Details

analyze96.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample29.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	76×	body	1024	valid
5.0ms	126×	body	128	valid
4.0ms	37×	body	512	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

20.1b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
1.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite350.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

19.5b

Rules

127×	`add-sqr-sqrt_binary64_1464`
118×	`times-frac_binary64_1448`
117×	`*-un-lft-identity_binary64_1442`
76×	`sqrt-prod_binary64_1458`
56×	`add-cube-cbrt_binary64_1477`
27×	`cancel-sign-sub-inv_binary64_1408`
25×	`difference-of-squares_binary64_1411`
13×	`distribute-lft-out--_binary64_1394` `associate-/r*_binary64_1386`
12×	`add-exp-log_binary64_1480`
11×	`distribute-lft-out_binary64_1393`
9×	`pow1_binary64_1503`
8×	`add-cbrt-cube_binary64_1478`
7×	`div-inv_binary64_1439`
6×	`add-log-exp_binary64_1481` `sqrt-div_binary64_1459` `pow-flip_binary64_1516` `associate-/l*_binary64_1387`
4×	`associate-/r/_binary64_1388` `div-exp_binary64_1493`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460`
2×	`inv-pow_binary64_1527` `1-exp_binary64_1486` `rec-exp_binary64_1492` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`diff-log_binary64_1534` `frac-sub_binary64_1451` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `rem-sqrt-square_binary64_1455`

Counts

4 → 189

Calls

4 calls:

38.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3837 to 2945 computations (23.2% saved)

series89.0ms (1%)

Error

19.8b

Counts

4 → 18

Calls

4 calls:

25.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))
14.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 561 to 462 computations (17.6% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune249.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	195	12	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	12	208

Error

19.5b

Counts

208 → 12

Compiler

Compiled 3646 to 2720 computations (25.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
1.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite180.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

19.5b

Rules

46×	`add-sqr-sqrt_binary64_1464`
42×	`sqrt-prod_binary64_1458`
38×	`*-un-lft-identity_binary64_1442`
13×	`add-cube-cbrt_binary64_1477`
12×	`difference-of-squares_binary64_1411`
11×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
10×	`times-frac_binary64_1448` `associate-/l*_binary64_1387`
9×	`pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
7×	`associate-r_binary64_1382`
6×	`add-log-exp_binary64_1481` `cancel-sign-sub-inv_binary64_1408` `sqrt-div_binary64_1459` `associate-l_binary64_1383`
5×	`distribute-lft-out_binary64_1393`
4×	`unswap-sqr_binary64_1410` `associate-*r/_binary64_1384`
3×	`pow1/2_binary64_1522` `pow-prod-down_binary64_1513` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `sqrt-unprod_binary64_1462` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455`

Counts

4 → 113

Calls

4 calls:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2641 to 1665 computations (37% saved)

series149.0ms (1.6%)

Error

19.4b

Counts

4 → 18

Calls

4 calls:

57.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
31.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
26.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
18.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 782 to 587 computations (24.9% saved)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5277	2138

prune141.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	141	2	143

Error

0.2b

Counts

143 → 2

Compiler

Compiled 2569 to 1638 computations (36.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite342.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

118×	`*-un-lft-identity_binary64_1442`
78×	`times-frac_binary64_1448`
55×	`sqrt-prod_binary64_1458`
47×	`add-sqr-sqrt_binary64_1464`
45×	`distribute-lft-out_binary64_1393`
39×	`add-cube-cbrt_binary64_1477`
32×	`add-exp-log_binary64_1480`
27×	`associate-/l*_binary64_1387`
20×	`add-cbrt-cube_binary64_1478`
14×	`div-exp_binary64_1493`
9×	`pow1_binary64_1503`
8×	`associate-/r/_binary64_1388`
7×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386`
6×	`add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-l_binary64_1383`
5×	`prod-exp_binary64_1491`
4×	`unswap-sqr_binary64_1410` `sqrt-div_binary64_1459` `associate-*r/_binary64_1384` `div-inv_binary64_1439`
3×	`pow-prod-down_binary64_1513` `cbrt-unprod_binary64_1475` `1-exp_binary64_1486` `rec-exp_binary64_1492`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`sqrt-unprod_binary64_1462` `*-commutative_binary64_1373` `associate-/l/_binary64_1389` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 166

Calls

4 calls:

21.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 4418 to 3053 computations (30.9% saved)

series114.0ms (1.2%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

44.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
26.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
17.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 561 to 452 computations (19.4% saved)

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune240.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	174	9	183

Error

0.0b

Counts

183 → 9

Compiler

Compiled 4156 to 2867 computations (31% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite622.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

234×	`times-frac_binary64_1448`
159×	`*-un-lft-identity_binary64_1442`
156×	`add-sqr-sqrt_binary64_1464`
119×	`add-cube-cbrt_binary64_1477`
87×	`sqrt-prod_binary64_1458`
49×	`distribute-lft-out_binary64_1393`
21×	`associate-/l*_binary64_1387`
20×	`associate-/r/_binary64_1388`
19×	`add-exp-log_binary64_1480`
13×	`add-cbrt-cube_binary64_1478`
12×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
11×	`associate-/r*_binary64_1386`
10×	`div-inv_binary64_1439`
9×	`pow1_binary64_1503`
8×	`div-exp_binary64_1493`
7×	`associate-r_binary64_1382`
6×	`add-log-exp_binary64_1481` `associate-l_binary64_1383`
4×	`unswap-sqr_binary64_1410` `sqrt-div_binary64_1459` `cbrt-undiv_binary64_1476`
3×	`pow-prod-down_binary64_1513`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `associate-*r/_binary64_1384` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `sqrt-unprod_binary64_1462` `*-commutative_binary64_1373` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `associate-/l/_binary64_1389` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 252

Calls

4 calls:

17.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 7993 to 5774 computations (27.8% saved)

series143.0ms (1.5%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

39.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
36.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
27.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
23.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 813 to 681 computations (16.2% saved)

simplify159.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4896	9188
1	4896	9188

prune463.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	271	2	273
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	276	6	282

Error

0.0b

Counts

282 → 6

Compiler

Compiled 7292 to 5201 computations (28.7% saved)

regimes691.0ms (7.5%)

Accuracy

Total 0.3b remaining (98.9%)

Threshold costs 0.3b (98.9%)

Compiler

Compiled 8750 to 7013 computations (19.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	37
1	18	37

end0.0ms (0%)

sample4.9s (52.8%)

Algorithm

1×

intervals

Results

339.0ms	2219×	body	1024	valid
162.0ms	4230×	body	128	valid
117.0ms	1058×	body	512	valid
39.0ms	493×	body	256	valid

Compiler

Compiled 4334 to 3471 computations (19.9% saved)

Details

analyze96.0ms (1%)

sample29.0ms (0.3%)

simplify11.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

rewrite350.0ms (3.8%)

series89.0ms (1%)

simplify93.0ms (1%)

prune249.0ms (2.7%)

localize8.0ms (0.1%)

rewrite180.0ms (2%)

series149.0ms (1.6%)

simplify62.0ms (0.7%)

prune141.0ms (1.5%)

localize9.0ms (0.1%)

rewrite342.0ms (3.7%)

series114.0ms (1.2%)

simplify96.0ms (1%)

prune240.0ms (2.6%)

localize11.0ms (0.1%)

rewrite622.0ms (6.7%)

series143.0ms (1.5%)

simplify159.0ms (1.7%)

prune463.0ms (5%)

regimes691.0ms (7.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.9s (52.8%)

Profiling