Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	78×	body	1024	valid
4.0ms	131×	body	128	valid
3.0ms	29×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify243.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

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: 30.5b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite74.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_1455`
88×	`times-frac_binary64_1461`
85×	`add-sqr-sqrt_binary64_1477`
37×	`add-cube-cbrt_binary64_1490`
34×	`cancel-sign-sub-inv_binary64_1421`
27×	`distribute-lft-out_binary64_1406`
22×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
11×	`associate-/r*_binary64_1399`
9×	`difference-of-sqr-1_binary64_1425`
7×	`add-cbrt-cube_binary64_1491` `associate-/l*_binary64_1400` `add-exp-log_binary64_1493`
6×	`associate-/r/_binary64_1401`
5×	`add-log-exp_binary64_1494`
3×	`pow1_binary64_1516` `flip--_binary64_1430` `div-inv_binary64_1452` `flip3--_binary64_1459`
2×	`flip-+_binary64_1429` `associate-/l/_binary64_1402` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `flip3-+_binary64_1458`
1×	`diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448`

Counts

3 → 147

Calls

3 calls:

45.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series130.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

81.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
25.0ms	(/.f64 x (+.f64 x 1))
24.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify80.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5369	2774

prune703.0ms (21.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0b

Counts

157 → 4

Compiler

Compiled 13220 to 9824 computations (25.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
7.6b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

rewrite55.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_1477`
69×	`*-un-lft-identity_binary64_1455`
56×	`times-frac_binary64_1461`
37×	`add-cube-cbrt_binary64_1490`
27×	`associate-r_binary64_1395`
19×	`add-exp-log_binary64_1493`
14×	`difference-of-squares_binary64_1424`
13×	`add-cbrt-cube_binary64_1491`
11×	`associate-/r*_binary64_1399`
7×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516` `difference-of-sqr-1_binary64_1425`
6×	`associate-/r/_binary64_1401` `add-log-exp_binary64_1494` `associate-/l*_binary64_1400` `frac-sub_binary64_1464`
5×	`distribute-lft-out_binary64_1406` `flip-+_binary64_1429` `div-exp_binary64_1506` `flip3-+_binary64_1458`
4×	`prod-exp_binary64_1504` `frac-times_binary64_1465` `associate-l_binary64_1396` `associate-*l/_binary64_1398`
3×	`flip--_binary64_1430` `cbrt-undiv_binary64_1489` `div-inv_binary64_1452` `flip3--_binary64_1459` `unswap-sqr_binary64_1423`
2×	`associate-*r/_binary64_1397` `1-exp_binary64_1499` `clear-num_binary64_1454` `un-div-inv_binary64_1453` `frac-2neg_binary64_1466` `cbrt-unprod_binary64_1488` `rec-exp_binary64_1505`
1×	`inv-pow_binary64_1540` `pow-flip_binary64_1529` `*-commutative_binary64_1386` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `pow-prod-down_binary64_1526`

Counts

4 → 155

Calls

4 calls:

17.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
13.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series146.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
26.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
24.0ms	(/.f64 x (+.f64 x 1))
18.0ms	(/.f64 1 (-.f64 x 1))

