Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 39 to 32 computations (17.9% saved)

simplify240.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4910	29
1	4910	29

prune3.0ms (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: 0.0b

Counts

2 → 1

Compiler

Compiled 38 to 30 computations (21.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
0.2b	(.f64 3 (.f64 v v))

rewrite53.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_1464`
26×	`associate-l_binary64_1383`
23×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `*-un-lft-identity_binary64_1442`
22×	`times-frac_binary64_1448` `add-cube-cbrt_binary64_1477`
20×	`sqrt-prod_binary64_1458`
18×	`sqrt-div_binary64_1459` `frac-times_binary64_1452`
17×	`pow1_binary64_1503`
15×	`flip3--_binary64_1446` `flip--_binary64_1417`
12×	`associate-r_binary64_1382`
10×	`associate-*r/_binary64_1384` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
9×	`associate-*l/_binary64_1385`
7×	`pow-prod-down_binary64_1513` `unswap-sqr_binary64_1410`
4×	`add-log-exp_binary64_1481`
3×	`*-commutative_binary64_1373`
2×	`cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `difference-of-squares_binary64_1411` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `pow1/2_binary64_1522`

Counts

4 → 129

Calls

4 calls:

15.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
13.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
7.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

series384.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
114.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
59.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
35.0ms	(.f64 3 (.f64 v v))

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5421	3693

prune232.0ms (5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Merged error: 0b

Counts

142 → 4

Compiler

Compiled 3945 to 2938 computations (25.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))) 3))
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
0.2b	(.f64 3 (.f64 v v))
1.0b	(pow.f64 (.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))) 3)

rewrite69.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`frac-times_binary64_1452`
36×	`flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
34×	`cube-div_binary64_1471`
28×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
24×	`associate-r/_binary64_1384` `associate-l/_binary64_1385`
20×	`pow1_binary64_1503`
17×	`cbrt-div_binary64_1474`
13×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
10×	`add-sqr-sqrt_binary64_1464`
9×	`pow-prod-down_binary64_1513` `*-un-lft-identity_binary64_1442`
8×	`cbrt-prod_binary64_1473` `add-cube-cbrt_binary64_1477`
6×	`associate-r_binary64_1382`
4×	`pow-exp_binary64_1510` `associate-l_binary64_1383` `add-log-exp_binary64_1481` `rem-cube-cbrt_binary64_1465`
3×	`pow-unpow_binary64_1519` `pow-pow_binary64_1514`
2×	`cbrt-undiv_binary64_1476` `cube-mult_binary64_1472` `cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `cube-prod_binary64_1470` `*-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `distribute-rgt-in_binary64_1392` `difference-of-squares_binary64_1411` `div-exp_binary64_1493` `unpow-prod-down_binary64_1521`
1×	`pow1/3_binary64_1524` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410` `rem-cbrt-cube_binary64_1466`

Counts

4 → 140

Calls

4 calls:

17.0ms	(pow.f64 (.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))) 3)
16.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
6.0ms	(.f64 3 (.f64 v v))
6.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))) 3))

series799.0ms (17.4%)

Counts

4 → 12

Calls

4 calls:

464.0ms	(pow.f64 (.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))) 3)
153.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
146.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))) 3))
35.0ms	(.f64 3 (.f64 v v))

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4982	5594
1	4982	5594

prune302.0ms (6.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	152	4	156

Merged error: 0b

Counts

156 → 4

Compiler

Compiled 5072 to 3856 computations (24% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 1 (pow.f64 v 4)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))
0.0b	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.0b	(/.f64 (.f64 (-.f64 1 (pow.f64 v 4)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (.f64 4 (+.f64 (.f64 v v) 1)))
0.2b	(.f64 3 (.f64 v v))

rewrite69.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
26×	`add-sqr-sqrt_binary64_1464`
20×	`associate-*r/_binary64_1384`
19×	`associate-l_binary64_1383`
18×	`pow1_binary64_1503`
16×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
15×	`*-un-lft-identity_binary64_1442`
14×	`sqrt-div_binary64_1459`
13×	`flip3--_binary64_1446` `flip--_binary64_1417`
10×	`sqrt-prod_binary64_1458` `add-cube-cbrt_binary64_1477`
9×	`pow-prod-down_binary64_1513`
8×	`associate-r_binary64_1382` `associate-/l/_binary64_1389` `frac-times_binary64_1452`
6×	`cbrt-undiv_binary64_1476` `difference-of-squares_binary64_1411` `div-exp_binary64_1493`
5×	`unswap-sqr_binary64_1410`
4×	`add-log-exp_binary64_1481` `associate-*l/_binary64_1385`
3×	`*-commutative_binary64_1373`
2×	`sqrt-pow1_binary64_1460` `associate-/r/_binary64_1388` `sqr-pow_binary64_1414` `pow1/2_binary64_1522` `unpow-prod-down_binary64_1521`
1×	`associate-/r_binary64_1386` `times-frac_binary64_1448` `div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l_binary64_1387` `sqrt-unprod_binary64_1462` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394`

