Details

analyze91.0ms (1%)

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)

sample46.0ms (0.5%)

Algorithm

1×

intervals

Results

24.0ms	78×	body	2048	valid
6.0ms	31×	body	1024	valid
5.0ms	125×	body	128	valid
1.0ms	11×	body	512	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune3.0ms (0%)

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

14.5b

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	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite98.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

14.4b

Rules

24×	`*-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×	`add-log-exp_binary64_1481` `cancel-sign-sub-inv_binary64_1408`
5×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
4×	`difference-of-squares_binary64_1411`
3×	`pow1_binary64_1503` `distribute-lft-out_binary64_1393` `distribute-lft-out--_binary64_1394` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
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` `sum-log_binary64_1533` `flip3-+_binary64_1445` `flip-+_binary64_1416` `+-commutative_binary64_1372`

Counts

3 → 64

Calls

3 calls:

10.0ms	(-.f64 1 (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))

Compiler

Compiled 1213 to 1101 computations (9.2% saved)

series138.0ms (1.5%)

Error

14.5b

Counts

3 → 9

Calls

3 calls:

66.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
39.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
26.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 306 to 298 computations (2.6% saved)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4821	1162
1	4821	1162

prune79.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Error

14.0b

Counts

74 → 4

Compiler

Compiled 1182 to 1075 computations (9.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.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 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite331.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

89×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
62×	`times-frac_binary64_1448`
33×	`add-cube-cbrt_binary64_1477`
32×	`distribute-lft-out_binary64_1393`
16×	`difference-of-squares_binary64_1411` `sqrt-prod_binary64_1458`
13×	`cancel-sign-sub-inv_binary64_1408`
9×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
8×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `distribute-lft-out--_binary64_1394`
4×	`pow1_binary64_1503`
3×	`div-inv_binary64_1439`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389` `flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `div-sub_binary64_1447` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 133

Calls

4 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))))))
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))

Compiler

Compiled 4029 to 3630 computations (9.9% saved)

series300.0ms (3.3%)

Error

14.0b

Counts

4 → 12

Calls

4 calls:

147.0ms	(/.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))))))
60.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
47.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
34.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 720 to 673 computations (6.5% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5064	3779

prune264.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	145	4	149

Error

14.0b

Counts

149 → 4

Compiler

Compiled 3863 to 3471 computations (10.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (log.f64 (exp.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))))))
1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.1b	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite477.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

123×	`*-un-lft-identity_binary64_1442`
114×	`add-sqr-sqrt_binary64_1464`
87×	`times-frac_binary64_1448`
56×	`log-pow_binary64_1531`
48×	`exp-prod_binary64_1494` `distribute-lft-out_binary64_1393`
45×	`add-cube-cbrt_binary64_1477`
26×	`cancel-sign-sub-inv_binary64_1408`
24×	`sqrt-prod_binary64_1458`
18×	`difference-of-squares_binary64_1411`
17×	`log-prod_binary64_1528`
14×	`exp-sum_binary64_1488`
12×	`pow1_binary64_1503`
10×	`associate-/l*_binary64_1387`
9×	`distribute-lft-out--_binary64_1394`
8×	`add-log-exp_binary64_1481`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-/r*_binary64_1386`
3×	`div-inv_binary64_1439`
2×	`exp-diff_binary64_1490` `log-div_binary64_1529` `sub-neg_binary64_1435` `flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416`
1×	`rem-log-exp_binary64_1483` `diff-log_binary64_1534` `flip3--_binary64_1446` `flip--_binary64_1417` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 165

Calls

4 calls:

26.0ms	(/.f64 (log.f64 (exp.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))))))
10.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
9.0ms	(+.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)))

Compiler

Compiled 5513 to 5016 computations (9% saved)

series498.0ms (5.4%)

Error

14.0b

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 (log.f64 (exp.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))))))
134.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
65.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
42.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 810 to 763 computations (5.8% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5027	5000

prune343.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	177	4	181

Error

14.0b

Counts

181 → 4

Compiler

Compiled 4844 to 4365 computations (9.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
1.1b	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite1.2s (13%)

Algorithm

1×	rewrite-expression-head

Error

13.7b

Rules

176×	`add-sqr-sqrt_binary64_1464`
93×	`times-frac_binary64_1448`
80×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
72×	`difference-of-squares_binary64_1411`
71×	`*-un-lft-identity_binary64_1442`
36×	`add-cube-cbrt_binary64_1477`
33×	`associate-/l*_binary64_1387`
32×	`sqr-pow_binary64_1414` `cancel-sign-sub-inv_binary64_1408`
15×	`distribute-lft-out--_binary64_1394`
12×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481` `associate-/r/_binary64_1388`
7×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
5×	`pow1_binary64_1503` `div-inv_binary64_1439`
4×	`frac-times_binary64_1452` `distribute-lft-out_binary64_1393`
3×	`difference-cubes_binary64_1444` `pow-unpow_binary64_1519` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `unpow3_binary64_1508` `cube-mult_binary64_1472` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `associate-/l/_binary64_1389` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `sqrt-prod_binary64_1458`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `cube-div_binary64_1471` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `associate-/r*_binary64_1386` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 225

Calls

4 calls:

57.0ms	(/.f64 (-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))))
26.0ms	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 11514 to 10349 computations (10.1% saved)

series671.0ms (7.3%)

Error

14.0b

Counts

4 → 12

Calls

4 calls:

417.0ms	(/.f64 (-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))))
100.0ms	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
65.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
65.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 1386 to 1267 computations (8.6% saved)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5060	8478

prune1.0s (11.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	235	6	241

Error

13.7b

Counts

241 → 6

Compiler

Compiled 10691 to 9555 computations (10.6% saved)

regimes605.0ms (6.6%)

Accuracy

Total 0.3b remaining (1.9%)

Threshold costs 0.3b (1.9%)

Compiler

Compiled 9103 to 8417 computations (7.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	55
1	45	55

end0.0ms (0%)

sample2.5s (27.8%)

Algorithm

1×

intervals

Results

569.0ms	2156×	body	2048	valid
194.0ms	1002×	body	1024	valid
179.0ms	4132×	body	128	valid
63.0ms	467×	body	512	valid
21.0ms	243×	body	256	valid

Compiler

Compiled 1336 to 1236 computations (7.5% saved)

Details

analyze91.0ms (1%)

sample46.0ms (0.5%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite98.0ms (1.1%)

series138.0ms (1.5%)

simplify99.0ms (1.1%)

prune79.0ms (0.9%)

localize9.0ms (0.1%)

rewrite331.0ms (3.6%)

series300.0ms (3.3%)

simplify92.0ms (1%)

prune264.0ms (2.9%)

localize12.0ms (0.1%)

rewrite477.0ms (5.2%)

series498.0ms (5.4%)

simplify92.0ms (1%)

prune343.0ms (3.7%)

localize20.0ms (0.2%)

rewrite1.2s (13%)

series671.0ms (7.3%)

simplify114.0ms (1.2%)

prune1.0s (11.1%)

regimes605.0ms (6.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (27.8%)

Profiling