Details

analyze149.0ms (2%)

Algorithm

2×	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
0%	100%	0%	0
100%	0%	0%	1
100%	0%	0%	1

Compiler

Compiled 26 to 26 computations (0% saved)

sample213.0ms (2.8%)

Algorithm

2×

intervals

Results

39.0ms	137×	body	2048	valid
11.0ms	265×	body	128	valid
10.0ms	52×	body	1024	valid
6.0ms	42×	body	512	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 3366 to 3624 computations (-7.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

16.1b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(hypot.f64 1 x)
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)))))

rewrite103.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

16.0b

Rules

22×	`*-un-lft-identity_binary64_1442`
21×	`add-sqr-sqrt_binary64_1464`
13×	`add-cube-cbrt_binary64_1477`
9×	`times-frac_binary64_1448`
8×	`sqrt-prod_binary64_1458`
7×	`cancel-sign-sub-inv_binary64_1408`
5×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
4×	`difference-of-squares_binary64_1411`
3×	`pow1_binary64_1503` `distribute-lft-out--_binary64_1394` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`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

3 → 59

Calls

3 calls:

9.0ms	(-.f64 1 (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 1094 to 992 computations (9.3% saved)

series151.0ms (2%)

Error

16.1b

Counts

3 → 9

Calls

3 calls:

96.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
39.0ms	(/.f64 1/2 (hypot.f64 1 x))
9.0ms	(hypot.f64 1 x)

Compiler

Compiled 288 to 280 computations (2.8% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5036	1025

prune90.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Error

15.6b

Counts

69 → 4

Compiler

Compiled 1100 to 1001 computations (9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite363.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

15.3b

Rules

95×	`add-sqr-sqrt_binary64_1464`
92×	`*-un-lft-identity_binary64_1442`
71×	`times-frac_binary64_1448`
41×	`add-cube-cbrt_binary64_1477`
28×	`distribute-lft-out_binary64_1393`
16×	`difference-of-squares_binary64_1411`
14×	`sqrt-prod_binary64_1458`
13×	`cancel-sign-sub-inv_binary64_1408`
12×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
10×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`distribute-lft-out--_binary64_1394`
6×	`add-log-exp_binary64_1481`
4×	`pow1_binary64_1503` `div-inv_binary64_1439`
3×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `div-sub_binary64_1447` `flip3-+_binary64_1445` `flip-+_binary64_1416`

Counts

4 → 146

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))))))
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))

Compiler

Compiled 4316 to 3882 computations (10.1% saved)

series402.0ms (5.3%)

Error

15.6b

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.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))))))
75.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
47.0ms	(/.f64 1/2 (hypot.f64 1 x))
43.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 702 to 655 computations (6.7% saved)

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4885	3848
1	4885	3848

prune332.0ms (4.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

15.3b

Counts

162 → 4

Compiler

Compiled 4198 to 3771 computations (10.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.1b	(exp.f64 (log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
1.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite204.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

15.3b

Rules

41×	`add-sqr-sqrt_binary64_1464`
40×	`*-un-lft-identity_binary64_1442`
20×	`log-prod_binary64_1528`
17×	`add-cube-cbrt_binary64_1477`
16×	`sqrt-prod_binary64_1458`
12×	`difference-of-squares_binary64_1411`
10×	`exp-sum_binary64_1488`
9×	`distribute-lft-out--_binary64_1394` `times-frac_binary64_1448`
7×	`add-exp-log_binary64_1480` `cancel-sign-sub-inv_binary64_1408`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503` `add-cbrt-cube_binary64_1478`
4×	`distribute-lft-out_binary64_1393` `exp-prod_binary64_1494` `log-div_binary64_1529`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`log-pow_binary64_1531` `exp-diff_binary64_1490`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `rem-log-exp_binary64_1483`

Counts

4 → 97

Calls

4 calls:

10.0ms	(exp.f64 (log.f64 (-.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)))))
9.0ms	(log.f64 (-.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 2198 to 2026 computations (7.8% saved)

series632.0ms (8.4%)

Error

15.3b

Counts

4 → 12

Calls

4 calls:

250.0ms	(exp.f64 (log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
239.0ms	(log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
93.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
39.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 486 to 475 computations (2.3% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4839	2124
1	4839	2124

prune160.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Error

15.3b

Counts

113 → 4

Compiler

Compiled 2033 to 1868 computations (8.1% saved)

localize14.0ms (0.2%)

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)))))
1.0b	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

rewrite681.0ms (9%)

Algorithm

1×	rewrite-expression-head

Error

15.3b

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-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
12×	`difference-of-squares_binary64_1411`
11×	`associate-r_binary64_1382`
8×	`pow1_binary64_1503`
6×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`div-inv_binary64_1439` `associate-l_binary64_1383`
4×	`flip3--_binary64_1446` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394` `frac-times_binary64_1452` `rem-sqrt-square_binary64_1455`
3×	`sub-neg_binary64_1435` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-l/_binary64_1385` `associate-r/_binary64_1384` `distribute-lft-out_binary64_1393` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 155

Calls

4 calls:

24.0ms	(*.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))))
6.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 6813 to 6162 computations (9.6% saved)

series593.0ms (7.8%)

Error

15.3b

Counts

4 → 12

Calls

4 calls:

256.0ms	(*.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)))))
122.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
99.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
91.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 1215 to 1132 computations (6.8% saved)

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5051	4538

prune564.0ms (7.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	166	5	171

Error

15.3b

Counts

171 → 5

Compiler

Compiled 6393 to 5772 computations (9.7% saved)

regimes454.0ms (6%)

Accuracy

Total 0.3b remaining (1.8%)

Threshold costs 0.3b (1.8%)

Compiler

Compiled 4938 to 4637 computations (6.1% 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%)

sample2.1s (27.6%)

Algorithm

1×

intervals

Results

568.0ms	2165×	body	2048	valid
201.0ms	1000×	body	1024	valid
182.0ms	4084×	body	128	valid
67.0ms	491×	body	512	valid
22.0ms	260×	body	256	valid

Compiler

Compiled 723 to 680 computations (5.9% saved)

Details

analyze149.0ms (2%)

sample213.0ms (2.8%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite103.0ms (1.4%)

series151.0ms (2%)

simplify80.0ms (1.1%)

prune90.0ms (1.2%)

localize9.0ms (0.1%)

rewrite363.0ms (4.8%)

series402.0ms (5.3%)

simplify90.0ms (1.2%)

prune332.0ms (4.4%)

localize9.0ms (0.1%)

rewrite204.0ms (2.7%)

series632.0ms (8.4%)

simplify74.0ms (1%)

prune160.0ms (2.1%)

localize14.0ms (0.2%)

rewrite681.0ms (9%)

series593.0ms (7.8%)

simplify81.0ms (1.1%)

prune564.0ms (7.5%)

regimes454.0ms (6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (27.6%)

Profiling