Details

analyze7.0ms (0.2%)

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)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify211.0ms (7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4983	13
1	4983	13

prune6.0ms (0.2%)

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: 0.5b

Counts

2 → 2

Compiler

Compiled 77 to 58 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
0.5b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.7b	(/.f64 1 (*.f64 i i))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_1477`
40×	`times-frac_binary64_1461` `*-un-lft-identity_binary64_1455`
20×	`add-cube-cbrt_binary64_1490`
16×	`add-exp-log_binary64_1493`
15×	`difference-of-squares_binary64_1424`
11×	`pow1_binary64_1516`
10×	`distribute-lft-out--_binary64_1407` `add-cbrt-cube_binary64_1491`
9×	`associate-/r*_binary64_1399`
8×	`div-inv_binary64_1452`
7×	`cancel-sign-sub-inv_binary64_1421`
6×	`pow-flip_binary64_1529` `associate-/l*_binary64_1400`
5×	`div-exp_binary64_1506` `add-log-exp_binary64_1494`
3×	`prod-exp_binary64_1504` `cbrt-undiv_binary64_1489`
2×	`associate-/r/_binary64_1401` `1-exp_binary64_1499` `clear-num_binary64_1454` `flip--_binary64_1430` `frac-2neg_binary64_1466` `rec-exp_binary64_1505` `flip3--_binary64_1459`
1×	`inv-pow_binary64_1540` `pow-plus_binary64_1518` `pow2_binary64_1536` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `sub-neg_binary64_1448` `pow-prod-up_binary64_1525` `pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`

Counts

3 → 104

Calls

3 calls:

9.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
7.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
5.0ms	(/.f64 1 (*.f64 i i))

series106.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
33.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
24.0ms	(/.f64 1 (*.f64 i i))

simplify66.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4941	1524
1	4941	1524

prune138.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	3	115

Merged error: 0b

Counts

115 → 3

Compiler

Compiled 2153 to 1664 computations (22.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite56.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64_1455`
69×	`add-sqr-sqrt_binary64_1477`
58×	`times-frac_binary64_1461`
41×	`add-cube-cbrt_binary64_1490`
21×	`associate-r_binary64_1395`
20×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
18×	`associate-l_binary64_1396`
9×	`associate-/r*_binary64_1399`
8×	`associate-/r/_binary64_1401` `distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
7×	`distribute-lft-out_binary64_1406`
6×	`pow1_binary64_1516` `div-exp_binary64_1506` `add-log-exp_binary64_1494` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400`
4×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `unswap-sqr_binary64_1423`
3×	`flip--_binary64_1430` `cancel-sign-sub-inv_binary64_1421` `flip3--_binary64_1459`
2×	`flip-+_binary64_1429` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `flip3-+_binary64_1458`
1×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `-commutative_binary64_1386` `diff-log_binary64_1547` `sub-neg_binary64_1448` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526`

Counts

4 → 149

Calls

4 calls:

24.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
6.0ms	(/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i))))
6.0ms	(/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i))))
4.0ms	(-.f64 2 (fabs.f64 (/.f64 1 i)))

series319.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
71.0ms	(/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i))))
60.0ms	(/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i))))
17.0ms	(-.f64 2 (fabs.f64 (/.f64 1 i)))

simplify92.0ms (3%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5339	3510

prune261.0ms (8.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	161	3	164

Merged error: 0b

Counts

164 → 3

Compiler

Compiled 3961 to 3529 computations (10.9% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.2b	(.f64 (.f64 i i) -1/4)

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `cancel-sign-sub-inv_binary64_1421` `add-exp-log_binary64_1493`
6×	`add-sqr-sqrt_binary64_1477`
5×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
4×	`add-log-exp_binary64_1494`
3×	`prod-exp_binary64_1504` `associate-r_binary64_1395` `unpow-prod-down_binary64_1534` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
1×	`-commutative_binary64_1386` `sqr-pow_binary64_1427` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459` `associate-l*_binary64_1396` `unswap-sqr_binary64_1423`

Counts

2 → 37

Calls

2 calls:

8.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
6.0ms	(.f64 (.f64 i i) -1/4)

series155.0ms (5.1%)

Counts

2 → 6

Calls

2 calls:

112.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
43.0ms	(.f64 (.f64 i i) -1/4)

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4936	468
1	4936	468

prune43.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	43	3	46

Merged error: 0b

Counts

46 → 3

Compiler

Compiled 809 to 568 computations (29.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (*.f64 i i) (*.f64 i i))

15.8b

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

44.6b

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

rewrite125.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

302×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
168×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
114×	`pow1_binary64_1516`
76×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
38×	`times-frac_binary64_1461`
36×	`pow-prod-up_binary64_1525`
23×	`pow-prod-down_binary64_1526`
22×	`add-sqr-sqrt_binary64_1477` `pow-sqr_binary64_1428` `*-un-lft-identity_binary64_1455`
18×	`pow-plus_binary64_1518`
16×	`add-cube-cbrt_binary64_1490`
13×	`pow2_binary64_1536`
12×	`difference-of-squares_binary64_1424`
9×	`div-inv_binary64_1452`
7×	`associate-/r*_binary64_1399`
6×	`associate-/l*_binary64_1400` `difference-of-sqr-1_binary64_1425`
3×	`add-log-exp_binary64_1494`
2×	`associate-/r/_binary64_1401` `clear-num_binary64_1454` `frac-2neg_binary64_1466`
1×	`associate-r_binary64_1395` `swap-sqr_binary64_1422` `associate-/l/_binary64_1402` `-commutative_binary64_1386` `flip--_binary64_1430` `flip3--_binary64_1459` `associate-l*_binary64_1396` `unswap-sqr_binary64_1423`

Counts

3 → 232

Calls

3 calls:

40.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

29.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

10.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

series143.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

60.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

42.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

40.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

simplify99.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4834	3454
1	4834	3454

prune280.0ms (9.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	241	3	244

Merged error: 0b

Counts

244 → 3

Compiler

Compiled 4867 to 3610 computations (25.8% saved)

regimes26.0ms (0.9%)

Compiler: Compiled 166 to 126 computations (24.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	26
1	24	26

end0.0ms (0%)

sample741.0ms (24.4%)

Algorithm

1×

intervals

Results

416.0ms	8000×	body	128	valid
94.0ms	8000×	pre	128	true

Compiler

Compiled 103 to 82 computations (20.4% saved)

Details

analyze7.0ms (0.2%)

sample22.0ms (0.7%)

simplify211.0ms (7%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite29.0ms (1%)

series106.0ms (3.5%)

simplify66.0ms (2.2%)

prune138.0ms (4.6%)

localize9.0ms (0.3%)

rewrite56.0ms (1.8%)

series319.0ms (10.5%)

simplify92.0ms (3%)

prune261.0ms (8.6%)

localize10.0ms (0.3%)

rewrite20.0ms (0.6%)

series155.0ms (5.1%)

simplify54.0ms (1.8%)

prune43.0ms (1.4%)

localize9.0ms (0.3%)

rewrite125.0ms (4.1%)

series143.0ms (4.7%)

simplify99.0ms (3.3%)

prune280.0ms (9.2%)

regimes26.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample741.0ms (24.4%)

Profiling