Details

analyze157.0ms (2.3%)

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)

sample27.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	71×	body	1024	valid
5.0ms	138×	body	128	valid
3.0ms	28×	body	512	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune7.0ms (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

21.5b

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))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite406.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

20.8b

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:

37.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 2811 to 2163 computations (23.1% saved)

series126.0ms (1.8%)

Error

21.2b

Counts

4 → 18

Calls

4 calls:

39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
30.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 x 1))
18.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 486 to 413 computations (15% saved)

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune197.0ms (2.9%)

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

20.8b

Counts

208 → 12

Compiler

Compiled 1878 to 1443 computations (23.2% 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)))
3.6b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite267.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

20.5b

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:

21.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2040 to 1298 computations (36.4% saved)

series214.0ms (3.1%)

Error

20.7b

Counts

4 → 16

Calls

4 calls:

92.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
48.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
34.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
25.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 610 to 470 computations (23% saved)

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5146	2109

prune145.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	137	4	141

Error

0.3b

Counts

141 → 4

Compiler

Compiled 1698 to 1106 computations (34.9% saved)

localize10.0ms (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)))
0.3b	(/.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)))

rewrite448.0ms (6.5%)

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:

20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 3625 to 2490 computations (31.3% saved)

series172.0ms (2.5%)

Error

0.1b

Counts

4 → 14

Calls

4 calls:

75.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
40.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
27.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
23.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 449 to 377 computations (16% saved)

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5020	3663

prune246.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	172	8	180
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Error

0.0b

Counts

184 → 9

Compiler

Compiled 2681 to 1859 computations (30.7% saved)

localize12.0ms (0.2%)

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

rewrite650.0ms (9.4%)

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:

13.0ms	(/.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 6283 to 4529 computations (27.9% saved)

series206.0ms (3%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

65.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
50.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
37.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
36.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 650 to 552 computations (15.1% saved)

simplify136.0ms (2%)

Algorithm

1×	egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4979	9116
1	4979	9116

prune370.0ms (5.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	270	9	279

Error

0.0b

Counts

279 → 9

Compiler

Compiled 4041 to 2886 computations (28.6% saved)

regimes1.7s (25.3%)

Accuracy

Total 0.3b remaining (93.3%)

Threshold costs 0.3b (93.3%)

Compiler

Compiled 17018 to 13634 computations (19.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end2.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

sample1.1s (15.6%)

Algorithm

1×

intervals

Results

326.0ms	2186×	body	1024	valid
170.0ms	4322×	body	128	valid
107.0ms	976×	body	512	valid
37.0ms	516×	body	256	valid

Compiler

Compiled 236 to 192 computations (18.6% saved)

Details

analyze157.0ms (2.3%)

sample27.0ms (0.4%)

simplify10.0ms (0.1%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite406.0ms (5.9%)

series126.0ms (1.8%)

simplify87.0ms (1.3%)

prune197.0ms (2.9%)

localize8.0ms (0.1%)

rewrite267.0ms (3.9%)

series214.0ms (3.1%)

simplify61.0ms (0.9%)

prune145.0ms (2.1%)

localize10.0ms (0.1%)

rewrite448.0ms (6.5%)

series172.0ms (2.5%)

simplify97.0ms (1.4%)

prune246.0ms (3.6%)

localize12.0ms (0.2%)

rewrite650.0ms (9.4%)

series206.0ms (3%)

simplify136.0ms (2%)

prune370.0ms (5.4%)

regimes1.7s (25.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end2.0ms (0%)

sample1.1s (15.6%)

Profiling