Counts

4 → 119

Calls

4 calls:

21.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 v 4)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (.f64 4 (+.f64 (.f64 v v) 1)))
16.0ms	(.f64 (-.f64 1 (pow.f64 v 4)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))
9.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
7.0ms	(.f64 3 (.f64 v v))

series441.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 v 4)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (.f64 4 (+.f64 (.f64 v v) 1)))
116.0ms	(.f64 (-.f64 1 (pow.f64 v 4)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))
84.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
39.0ms	(.f64 3 (.f64 v v))

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4924	3632
1	4924	3632

prune255.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Merged error: 0b

Counts

135 → 4

Compiler

Compiled 4368 to 3273 computations (25.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (.f64 (pow.f64 v 4) 3/32) 1/4) (.f64 (*.f64 v v) 5/8))
0.0b	(.f64 (sqrt.f64 2) (-.f64 (+.f64 (.f64 (pow.f64 v 4) 3/32) 1/4) (.f64 (.f64 v v) 5/8)))
0.1b	(*.f64 (pow.f64 v 4) 3/32)
0.2b	(.f64 (.f64 v v) 5/8)

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1464`
16×	`add-exp-log_binary64_1480`
14×	`associate-l_binary64_1383`
13×	`add-cbrt-cube_binary64_1478`
11×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-r_binary64_1382` `add-log-exp_binary64_1481`
7×	`prod-exp_binary64_1491`
6×	`unswap-sqr_binary64_1410`
5×	`cbrt-unprod_binary64_1475`
4×	`pow-prod-down_binary64_1513` `sqrt-prod_binary64_1458` `unpow-prod-down_binary64_1521`
3×	`associate--l+_binary64_1379` `cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `*-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
2×	`associate-*r/_binary64_1384` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `sqr-pow_binary64_1414`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `pow-to-exp_binary64_1511`

Counts

4 → 88

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 2) (-.f64 (+.f64 (.f64 (pow.f64 v 4) 3/32) 1/4) (.f64 (.f64 v v) 5/8)))
9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 v 4) 3/32) 1/4) (.f64 (*.f64 v v) 5/8))
7.0ms	(.f64 (.f64 v v) 5/8)
6.0ms	(*.f64 (pow.f64 v 4) 3/32)

series204.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(.f64 (sqrt.f64 2) (-.f64 (+.f64 (.f64 (pow.f64 v 4) 3/32) 1/4) (.f64 (.f64 v v) 5/8)))
50.0ms	(*.f64 (pow.f64 v 4) 3/32)
46.0ms	(-.f64 (+.f64 (.f64 (pow.f64 v 4) 3/32) 1/4) (.f64 (*.f64 v v) 5/8))
38.0ms	(.f64 (.f64 v v) 5/8)

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	1782
1	4936	1782

prune122.0ms (2.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	100	4	104

Merged error: 0b

Counts

104 → 4

Compiler

Compiled 2169 to 1678 computations (22.6% saved)

regimes86.0ms (1.9%)

Compiler: Compiled 1090 to 891 computations (18.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	34
1	56	34

end0.0ms (0%)

sample861.0ms (18.8%)

Algorithm

1×

intervals

Results

393.0ms	8000×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 390 to 320 computations (17.9% saved)

Details

analyze5.0ms (0.1%)

sample18.0ms (0.4%)

simplify240.0ms (5.2%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

rewrite53.0ms (1.2%)

series384.0ms (8.4%)

simplify80.0ms (1.7%)

prune232.0ms (5%)

localize13.0ms (0.3%)

rewrite69.0ms (1.5%)

series799.0ms (17.4%)

simplify96.0ms (2.1%)

prune302.0ms (6.6%)

localize15.0ms (0.3%)

rewrite69.0ms (1.5%)

series441.0ms (9.6%)

simplify98.0ms (2.1%)

prune255.0ms (5.5%)

localize10.0ms (0.2%)

rewrite45.0ms (1%)

series204.0ms (4.4%)

simplify76.0ms (1.6%)

prune122.0ms (2.7%)

regimes86.0ms (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample861.0ms (18.8%)

Profiling