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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms	69×	body	2048	valid
8.0ms	140×	body	128	valid
5.0ms	29×	body	1024	valid
1.0ms	11×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify94.0ms (1.5%)

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

Error

13.3b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize8.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1403`
24×	`add-sqr-sqrt_binary64_1425`
15×	`add-cube-cbrt_binary64_1438`
12×	`sqrt-prod_binary64_1419`
9×	`times-frac_binary64_1409`
8×	`add-log-exp_binary64_1442`
7×	`cancel-sign-sub-inv_binary64_1369`
6×	`add-exp-log_binary64_1441` `add-cbrt-cube_binary64_1439`
5×	`pow1_binary64_1464`
4×	`difference-of-squares_binary64_1372` `distribute-lft-out_binary64_1354`
3×	`associate-/r_binary64_1347` `associate-/l_binary64_1348` `distribute-lft-out--_binary64_1355`
2×	`flip3-+_binary64_1406` `sqrt-div_binary64_1420` `flip-+_binary64_1377`
1×	`frac-2neg_binary64_1414` `div-inv_binary64_1400` `+-commutative_binary64_1333` `sub-neg_binary64_1396` `cbrt-undiv_binary64_1437` `clear-num_binary64_1402` `diff-log_binary64_1495` `flip--_binary64_1378` `pow1/2_binary64_1483` `sqrt-pow1_binary64_1421` `sum-log_binary64_1494` `div-exp_binary64_1454` `rem-sqrt-square_binary64_1416` `flip3--_binary64_1407`

Counts

4 → 80

Calls

8 calls:

11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
6.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series183.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(-.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))))
37.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
28.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 276 to 276 computations (0% saved)

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4823	1444
1	4823	1444

prune103.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	2	93

Error

12.8b

Counts

93 → 2

Compiler

Compiled 1428 to 1296 computations (9.2% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_1425`
92×	`*-un-lft-identity_binary64_1403`
71×	`times-frac_binary64_1409`
41×	`add-cube-cbrt_binary64_1438`
28×	`distribute-lft-out_binary64_1354`
16×	`difference-of-squares_binary64_1372`
14×	`sqrt-prod_binary64_1419`
13×	`cancel-sign-sub-inv_binary64_1369`
12×	`associate-/r_binary64_1347` `associate-/l_binary64_1348`
10×	`add-exp-log_binary64_1441` `add-cbrt-cube_binary64_1439`
8×	`distribute-lft-out--_binary64_1355`
6×	`add-log-exp_binary64_1442`
4×	`div-inv_binary64_1400` `pow1_binary64_1464`
3×	`frac-2neg_binary64_1414` `cbrt-undiv_binary64_1437` `clear-num_binary64_1402` `div-exp_binary64_1454`
2×	`associate-/l/_binary64_1350` `associate-/r/_binary64_1349` `flip--_binary64_1378` `flip3--_binary64_1407`
1×	`flip3-+_binary64_1406` `div-sub_binary64_1408` `sub-neg_binary64_1396` `diff-log_binary64_1495` `flip-+_binary64_1377`

Counts

4 → 146

Calls

8 calls:

19.0ms	(/.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))))))
8.0ms	(-.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))
0.0ms	(hypot.f64 1 x)

series255.0ms (4%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.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))))))
43.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
32.0ms	(/.f64 1/2 (hypot.f64 1 x))
31.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 468 to 444 computations (5.1% saved)

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4885	3848
1	4885	3848

prune307.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	3	160

Error

12.6b

Counts

160 → 3

Compiler

Compiled 4178 to 3752 computations (10.2% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(hypot.f64 1 x)
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(+.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))
0.2b	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.9b	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite187.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`times-frac_binary64_1409` `*-un-lft-identity_binary64_1403`
224×	`add-sqr-sqrt_binary64_1425`
141×	`add-cube-cbrt_binary64_1438`
124×	`distribute-lft-out_binary64_1354`
84×	`cancel-sign-sub-inv_binary64_1369`
62×	`sqrt-prod_binary64_1419`
19×	`div-inv_binary64_1400` `associate-/l*_binary64_1348`
13×	`add-exp-log_binary64_1441` `add-cbrt-cube_binary64_1439`
12×	`associate-/r*_binary64_1347`
11×	`distribute-lft-out--_binary64_1355`
8×	`associate-/r/_binary64_1349`
6×	`difference-of-squares_binary64_1372` `add-log-exp_binary64_1442`
5×	`cbrt-undiv_binary64_1437` `div-exp_binary64_1454`
4×	`flip3-+_binary64_1406` `pow1_binary64_1464` `flip-+_binary64_1377`
3×	`frac-2neg_binary64_1414` `clear-num_binary64_1402` `distribute-rgt-out--_binary64_1357`
1×	`sub-div_binary64_1410` `associate-/l/_binary64_1350` `sub-neg_binary64_1396` `diff-log_binary64_1495` `flip--_binary64_1378` `frac-sub_binary64_1412` `flip3--_binary64_1407`

