Details

analyze2.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 13 to 13 computations (0% saved)

sample42.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	61×	body	2048	valid
12.0ms	39×	body	1024	valid
6.0ms	125×	body	128	valid
3.0ms	24×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify166.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune8.0ms (0.2%)

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: 19.2b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_1425`
19×	`add-sqr-sqrt_binary64_1446`
11×	`add-cube-cbrt_binary64_1457`
9×	`times-frac_binary64_1431`
7×	`add-log-exp_binary64_1461`
5×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
4×	`sqrt-prod_binary64_1440` `difference-of-squares_binary64_1394`
3×	`associate-/r_binary64_1371` `distribute-lft-out--_binary64_1379` `associate-/l_binary64_1372` `pow1_binary64_1483`
2×	`distribute-lft-out_binary64_1378`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `frac-2neg_binary64_1436` `flip3-+_binary64_1428` `sub-neg_binary64_1418` `clear-num_binary64_1424` `div-inv_binary64_1422` `sum-log_binary64_1513` `flip-+_binary64_1399` `div-exp_binary64_1473` `+-commutative_binary64_1357` `flip3--_binary64_1429` `cbrt-undiv_binary64_1456`

Counts

3 → 57

Calls

3 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

series225.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

119.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
62.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
44.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5043	1055

prune77.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	3	67

Merged error: 18.7b

Counts

67 → 3

Compiler

Compiled 1117 to 1015 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.3b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1446`
24×	`*-un-lft-identity_binary64_1425`
20×	`add-cube-cbrt_binary64_1457`
19×	`times-frac_binary64_1431`
8×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
6×	`associate-/r_binary64_1371` `associate-/l_binary64_1372`
4×	`pow1_binary64_1483`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `div-inv_binary64_1422` `difference-of-squares_binary64_1394` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `distribute-lft-out--_binary64_1379` `flip3-+_binary64_1428` `sub-neg_binary64_1418` `distribute-lft-out_binary64_1378` `sum-log_binary64_1513` `flip-+_binary64_1399` `+-commutative_binary64_1357` `flip3--_binary64_1429`

Counts

4 → 80

Calls

4 calls:

10.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

series210.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
66.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
39.0ms	(/.f64 1/2 (hypot.f64 1 x))
38.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4868	1251
1	4868	1251

prune140.0ms (3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	93	2	95

Merged error: 18.5b

Counts

95 → 2

Compiler

Compiled 2210 to 1978 computations (10.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1446`
33×	`*-un-lft-identity_binary64_1425`
16×	`sqrt-prod_binary64_1440` `difference-of-squares_binary64_1394`
12×	`distribute-lft-out--_binary64_1379`
10×	`cbrt-prod_binary64_1453` `add-log-exp_binary64_1461`
5×	`add-cube-cbrt_binary64_1457`
4×	`flip--_binary64_1400` `distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `flip3--_binary64_1429` `add-exp-log_binary64_1460`
3×	`diff-log_binary64_1514` `sub-neg_binary64_1418`
2×	`cbrt-div_binary64_1454`
1×	`pow1/3_binary64_1504`

Counts

4 → 74

Calls

4 calls:

13.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

series783.0ms (16.5%)

Counts

4 → 12

Calls

4 calls:

444.0ms	(cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
116.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
112.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
110.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4855	1920
1	4855	1920

prune226.0ms (4.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 18.5b

Counts

88 → 2

Compiler

Compiled 3640 to 3340 computations (8.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1446`
32×	`*-un-lft-identity_binary64_1425`
16×	`sqrt-prod_binary64_1440` `difference-of-squares_binary64_1394`
12×	`distribute-lft-out--_binary64_1379` `add-log-exp_binary64_1461`
4×	`flip--_binary64_1400` `diff-log_binary64_1514` `add-cube-cbrt_binary64_1457` `sub-neg_binary64_1418` `distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `flip3--_binary64_1429` `add-exp-log_binary64_1460`

Counts

4 → 72

Calls

4 calls:

11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series453.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
116.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
111.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
110.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify105.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4843	1852
1	4843	1852

prune324.0ms (6.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	2	86

Merged error: 18.5b

Counts

86 → 2

Compiler

Compiled 4672 to 4297 computations (8% saved)

regimes174.0ms (3.7%)

Compiler: Compiled 1998 to 1900 computations (4.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	27
1	30	27

end0.0ms (0%)

sample1.4s (29.3%)

Algorithm

1×

intervals

Results

505.0ms	2063×	body	2048	valid
178.0ms	4232×	body	128	valid
172.0ms	935×	body	1024	valid
66.0ms	522×	body	512	valid
20.0ms	248×	body	256	valid

Compiler

Compiled 303 to 289 computations (4.6% saved)

Details

analyze2.0ms (0%)

sample42.0ms (0.9%)

simplify166.0ms (3.5%)

prune8.0ms (0.2%)

localize7.0ms (0.2%)

rewrite25.0ms (0.5%)

series225.0ms (4.8%)

simplify68.0ms (1.4%)

prune77.0ms (1.6%)

localize9.0ms (0.2%)

rewrite30.0ms (0.6%)

series210.0ms (4.4%)

simplify68.0ms (1.4%)

prune140.0ms (3%)

localize11.0ms (0.2%)

rewrite54.0ms (1.1%)

series783.0ms (16.5%)

simplify70.0ms (1.5%)

prune226.0ms (4.8%)

localize17.0ms (0.4%)

rewrite53.0ms (1.1%)

series453.0ms (9.6%)

simplify105.0ms (2.2%)

prune324.0ms (6.8%)

regimes174.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (29.3%)

Profiling