Details

analyze7.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 29 to 20 computations (31% saved)

sample29.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify169.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5047	13

prune5.0ms (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: 0.9b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 1 (*.f64 i i))
1.0b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1464`
35×	`times-frac_binary64_1448`
33×	`*-un-lft-identity_binary64_1442`
17×	`add-cube-cbrt_binary64_1477`
15×	`add-exp-log_binary64_1480`
12×	`difference-of-squares_binary64_1411`
10×	`pow1_binary64_1503`
9×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478`
8×	`distribute-lft-out--_binary64_1394`
6×	`div-inv_binary64_1439` `associate-/l*_binary64_1387` `pow-flip_binary64_1516`
5×	`div-exp_binary64_1493`
3×	`cbrt-undiv_binary64_1476` `prod-exp_binary64_1491`
2×	`associate-/r/_binary64_1388` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453`
1×	`pow2_binary64_1523` `inv-pow_binary64_1527` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `flip--_binary64_1417` `pow-prod-up_binary64_1512`

Counts

2 → 81

Calls

2 calls:

16.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
7.0ms	(/.f64 1 (*.f64 i i))

series39.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
17.0ms	(/.f64 1 (*.f64 i i))

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5049	1212

prune106.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0b

Counts

89 → 4

Compiler

Compiled 1256 to 961 computations (23.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 2 (/.f64 1 i))
0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite100.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`add-sqr-sqrt_binary64_1464`
108×	`*-un-lft-identity_binary64_1442`
107×	`times-frac_binary64_1448`
55×	`add-cube-cbrt_binary64_1477`
30×	`associate-r_binary64_1382`
24×	`difference-of-squares_binary64_1411`
21×	`associate-l_binary64_1383`
20×	`add-cbrt-cube_binary64_1478` `div-inv_binary64_1439` `add-exp-log_binary64_1480`
16×	`distribute-lft-out--_binary64_1394`
14×	`distribute-lft-out_binary64_1393`
13×	`associate-/r*_binary64_1386` `cancel-sign-sub-inv_binary64_1408`
8×	`associate-/r/_binary64_1388`
6×	`cbrt-undiv_binary64_1476` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481` `pow1_binary64_1503` `div-exp_binary64_1493`
4×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
3×	`flip3--_binary64_1446` `flip--_binary64_1417`
2×	`clear-num_binary64_1441` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`associate-r/_binary64_1384` `sub-neg_binary64_1435` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `diff-log_binary64_1534` `frac-times_binary64_1452` `associate-*l/_binary64_1385`

Counts

4 → 190

Calls

4 calls:

31.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
13.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
11.0ms	(-.f64 2 (/.f64 1 i))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

series72.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
23.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
15.0ms	(-.f64 2 (/.f64 1 i))
10.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4910	3644
1	4910	3644

prune410.0ms (6.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	202	4	206

Merged error: 0b

Counts

206 → 4

Compiler

Compiled 4399 to 3815 computations (13.3% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
0.1b	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
0.3b	(/.f64 1 (*.f64 i i))
33.2b	(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite196.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

528×	`times-frac_binary64_1448`
424×	`add-sqr-sqrt_binary64_1464`
388×	`*-un-lft-identity_binary64_1442`
273×	`sqrt-prod_binary64_1458`
156×	`add-cube-cbrt_binary64_1477`
152×	`difference-of-squares_binary64_1411`
57×	`distribute-lft-out--_binary64_1394`
49×	`distribute-lft-out_binary64_1393`
38×	`div-inv_binary64_1439`
34×	`associate-/r/_binary64_1388`
24×	`associate-/l*_binary64_1387`
22×	`add-exp-log_binary64_1480`
21×	`pow1_binary64_1503`
19×	`associate-/r*_binary64_1386`
16×	`add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
12×	`pow-flip_binary64_1516`
8×	`sqrt-pow1_binary64_1460` `div-exp_binary64_1493`
6×	`cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481`
3×	`rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `prod-exp_binary64_1491`
2×	`pow2_binary64_1523` `inv-pow_binary64_1527` `pow-plus_binary64_1505` `1-exp_binary64_1486` `pow-prod-down_binary64_1513` `rec-exp_binary64_1492` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
1×	`cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `pow1/2_binary64_1522`

Counts

4 → 393

Calls

4 calls:

