Details

analyze8.0ms (0.2%)

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)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

15.0ms	63×	body	1024	valid
9.0ms	137×	body	128	valid
7.0ms	39×	body	512	valid
2.0ms	7×	body	2048	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify425.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune4.0ms (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: 29.1b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize12.0ms (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))
2.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite130.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_1425`
60×	`times-frac_binary64_1431`
57×	`add-sqr-sqrt_binary64_1446`
25×	`add-cube-cbrt_binary64_1457`
20×	`distribute-lft-out_binary64_1378`
18×	`distribute-lft-out--_binary64_1379`
14×	`difference-of-squares_binary64_1394`
11×	`associate-/r*_binary64_1371`
7×	`add-cbrt-cube_binary64_1458` `associate-/l*_binary64_1372` `add-exp-log_binary64_1460`
5×	`difference-of-sqr-1_binary64_1395` `add-log-exp_binary64_1461`
4×	`associate-/r/_binary64_1373`
3×	`pow1_binary64_1483`
2×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `flip3-+_binary64_1428` `clear-num_binary64_1424` `div-inv_binary64_1422` `flip-+_binary64_1399` `div-exp_binary64_1473` `associate-/l/_binary64_1374` `flip3--_binary64_1429` `cbrt-undiv_binary64_1456`
1×	`diff-log_binary64_1514` `sub-neg_binary64_1418` `frac-sub_binary64_1434`

Counts

3 → 113

Calls

3 calls:

76.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
17.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
10.0ms	(/.f64 x (+.f64 x 1))

series238.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

140.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
50.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
48.0ms	(/.f64 x (+.f64 x 1))

simplify135.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5940	2299

prune326.0ms (6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

Compiler

Compiled 2550 to 1821 computations (28.6% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.1b	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
7.2b	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
14.0b	(/.f64 x (+.f64 (*.f64 x x) -1))

rewrite137.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_1425`
64×	`add-sqr-sqrt_binary64_1446`
53×	`times-frac_binary64_1431`
35×	`add-cube-cbrt_binary64_1457`
18×	`associate-l_binary64_1368`
13×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
12×	`difference-of-squares_binary64_1394`
11×	`associate-/r*_binary64_1371`
8×	`distribute-lft-out_binary64_1378`
7×	`associate-r_binary64_1367` `difference-of-sqr--1_binary64_1396` `associate-/l*_binary64_1372`
6×	`flip--_binary64_1400` `distribute-lft-out--_binary64_1379` `difference-of-sqr-1_binary64_1395` `associate-/r/_binary64_1373` `pow1_binary64_1483` `flip3--_binary64_1429` `add-log-exp_binary64_1461`
5×	`sub-neg_binary64_1418` `frac-sub_binary64_1434`
4×	`associate-*r/_binary64_1369` `frac-times_binary64_1435`
3×	`flip3-+_binary64_1428` `div-inv_binary64_1422` `flip-+_binary64_1399` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
2×	`distribute-lft-in_binary64_1376` `frac-2neg_binary64_1436` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `associate--l+_binary64_1364` `distribute-rgt-in_binary64_1377` `associate-/l/_binary64_1374` `associate-*l/_binary64_1370`
1×	`diff-log_binary64_1514` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 153

Calls

4 calls:

42.0ms	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
29.0ms	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
16.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
12.0ms	(/.f64 x (+.f64 (*.f64 x x) -1))

series432.0ms (8%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
106.0ms	(/.f64 x (+.f64 (*.f64 x x) -1))
75.0ms	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
50.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify140.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4988	3017
1	4988	3017

prune368.0ms (6.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	165	4	169

Merged error: 0.0b

Counts

169 → 4

Compiler

Compiled 4226 to 2768 computations (34.5% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
4×	`associate-r_binary64_1367`
3×	`add-cube-cbrt_binary64_1457` `associate-l_binary64_1368` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460`
2×	`associate-*r/_binary64_1369`
1×	`distribute-lft-in_binary64_1376` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `flip3-+_binary64_1428` `cbrt-unprod_binary64_1455` `distribute-lft-out_binary64_1378` `distribute-rgt-in_binary64_1377` `flip-+_binary64_1399` `add-log-exp_binary64_1461` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