Counts

4 → 285

Calls

8 calls:

118.0ms	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
15.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.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))
0.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series494.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
143.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.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 756 to 708 computations (6.3% saved)

simplify134.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4963	10522
1	4963	10522

prune1.0s (15.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	297	3	300

Error

12.6b

Counts

300 → 3

Compiler

Compiled 11625 to 10468 computations (10% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(hypot.f64 1 x)
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(+.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	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.9b	(-.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))
22.5b	(cbrt.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64_1425`
70×	`cbrt-prod_binary64_1434`
65×	`times-frac_binary64_1409`
60×	`*-un-lft-identity_binary64_1403`
58×	`add-cube-cbrt_binary64_1438`
41×	`cube-prod_binary64_1431` `unpow-prod-down_binary64_1482`
35×	`cancel-sign-sub-inv_binary64_1369`
9×	`add-exp-log_binary64_1441` `add-cbrt-cube_binary64_1439`
7×	`div-inv_binary64_1400` `difference-of-squares_binary64_1372`
6×	`add-log-exp_binary64_1442`
5×	`pow1_binary64_1464`
4×	`sqr-pow_binary64_1375`
3×	`pow-unpow_binary64_1480` `associate-/r_binary64_1347` `cube-mult_binary64_1433` `associate-/l_binary64_1348` `unpow3_binary64_1469`
2×	`rem-cube-cbrt_binary64_1426` `cube-div_binary64_1432` `cbrt-undiv_binary64_1437` `pow-exp_binary64_1471` `div-exp_binary64_1454`
1×	`frac-2neg_binary64_1414` `cbrt-div_binary64_1435` `pow-pow_binary64_1475` `pow1/3_binary64_1485` `rem-cbrt-cube_binary64_1427` `sub-neg_binary64_1396` `pow-to-exp_binary64_1472` `clear-num_binary64_1402` `diff-log_binary64_1495` `flip--_binary64_1378` `flip3--_binary64_1407` `distribute-lft-out--_binary64_1355`

Counts

4 → 169

Calls

8 calls:

17.0ms	(-.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))
5.0ms	(cbrt.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series180.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
46.0ms	(-.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))
35.0ms	(cbrt.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
34.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 480 to 456 computations (5% saved)

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5291	2535

prune317.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	181	3	184

Error

12.6b

Counts

184 → 3

Compiler

Compiled 4435 to 3994 computations (9.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	175	439
1	175	439

regimes248.0ms (3.9%)

Accuracy

Total 0.3b remaining (1.8%)

Threshold costs 0.3b (1.8%)

Compiler

Compiled 2285 to 2216 computations (3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	44
1	38	44

end0.0ms (0%)

sample2.3s (36.7%)

Algorithm

1×

intervals

Results

513.0ms	2082×	body	2048	valid
191.0ms	1028×	body	1024	valid
181.0ms	4165×	body	128	valid
58.0ms	450×	body	512	valid
25.0ms	275×	body	256	valid

Compiler

Compiled 883 to 848 computations (4% saved)

Pareto

0.46469198411866103

Details

analyze2.0ms (0%)

sample39.0ms (0.6%)

simplify94.0ms (1.5%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite36.0ms (0.6%)

series183.0ms (2.9%)

simplify99.0ms (1.6%)

prune103.0ms (1.6%)

localize10.0ms (0.2%)

rewrite51.0ms (0.8%)

series255.0ms (4%)

simplify93.0ms (1.5%)

prune307.0ms (4.8%)

localize13.0ms (0.2%)

rewrite187.0ms (2.9%)

series494.0ms (7.8%)

simplify134.0ms (2.1%)

prune1.0s (15.8%)

localize14.0ms (0.2%)

rewrite49.0ms (0.8%)

series180.0ms (2.8%)

simplify80.0ms (1.3%)

prune317.0ms (5%)

simplify8.0ms (0.1%)

regimes248.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (36.7%)

Profiling