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)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	62×	body	1024	valid
5.0ms	140×	body	128	valid
3.0ms	29×	body	512	valid
2.0ms	11×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify249.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

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: 29.5b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite72.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 114

Calls

2 calls:

45.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series99.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

71.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
28.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5330	2309

prune410.0ms (11.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	117	4	121

Merged error: 0.0b

Counts

121 → 4

Compiler

Compiled 7323 to 5505 computations (24.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x 1) (+.f64 x 1))
0.0b	(/.f64 1 (/.f64 (-.f64 x 1) (+.f64 x 1)))
3.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 x 1))))

rewrite195.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Rules

449×	`times-frac_binary64_1461`
399×	`*-un-lft-identity_binary64_1455`
335×	`add-sqr-sqrt_binary64_1477`
170×	`add-cube-cbrt_binary64_1490`
107×	`cancel-sign-sub-inv_binary64_1421`
76×	`difference-of-squares_binary64_1424`
58×	`distribute-lft-out_binary64_1406`
38×	`associate-/r*_binary64_1399`
37×	`distribute-lft-out--_binary64_1407`
33×	`difference-of-sqr-1_binary64_1425`
18×	`associate-/r/_binary64_1401`
16×	`add-exp-log_binary64_1493`
11×	`div-inv_binary64_1452`
10×	`add-cbrt-cube_binary64_1491` `associate-/l*_binary64_1400`
8×	`flip-+_binary64_1429` `div-exp_binary64_1506` `flip3-+_binary64_1458`
5×	`add-log-exp_binary64_1494`
4×	`pow1_binary64_1516` `cbrt-undiv_binary64_1489`
2×	`associate-/l/_binary64_1402` `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-flip_binary64_1529` `diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `div-sub_binary64_1460`

Counts

3 → 349

Calls

3 calls:

111.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 x 1))))
15.0ms	(/.f64 1 (/.f64 (-.f64 x 1) (+.f64 x 1)))
10.0ms	(/.f64 (-.f64 x 1) (+.f64 x 1))

series123.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

72.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 x 1))))
26.0ms	(/.f64 1 (/.f64 (-.f64 x 1) (+.f64 x 1)))
24.0ms	(/.f64 (-.f64 x 1) (+.f64 x 1))

simplify338.0ms (9.4%)

Algorithm

1×	egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5316	8316

prune516.0ms (14.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	358	0	358
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	358	4	362

Merged error: 0.0b

Counts

362 → 4

Compiler

Compiled 8230 to 6046 computations (26.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite9.0ms (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))

series62.0ms (1.7%)

Counts

1 → 3

Calls

1 calls:

62.0ms

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

simplify74.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5387	233

prune19.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0.0b

Counts

30 → 4

Compiler

Compiled 302 to 219 computations (27.5% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 3 (pow.f64 x 3))
0.2b	(/.f64 -1 (*.f64 x x))
6.0b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite68.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

45.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.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))

series105.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(/.f64 3 (pow.f64 x 3))
32.0ms	(/.f64 -1 (*.f64 x x))
29.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify91.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4961	2020
1	4961	2020

prune171.0ms (4.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	126	6	132

Merged error: 0.0b

Counts

132 → 6

Compiler

Compiled 3140 to 2263 computations (27.9% saved)

regimes45.0ms (1.3%)

Compiler: Compiled 246 to 198 computations (19.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	65
1	81	65

end0.0ms (0%)

sample829.0ms (23%)

Algorithm

1×

intervals

Results

243.0ms	1973×	body	1024	valid
154.0ms	4319×	body	128	valid
93.0ms	1019×	body	512	valid
31.0ms	494×	body	256	valid
30.0ms	195×	body	2048	valid

Compiler

Compiled 167 to 133 computations (20.4% saved)

Details

analyze4.0ms (0.1%)

sample23.0ms (0.6%)

simplify249.0ms (6.9%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite72.0ms (2%)

series99.0ms (2.7%)

simplify75.0ms (2.1%)

prune410.0ms (11.4%)

localize7.0ms (0.2%)

rewrite195.0ms (5.4%)

series123.0ms (3.4%)

simplify338.0ms (9.4%)

prune516.0ms (14.3%)

localize4.0ms (0.1%)

rewrite9.0ms (0.2%)

series62.0ms (1.7%)

simplify74.0ms (2.1%)

prune19.0ms (0.5%)

localize10.0ms (0.3%)

rewrite68.0ms (1.9%)

series105.0ms (2.9%)

simplify91.0ms (2.5%)

prune171.0ms (4.7%)

regimes45.0ms (1.3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample829.0ms (23%)

Profiling