining (0.2%)

Threshold costs 0.0b (0.2%)

Compiler

Compiled 6835 to 6408 computations (6.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	31
1	32	31

end0.0ms (0%)

sample2.3s (41%)

Algorithm

1×

intervals

Results

538.0ms	2076×	body	2048	valid
195.0ms	1007×	body	1024	valid
175.0ms	4175×	body	128	valid
66.0ms	495×	body	512	valid
21.0ms	247×	body	256	valid

Compiler

Compiled 996 to 935 computations (6.1% saved)

Details

analyze97.0ms (1.7%)

sample43.0ms (0.8%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite121.0ms (2.2%)

series170.0ms (3%)

simplify85.0ms (1.5%)

prune96.0ms (1.7%)

localize9.0ms (0.2%)

rewrite113.0ms (2%)

series136.0ms (2.4%)

simplify59.0ms (1%)

prune98.0ms (1.7%)

localize12.0ms (0.2%)

rewrite146.0ms (2.6%)

series279.0ms (5%)

simplify82.0ms (1.5%)

prune124.0ms (2.2%)

localize15.0ms (0.3%)

rewrite378.0ms (6.7%)

series346.0ms (6.2%)

simplify65.0ms (1.2%)

prune319.0ms (5.7%)

regimes500.0ms (8.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (41%)

Profiling