46.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
10.0ms	(/.f64 1 (*.f64 i i))
9.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
9.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

series144.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
47.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
13.0ms	(/.f64 1 (*.f64 i i))
6.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

simplify298.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5181	15009

prune1.8s (28.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	404	1	405
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	406	3	409

Merged error: 0b

Counts

409 → 3

Compiler

Compiled 11669 to 10170 computations (12.8% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/4 (+.f64 (fabs.f64 (/.f64 1 i)) 2))
0.3b	(/.f64 1 (*.f64 i i))
22.9b	(cbrt.f64 (pow.f64 (/.f64 1/4 (+.f64 (fabs.f64 (/.f64 1 i)) 2)) 3))
33.2b	(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite61.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64_1442`
44×	`times-frac_binary64_1448`
42×	`cbrt-prod_binary64_1473`
36×	`add-sqr-sqrt_binary64_1464`
34×	`add-cube-cbrt_binary64_1477`
21×	`pow1_binary64_1503`
18×	`cube-prod_binary64_1470` `unpow-prod-down_binary64_1521`
17×	`add-exp-log_binary64_1480`
12×	`pow-flip_binary64_1516`
11×	`add-cbrt-cube_binary64_1478`
10×	`distribute-lft-out_binary64_1393`
8×	`sqrt-pow1_binary64_1460`
7×	`sqrt-prod_binary64_1458`
6×	`associate-/r/_binary64_1388` `associate-/l*_binary64_1387`
5×	`associate-/r*_binary64_1386` `div-inv_binary64_1439` `div-exp_binary64_1493`
4×	`add-log-exp_binary64_1481`
3×	`cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491`
2×	`pow2_binary64_1523` `inv-pow_binary64_1527` `clear-num_binary64_1441` `pow-plus_binary64_1505` `1-exp_binary64_1486` `pow-prod-down_binary64_1513` `rec-exp_binary64_1492` `pow-sqr_binary64_1415` `frac-2neg_binary64_1453` `pow-prod-up_binary64_1512`
1×	`cube-mult_binary64_1472` `cbrt-unprod_binary64_1475` `cbrt-div_binary64_1474` `sqrt-div_binary64_1459` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `pow1/3_binary64_1524` `pow1/2_binary64_1522` `cube-div_binary64_1471` `rem-cbrt-cube_binary64_1466`

Counts

4 → 144

Calls

4 calls:

17.0ms	(cbrt.f64 (pow.f64 (/.f64 1/4 (+.f64 (fabs.f64 (/.f64 1 i)) 2)) 3))
10.0ms	(/.f64 1 (*.f64 i i))
9.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))
8.0ms	(/.f64 1/4 (+.f64 (fabs.f64 (/.f64 1 i)) 2))

series135.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 1/4 (+.f64 (fabs.f64 (/.f64 1 i)) 2))
50.0ms	(cbrt.f64 (pow.f64 (/.f64 1/4 (+.f64 (fabs.f64 (/.f64 1 i)) 2)) 3))
21.0ms	(/.f64 1 (*.f64 i i))
6.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

simplify158.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4890	2153
1	4890	2153

prune400.0ms (6.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	156	3	159

Merged error: 0b

Counts

159 → 3

Compiler

Compiled 3796 to 3179 computations (16.3% saved)

regimes131.0ms (2.1%)

Compiler: Compiled 706 to 608 computations (13.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample1.7s (27.2%)

Algorithm

1×

intervals

Results

703.0ms	8000×	body	128	valid
156.0ms	8000×	pre	128	true

Compiler

Compiled 371 to 321 computations (13.5% saved)

Details

analyze7.0ms (0.1%)

sample29.0ms (0.5%)

simplify169.0ms (2.7%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite29.0ms (0.5%)

series39.0ms (0.6%)

simplify93.0ms (1.5%)

prune106.0ms (1.7%)

localize12.0ms (0.2%)

rewrite100.0ms (1.6%)

series72.0ms (1.2%)

simplify91.0ms (1.5%)

prune410.0ms (6.6%)

localize26.0ms (0.4%)

rewrite196.0ms (3.2%)

series144.0ms (2.3%)

simplify298.0ms (4.8%)

prune1.8s (28.6%)

localize31.0ms (0.5%)

rewrite61.0ms (1%)

series135.0ms (2.2%)

simplify158.0ms (2.5%)

prune400.0ms (6.4%)

regimes131.0ms (2.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (27.2%)

Profiling