1 → 23

Calls

1 calls:

12.0ms

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

series109.0ms (2%)

Counts

1 → 3

Calls

1 calls:

109.0ms

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

simplify145.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4875	233
1	4875	233

prune37.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	26	4	30

Merged error: 0.0b

Counts

30 → 4

Compiler

Compiled 333 to 243 computations (27% saved)

localize19.0ms (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))
0.2b	(/.f64 -1 (*.f64 x x))
7.2b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite182.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1431` `*-un-lft-identity_binary64_1425`
39×	`add-sqr-sqrt_binary64_1446`
35×	`add-cube-cbrt_binary64_1457`
14×	`add-exp-log_binary64_1460`
13×	`associate-/r*_binary64_1371`
12×	`unpow-prod-down_binary64_1501` `cube-prod_binary64_1450`
11×	`add-cbrt-cube_binary64_1458` `add-log-exp_binary64_1461`
9×	`unpow3_binary64_1488`
6×	`distribute-lft-out_binary64_1378` `associate-/l*_binary64_1372`
5×	`div-exp_binary64_1473`
4×	`distribute-rgt-out_binary64_1380` `div-inv_binary64_1422` `cube-mult_binary64_1452` `pow1_binary64_1483` `sqr-pow_binary64_1397`
3×	`frac-sub_binary64_1434` `cbrt-undiv_binary64_1456`
2×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `distribute-lft-out--_binary64_1379` `flip3-+_binary64_1428` `clear-num_binary64_1424` `sum-log_binary64_1513` `difference-of-squares_binary64_1394` `flip-+_binary64_1399` `frac-add_binary64_1433`
1×	`flip--_binary64_1400` `prod-exp_binary64_1471` `pow-to-exp_binary64_1491` `sub-neg_binary64_1418` `cbrt-unprod_binary64_1455` `pow-exp_binary64_1490` `distribute-rgt1-in_binary64_1383` `associate--r+_binary64_1363` `+-commutative_binary64_1357` `flip3--_binary64_1429`

Counts

4 → 128

Calls

4 calls:

81.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
56.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
11.0ms	(/.f64 3 (pow.f64 x 3))
9.0ms	(/.f64 -1 (*.f64 x x))

series428.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
95.0ms	(/.f64 3 (pow.f64 x 3))
61.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
58.0ms	(/.f64 -1 (*.f64 x x))

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5229	2228

prune278.0ms (5.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	139	5	144

Merged error: 0.0b

Counts

144 → 5

Compiler

Compiled 2890 to 1997 computations (30.9% saved)

regimes53.0ms (1%)

Compiler: Compiled 92 to 73 computations (20.7% saved)

bsearch63.0ms (1.2%)

Steps

Iters	Range		Point
10	2.8653701949221112e-05	2489540.0261881663	9177.919479012575
7	-189127.71728140858	-3348.1132572886618	-15408.542485374985

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	92	64
1	92	64

end0.0ms (0%)

sample1.6s (28.9%)

Algorithm

1×

intervals

Results

472.0ms	1948×	body	1024	valid
281.0ms	4322×	body	128	valid
189.0ms	1038×	body	512	valid
68.0ms	221×	body	2048	valid
64.0ms	471×	body	256	valid

Compiler

Compiled 147 to 114 computations (22.4% saved)

Details

analyze8.0ms (0.2%)

sample44.0ms (0.8%)

simplify425.0ms (7.8%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite130.0ms (2.4%)

series238.0ms (4.4%)

simplify135.0ms (2.5%)

prune326.0ms (6%)

localize20.0ms (0.4%)

rewrite137.0ms (2.5%)

series432.0ms (8%)

simplify140.0ms (2.6%)

prune368.0ms (6.8%)

localize9.0ms (0.2%)

rewrite15.0ms (0.3%)

series109.0ms (2%)

simplify145.0ms (2.7%)

prune37.0ms (0.7%)

localize19.0ms (0.3%)

rewrite182.0ms (3.4%)

series428.0ms (7.9%)

simplify92.0ms (1.7%)

prune278.0ms (5.1%)

regimes53.0ms (1%)

bsearch63.0ms (1.2%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.6s (28.9%)

Profiling