simplify70.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5032	2543

prune185.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	167	4	171

Merged error: 0b

Counts

171 → 4

Compiler

Compiled 3509 to 2547 computations (27.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.2b	(/.f64 3 (pow.f64 x 3))
0.4b	(/.f64 -1 (*.f64 x x))
5.8b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite100.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_1455`
68×	`times-frac_binary64_1461`
44×	`add-sqr-sqrt_binary64_1477`
40×	`add-cube-cbrt_binary64_1490`
14×	`unpow3_binary64_1521` `add-exp-log_binary64_1493`
13×	`associate-/r*_binary64_1399` `cancel-sign-sub-inv_binary64_1421`
12×	`unpow-prod-down_binary64_1534` `cube-prod_binary64_1483`
11×	`distribute-lft-out_binary64_1406` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
8×	`distribute-rgt-out_binary64_1408`
6×	`associate-/l*_binary64_1400` `div-inv_binary64_1452`
5×	`div-exp_binary64_1506`
4×	`cube-mult_binary64_1485` `pow1_binary64_1516` `sqr-pow_binary64_1427`
3×	`cbrt-undiv_binary64_1489` `frac-sub_binary64_1464`
2×	`distribute-lft-out--_binary64_1407` `flip-+_binary64_1429` `difference-of-squares_binary64_1424` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `flip3-+_binary64_1458` `distribute-rgt1-in_binary64_1411` `sum-log_binary64_1546` `frac-add_binary64_1463`
1×	`prod-exp_binary64_1504` `associate--r+_binary64_1391` `pow-to-exp_binary64_1524` `flip--_binary64_1430` `cbrt-unprod_binary64_1488` `sub-neg_binary64_1448` `pow-exp_binary64_1523` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

4 → 141

Calls

4 calls:

43.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
29.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))

series208.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
44.0ms	(/.f64 3 (pow.f64 x 3))
34.0ms	(/.f64 -1 (*.f64 x x))
30.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify95.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4952	2429
1	4952	2429

prune169.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	153	4	157

Merged error: 0b

Counts

157 → 4

Compiler

Compiled 3113 to 2198 computations (29.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 x (+.f64 3 x))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
4×	`associate-r_binary64_1395`
3×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-cube-cbrt_binary64_1490` `associate-l_binary64_1396` `add-exp-log_binary64_1493`
2×	`associate-*r/_binary64_1397`
1×	`prod-exp_binary64_1504` `distribute-lft-out_binary64_1406` `distribute-rgt-in_binary64_1405` `flip-+_binary64_1429` `add-log-exp_binary64_1494` `*-commutative_binary64_1386` `distribute-lft-in_binary64_1404` `cbrt-unprod_binary64_1488` `flip3-+_binary64_1458` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

1 → 23

Calls

1 calls:

7.0ms

(*.f64 x (+.f64 3 x))

series57.0ms (1.7%)

Counts

1 → 3

Calls

1 calls:

57.0ms

(*.f64 x (+.f64 3 x))

simplify71.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5387	233

prune16.0ms (0.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	26	4	30

Merged error: 0b

Counts

30 → 4

Compiler

Compiled 287 to 207 computations (27.9% saved)

regimes34.0ms (1%)

Compiler: Compiled 128 to 102 computations (20.3% saved)

bsearch37.0ms (1.1%)

Steps

Iters	Range		Point
10	6.678391225351904	484360414951.354	12064.14325946773
9	-4590392.709799706	-0.004645704772350229	-12595.975526924205

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	55
1	88	55

end0.0ms (0%)

sample795.0ms (23.8%)

Algorithm

1×

intervals

Results

264.0ms	1994×	body	1024	valid
152.0ms	4341×	body	128	valid
91.0ms	917×	body	512	valid
37.0ms	523×	body	256	valid
37.0ms	225×	body	2048	valid

Compiler

Compiled 101 to 80 computations (20.8% saved)

Details

analyze4.0ms (0.1%)

sample24.0ms (0.7%)

simplify243.0ms (7.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite74.0ms (2.2%)

series130.0ms (3.9%)

simplify80.0ms (2.4%)

prune703.0ms (21.1%)

localize8.0ms (0.2%)

rewrite55.0ms (1.6%)

series146.0ms (4.4%)

simplify70.0ms (2.1%)

prune185.0ms (5.5%)

localize10.0ms (0.3%)

rewrite100.0ms (3%)

series208.0ms (6.2%)

simplify95.0ms (2.8%)

prune169.0ms (5.1%)

localize4.0ms (0.1%)

rewrite8.0ms (0.2%)

series57.0ms (1.7%)

simplify71.0ms (2.1%)

prune16.0ms (0.5%)

regimes34.0ms (1%)

bsearch37.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample795.0ms (23.8%)

Profiling