Details

analyze12.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample21.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify232.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4946	22
1	4946	22

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 21.6b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
21.4b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1374`
7×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
5×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
4×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446` `add-log-exp_binary64_1461` `*-un-lft-identity_binary64_1425` `frac-times_binary64_1435`
3×	`flip--_binary64_1400` `times-frac_binary64_1431` `associate-/r*_binary64_1371` `flip3--_binary64_1429`
2×	`associate-r/_binary64_1369` `associate-/r/_binary64_1373` `div-exp_binary64_1473` `pow1_binary64_1483` `associate-l/_binary64_1370` `cbrt-undiv_binary64_1456`
1×	`frac-2neg_binary64_1436` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `div-inv_binary64_1422` `sum-log_binary64_1513` `associate-/l*_binary64_1372` `+-commutative_binary64_1357`

Counts

2 → 42

Calls

2 calls:

13.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series122.0ms (4.1%)

Counts

2 → 6

Calls

2 calls:

85.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
37.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify35.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5025	969

prune51.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Merged error: 0.2b

Counts

49 → 7

Compiler

Compiled 1162 to 244 computations (79% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite85.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64_1446`
96×	`times-frac_binary64_1431`
95×	`*-un-lft-identity_binary64_1425`
57×	`add-cube-cbrt_binary64_1457` `sqrt-prod_binary64_1440`
36×	`associate-l_binary64_1368`
30×	`associate-r_binary64_1367`
18×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
13×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
10×	`sqrt-div_binary64_1441`
9×	`unswap-sqr_binary64_1393`
8×	`pow1_binary64_1483`
6×	`associate-/r*_binary64_1371` `distribute-lft-out_binary64_1378` `associate-/r/_binary64_1373`
5×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `div-exp_binary64_1473` `associate-/l*_binary64_1372` `cbrt-undiv_binary64_1456`
4×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `add-log-exp_binary64_1461`
3×	`div-inv_binary64_1422`
2×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `associate-/l/_binary64_1374` `rem-sqrt-square_binary64_1438`
1×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-r/_binary64_1369` `div-sub_binary64_1430` `associate-l/_binary64_1370` `flip3--_binary64_1429` `*-commutative_binary64_1358` `frac-times_binary64_1435` `pow-prod-down_binary64_1493`

Counts

4 → 183

Calls

4 calls:

38.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series299.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
94.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
48.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
43.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify89.0ms (3%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4967	5945
1	4967	5945

prune172.0ms (5.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	195	7	202

Merged error: 0.2b

Counts

202 → 7

Compiler

Compiled 6791 to 661 computations (90.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (*.f64 y y)))))
21.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
21.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
21.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite98.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64_1446`
90×	`times-frac_binary64_1431`
84×	`cbrt-prod_binary64_1453`
67×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
24×	`difference-of-squares_binary64_1394`
21×	`associate-l_binary64_1368` `associate-r_binary64_1367` `swap-sqr_binary64_1392`
14×	`associate-/r/_binary64_1373`
12×	`associate-/l*_binary64_1372` `add-exp-log_binary64_1460`
11×	`pow1_binary64_1483`
10×	`add-cbrt-cube_binary64_1458`
9×	`associate-/r*_binary64_1371` `unswap-sqr_binary64_1393`
7×	`flip3-+_binary64_1428` `div-inv_binary64_1422` `flip-+_binary64_1399`
6×	`pow1/3_binary64_1504` `associate-/l/_binary64_1374`
4×	`cbrt-div_binary64_1454` `add-log-exp_binary64_1461`
3×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `clear-num_binary64_1424` `div-sub_binary64_1430` `div-exp_binary64_1473` `flip3--_binary64_1429` `cbrt-undiv_binary64_1456`
2×	`pow-sqr_binary64_1398` `pow-prod-up_binary64_1492` `pow-prod-down_binary64_1493`
1×	`prod-exp_binary64_1471` `pow-plus_binary64_1485` `cbrt-unprod_binary64_1455` `associate-r/_binary64_1369` `pow2_binary64_1503` `associate-l/_binary64_1370` `*-commutative_binary64_1358` `frac-times_binary64_1435`

Counts

4 → 201

Calls

4 calls:

27.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (*.f64 y y)))))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

series425.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (*.f64 y y)))))
65.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
65.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
65.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

simplify134.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4925	8541
1	4925	8541

prune245.0ms (8.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	213	7	220

Merged error: 0.2b

Counts

220 → 7

Compiler

Compiled 12965 to 972 computations (92.5% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	3	3
Total	7	7

Merged error: 0.2b

Counts

7 → 7

Compiler

Compiled 0 to 0 computations (0% saved)

regimes85.0ms (2.8%)

Compiler: Compiled 472 to 236 computations (50% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 15 to 9 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	50
1	27	50

end0.0ms (0%)

sample799.0ms (26.9%)

Algorithm

1×

intervals

Results

305.0ms	8000×	body	128	valid
159.0ms	8000×	pre	128	true

Compiler

Compiled 239 to 122 computations (49% saved)

Details

analyze12.0ms (0.4%)

sample21.0ms (0.7%)

simplify232.0ms (7.8%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite22.0ms (0.7%)

series122.0ms (4.1%)

simplify35.0ms (1.2%)

prune51.0ms (1.7%)

localize11.0ms (0.4%)

rewrite85.0ms (2.9%)

series299.0ms (10.1%)

simplify89.0ms (3%)

prune172.0ms (5.8%)

localize11.0ms (0.4%)

rewrite98.0ms (3.3%)

series425.0ms (14.3%)

simplify134.0ms (4.5%)

prune245.0ms (8.2%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

regimes85.0ms (2.8%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample799.0ms (26.9%)

Profiling