Details

analyze456.0ms (6.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	171×	body	128	valid
8.0ms	34×	body	2048	valid
6.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	7×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify245.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 34.4b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_1516` `add-log-exp_binary64_1494` `*-un-lft-identity_binary64_1455`
9×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
7×	`add-sqr-sqrt_binary64_1477`
6×	`add-cube-cbrt_binary64_1490`
3×	`prod-exp_binary64_1504` `associate-r_binary64_1395` `sqrt-prod_binary64_1471` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
2×	`distribute-lft-out_binary64_1406` `sqrt-div_binary64_1472` `flip--_binary64_1430` `sum-log_binary64_1546` `flip3--_binary64_1459`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `distribute-rgt-neg-in_binary64_1413` `neg-log_binary64_1548` `neg-sub0_binary64_1450` `associate-+l-_binary64_1390` `-commutative_binary64_1386` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `+-commutative_binary64_1385` `associate-l*_binary64_1396`

Counts

4 → 60

Calls

4 calls:

10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series355.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
123.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
30.0ms	(.f64 (.f64 4 a) c)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5357	1184

prune284.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Merged error: 12.9b

Counts

73 → 9

Compiler

Compiled 5496 to 3854 computations (29.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
8.1b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite68.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
34×	`add-sqr-sqrt_binary64_1477` `times-frac_binary64_1461`
33×	`*-un-lft-identity_binary64_1455`
17×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
14×	`associate-/l*_binary64_1400`
13×	`prod-exp_binary64_1504` `add-cube-cbrt_binary64_1490` `cbrt-unprod_binary64_1488`
11×	`sqrt-prod_binary64_1471`
10×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
8×	`associate-/r*_binary64_1399` `add-log-exp_binary64_1494`
6×	`associate-/r/_binary64_1401` `cancel-sign-sub-inv_binary64_1421`
5×	`distribute-rgt-neg-in_binary64_1413` `pow1_binary64_1516` `flip--_binary64_1430` `flip3--_binary64_1459`
4×	`div-inv_binary64_1452`
2×	`sqrt-div_binary64_1472` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `diff-log_binary64_1547`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `neg-log_binary64_1548` `associate-/l/_binary64_1402` `neg-sub0_binary64_1450` `associate--l-_binary64_1393` `sub-neg_binary64_1448` `pow1/2_binary64_1535`

Counts

4 → 125

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
16.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series999.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

417.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
331.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
131.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4940	4228
1	4940	4228

prune572.0ms (7.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	128	9	137
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	135	11	146

Merged error: 8.2b

Counts

146 → 11

Compiler

Compiled 11856 to 8050 computations (32.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite76.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
35×	`add-sqr-sqrt_binary64_1477`
34×	`*-un-lft-identity_binary64_1455`
27×	`associate-r_binary64_1395`
23×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
22×	`times-frac_binary64_1461`
18×	`add-cube-cbrt_binary64_1490`
16×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
10×	`sqrt-prod_binary64_1471` `pow1_binary64_1516`
8×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424` `add-log-exp_binary64_1494`
6×	`cancel-sign-sub-inv_binary64_1421`
4×	`distribute-rgt-neg-in_binary64_1413`
3×	`flip--_binary64_1430` `flip3--_binary64_1459` `pow-prod-down_binary64_1526`
2×	`associate-*r/_binary64_1397` `associate-/r/_binary64_1401` `sqrt-div_binary64_1472` `diff-log_binary64_1547` `div-inv_binary64_1452`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `neg-log_binary64_1548` `associate-/l/_binary64_1402` `neg-sub0_binary64_1450` `clear-num_binary64_1454` `associate-/r_binary64_1399` `-commutative_binary64_1386` `associate--l-_binary64_1393` `frac-2neg_binary64_1466` `associate-/l_binary64_1400` `sub-neg_binary64_1448` `pow1/2_binary64_1535` `associate-l*_binary64_1396`

Counts

4 → 119

Calls

4 calls:

23.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
21.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series971.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

404.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
324.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
126.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4901	3363
1	4901	3363

prune288.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	131	11	142

Merged error: 8.1b

Counts

142 → 11

Compiler

Compiled 6081 to 3965 computations (34.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1477`
12×	`*-un-lft-identity_binary64_1455`
10×	`pow1_binary64_1516` `add-log-exp_binary64_1494`
9×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
8×	`add-cube-cbrt_binary64_1490`
7×	`sqrt-prod_binary64_1471` `cancel-sign-sub-inv_binary64_1421`
3×	`prod-exp_binary64_1504` `associate-r_binary64_1395` `flip--_binary64_1430` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `flip3--_binary64_1459` `pow-prod-down_binary64_1526`
2×	`sqrt-div_binary64_1472` `distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424` `sub-neg_binary64_1448`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `distribute-rgt-neg-in_binary64_1413` `neg-log_binary64_1548` `neg-sub0_binary64_1450` `-commutative_binary64_1386` `associate--l-_binary64_1393` `pow1/2_binary64_1535` `associate-l*_binary64_1396`

Counts

4 → 68

Calls

4 calls:

14.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series343.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.0ms	(.f64 (.f64 4 a) c)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5591	1423

prune328.0ms (4.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	82	9	91

Merged error: 7.2b

Counts

91 → 9

Compiler

Compiled 2358 to 1503 computations (36.3% saved)

regimes183.0ms (2.5%)

Compiler: Compiled 732 to 602 computations (17.8% saved)

bsearch109.0ms (1.5%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.134094891995538e+120
9	2.173626231849138e-227	1.6620553427918547e-219	2.227512516590462e-227
8	-9.73333868460494e+156	-4.49823275505298e+152	-1.3249665758399062e+154

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.134094891995538e+120

2.173626231849138e-227

1.6620553427918547e-219

2.227512516590462e-227

-9.73333868460494e+156

-4.49823275505298e+152

-1.3249665758399062e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	112
1	112	112

end0.0ms (0%)

sample1.4s (19.9%)

Algorithm

1×

intervals

Results

294.0ms	1104×	body	2048	valid
288.0ms	5258×	body	128	valid
137.0ms	682×	body	1024	valid
129.0ms	398×	body	4096	valid
58.0ms	372×	body	512	valid
34.0ms	662×	body	128	nan
19.0ms	360×	body	128	invalid
19.0ms	186×	body	256	valid

Compiler

Compiled 308 to 234 computations (24% saved)

Details

analyze456.0ms (6.3%)

sample41.0ms (0.6%)

simplify245.0ms (3.4%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite30.0ms (0.4%)

series355.0ms (4.9%)

simplify65.0ms (0.9%)

prune284.0ms (3.9%)

localize15.0ms (0.2%)

rewrite68.0ms (0.9%)

series999.0ms (13.8%)

simplify104.0ms (1.4%)

prune572.0ms (7.9%)

localize14.0ms (0.2%)

rewrite76.0ms (1%)

series971.0ms (13.4%)

simplify103.0ms (1.4%)

prune288.0ms (4%)

localize13.0ms (0.2%)

rewrite36.0ms (0.5%)

series343.0ms (4.7%)

simplify71.0ms (1%)

prune328.0ms (4.5%)

regimes183.0ms (2.5%)

bsearch109.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (19.9%)

Profiling