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)

sample37.0ms (0.8%)

Algorithm

1×

intervals

Results

15.0ms	61×	body	2048	valid
7.0ms	39×	body	1024	valid
5.0ms	125×	body	128	valid
3.0ms	24×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify173.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune5.0ms (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: 19.2b

Counts

2 → 1

Compiler

Compiled 42 to 42 computations (0% saved)

localize7.0ms (0.1%)

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)))))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1455`
21×	`add-sqr-sqrt_binary64_1477`
13×	`add-cube-cbrt_binary64_1490`
9×	`times-frac_binary64_1461`
8×	`sqrt-prod_binary64_1471`
7×	`add-log-exp_binary64_1494` `cancel-sign-sub-inv_binary64_1421`
5×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
4×	`difference-of-squares_binary64_1424`
3×	`distribute-lft-out_binary64_1406` `distribute-lft-out--_binary64_1407` `pow1_binary64_1516` `associate-/r_binary64_1399` `associate-/l_binary64_1400`
1×	`flip-+_binary64_1429` `div-exp_binary64_1506` `clear-num_binary64_1454` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

3 → 64

Calls

3 calls:

11.0ms	(-.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))

series226.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

118.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
59.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
48.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4821	1162
1	4821	1162

prune108.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 18.7b

Counts

74 → 3

Compiler

Compiled 1521 to 1403 computations (7.8% 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)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1477`
31×	`*-un-lft-identity_binary64_1455`
28×	`times-frac_binary64_1461`
27×	`add-cube-cbrt_binary64_1490`
13×	`cancel-sign-sub-inv_binary64_1421`
8×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
6×	`associate-/r_binary64_1399` `associate-/l_binary64_1400`
4×	`pow1_binary64_1516`
3×	`div-inv_binary64_1452`
2×	`difference-of-squares_binary64_1424` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466`
1×	`distribute-lft-out_binary64_1406` `distribute-lft-out--_binary64_1407` `flip-+_binary64_1429` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `sum-log_binary64_1546` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

4 → 93

Calls

4 calls:

9.0ms	(-.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))

series220.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
61.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
41.0ms	(/.f64 1/2 (hypot.f64 1 x))
40.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4900	1340
1	4900	1340

prune163.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Merged error: 18.5b

Counts

108 → 3

Compiler

Compiled 2528 to 2268 computations (10.3% saved)

localize12.0ms (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)))))

rewrite61.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_1455`
43×	`add-sqr-sqrt_binary64_1477`
28×	`sqrt-prod_binary64_1471`
21×	`cancel-sign-sub-inv_binary64_1421`
16×	`difference-of-squares_binary64_1424`
12×	`distribute-lft-out--_binary64_1407`
11×	`add-cube-cbrt_binary64_1490`
10×	`add-log-exp_binary64_1494` `cbrt-prod_binary64_1486`
7×	`distribute-lft-out_binary64_1406`
4×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `flip--_binary64_1430` `flip3--_binary64_1459` `add-exp-log_binary64_1493`
3×	`diff-log_binary64_1547` `sub-neg_binary64_1448`
2×	`cbrt-div_binary64_1487`
1×	`pow1/3_binary64_1537`

Counts

4 → 95

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

series800.0ms (16.6%)

Counts

4 → 12

Calls

4 calls:

451.0ms	(cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
117.0ms	(-.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)))))
115.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5384	2268

prune301.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	107	3	110

Merged error: 18.5b

Counts

110 → 3

Compiler

Compiled 4552 to 4179 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)))))

rewrite61.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_1455`
44×	`add-sqr-sqrt_binary64_1477`
32×	`sqrt-prod_binary64_1471`
28×	`cancel-sign-sub-inv_binary64_1421`
16×	`difference-of-squares_binary64_1424`
12×	`distribute-lft-out--_binary64_1407` `add-log-exp_binary64_1494` `add-cube-cbrt_binary64_1490`
8×	`distribute-lft-out_binary64_1406`
4×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459` `add-exp-log_binary64_1493`

Counts

4 → 100

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)))))
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)))))

series474.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
119.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
114.0ms	(-.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)))))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5058	2316

prune477.0ms (9.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	112	3	115

Merged error: 18.5b

Counts

115 → 3

Compiler

Compiled 6278 to 5777 computations (8% saved)

regimes27.0ms (0.6%)

Compiler: Compiled 234 to 220 computations (6% 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%)

sample1.2s (25.6%)

Algorithm

1×

intervals

Results

506.0ms	2063×	body	2048	valid
181.0ms	4232×	body	128	valid
169.0ms	935×	body	1024	valid
75.0ms	522×	body	512	valid
20.0ms	248×	body	256	valid

Compiler

Compiled 144 to 137 computations (4.9% saved)

Details

analyze2.0ms (0%)

sample37.0ms (0.8%)

simplify173.0ms (3.6%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite27.0ms (0.6%)

series226.0ms (4.7%)

simplify97.0ms (2%)

prune108.0ms (2.2%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series220.0ms (4.6%)

simplify71.0ms (1.5%)

prune163.0ms (3.4%)

localize12.0ms (0.2%)

rewrite61.0ms (1.3%)

series800.0ms (16.6%)

simplify79.0ms (1.6%)

prune301.0ms (6.3%)

localize17.0ms (0.4%)

rewrite61.0ms (1.3%)

series474.0ms (9.8%)

simplify90.0ms (1.9%)

prune477.0ms (9.9%)

regimes27.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (25.6%)

Profiling