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)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	50×	body	1024	valid
4.0ms	140×	body	128	valid
3.0ms	34×	body	512	valid
1.0ms	23×	body	256	valid
1.0ms	9×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify249.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune2.0ms (0%)

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: 28.3b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite78.0ms (1.5%)

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:

44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
9.0ms	(/.f64 x (+.f64 x 1))

series128.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
25.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
24.0ms	(/.f64 x (+.f64 x 1))

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5369	2774

prune770.0ms (15.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	5	157

Merged error: 0.0b

Counts

157 → 5

Compiler

Compiled 13822 to 10405 computations (24.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0b	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0b	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

rewrite227.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

636×	`*-un-lft-identity_binary64_1455`
384×	`times-frac_binary64_1461`
246×	`add-sqr-sqrt_binary64_1477`
161×	`distribute-lft-out_binary64_1406`
118×	`add-cube-cbrt_binary64_1490`
96×	`swap-sqr_binary64_1422`
66×	`difference-of-squares_binary64_1424`
52×	`associate-r_binary64_1395` `distribute-lft-out--_binary64_1407` `associate-l_binary64_1396`
32×	`difference-of-sqr-1_binary64_1425`
30×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
19×	`associate-/r/_binary64_1401`
18×	`pow1_binary64_1516` `frac-sub_binary64_1464`
14×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `associate-l/_binary64_1398`
12×	`associate-/r*_binary64_1399`
11×	`associate-/l/_binary64_1402`
9×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `div-inv_binary64_1452`
8×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `unswap-sqr_binary64_1423`
6×	`add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
4×	`associate-/l*_binary64_1400`
2×	`pow-plus_binary64_1518` `*-commutative_binary64_1386` `pow2_binary64_1536` `pow-prod-up_binary64_1525` `pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`
1×	`clear-num_binary64_1454` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `frac-add_binary64_1463` `div-sub_binary64_1460`

Counts

4 → 369

Calls

4 calls:

62.0ms	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
42.0ms	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
21.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
18.0ms	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

series371.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
113.0ms	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
42.0ms	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
31.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))

simplify171.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

381 → 381

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4964	13063
1	4964	13063

prune1.4s (27.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	381	5	386

Merged error: 0.0b

Counts

386 → 5

Compiler

Compiled 18370 to 13290 computations (27.7% 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 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
16.4b	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

rewrite58.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*r/_binary64_1397`
32×	`frac-sub_binary64_1464`
31×	`flip-+_binary64_1429` `flip3-+_binary64_1458` `*-un-lft-identity_binary64_1455`
20×	`frac-times_binary64_1465`
19×	`add-sqr-sqrt_binary64_1477`
18×	`associate-/l/_binary64_1402` `flip--_binary64_1430` `flip3--_binary64_1459`
17×	`add-cube-cbrt_binary64_1490`
10×	`pow1_binary64_1516` `associate-*l/_binary64_1398`
9×	`times-frac_binary64_1461`
8×	`associate--l+_binary64_1392`
7×	`add-cbrt-cube_binary64_1491` `cancel-sign-sub-inv_binary64_1421` `add-exp-log_binary64_1493`
6×	`distribute-lft-out_binary64_1406` `distribute-rgt-in_binary64_1405` `swap-sqr_binary64_1422` `distribute-lft-in_binary64_1404`
5×	`add-log-exp_binary64_1494`
4×	`associate-r_binary64_1395` `associate-l_binary64_1396`
3×	`associate-/r_binary64_1399` `associate-/l_binary64_1400` `sub-neg_binary64_1448`
2×	`associate-/r/_binary64_1401` `associate--r+_binary64_1391`
1×	`prod-exp_binary64_1504` `pow-plus_binary64_1518` `div-exp_binary64_1506` `clear-num_binary64_1454` `*-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `pow2_binary64_1536` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `pow-prod-up_binary64_1525` `div-sub_binary64_1460` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423` `pow-sqr_binary64_1428`

Counts

3 → 126

Calls

3 calls:

16.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
12.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
10.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

series107.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
38.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
19.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4914	3610
1	4914	3610

prune241.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	137	3	140

Merged error: 0b

Counts

140 → 3

Compiler

Compiled 4677 to 3176 computations (32.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 -1 (*.f64 x 3))
12.6b	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
9×	`times-frac_binary64_1461`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`associate-/r_binary64_1399` `associate-/l_binary64_1400`
2×	`associate-/r/_binary64_1401` `pow1_binary64_1516` `associate-/l/_binary64_1402` `flip--_binary64_1430` `flip3--_binary64_1459`
1×	`flip-+_binary64_1429` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `div-inv_binary64_1452` `div-sub_binary64_1460`

Counts

2 → 44

Calls

2 calls:

7.0ms	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))
3.0ms	(-.f64 -1 (*.f64 x 3))

series78.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

43.0ms	(-.f64 -1 (*.f64 x 3))
34.0ms	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5103	987

prune66.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0b

Counts

53 → 3

Compiler

Compiled 1165 to 840 computations (27.9% saved)

regimes18.0ms (0.4%)

Compiler: Compiled 41 to 34 computations (17.1% saved)

bsearch34.0ms (0.7%)

Steps

Iters	Range		Point
10	5.78468073694592	257515084647.99667	184738.744021783
7	-1.4178631761808248e+25	-6.9340651965767e+22	-5.038504731857301e+23

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	79	52
1	79	52

end0.0ms (0%)

sample744.0ms (14.8%)

Algorithm

1×

intervals

Results

233.0ms	1926×	body	1024	valid
142.0ms	4316×	body	128	valid
93.0ms	1024×	body	512	valid
35.0ms	229×	body	2048	valid
34.0ms	505×	body	256	valid

Compiler

Compiled 88 to 70 computations (20.5% saved)

Details

analyze4.0ms (0.1%)

sample21.0ms (0.4%)

simplify249.0ms (5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite78.0ms (1.5%)

series128.0ms (2.5%)

simplify80.0ms (1.6%)

prune770.0ms (15.3%)

localize11.0ms (0.2%)

rewrite227.0ms (4.5%)

series371.0ms (7.4%)

simplify171.0ms (3.4%)

prune1.4s (27.3%)

localize12.0ms (0.2%)

rewrite58.0ms (1.1%)

series107.0ms (2.1%)

simplify89.0ms (1.8%)

prune241.0ms (4.8%)

localize6.0ms (0.1%)

rewrite14.0ms (0.3%)

series78.0ms (1.5%)

simplify63.0ms (1.2%)

prune66.0ms (1.3%)

regimes18.0ms (0.4%)

bsearch34.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample744.0ms (14.8%)

Profiling