Details

analyze438.0ms (8%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	37×	body	2048	valid
9.0ms	170×	body	128	valid
5.0ms	25×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	8×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify422.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (261.0ms)

Iter	Nodes	Cost
0	1707	24
1	1707	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 3 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1446`
10×	`pow1_binary64_1483`
9×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`add-log-exp_binary64_1461` `*-un-lft-identity_binary64_1425`
6×	`add-cube-cbrt_binary64_1457`
4×	`sqrt-prod_binary64_1440`
3×	`flip--_binary64_1400` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-r_binary64_1367` `flip3--_binary64_1429` `pow-prod-down_binary64_1493`
2×	`diff-log_binary64_1514` `sub-neg_binary64_1418` `sqrt-div_binary64_1441` `difference-of-squares_binary64_1394`
1×	`distribute-lft-out--_binary64_1379` `associate-l_binary64_1368` `pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series345.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
33.0ms	(.f64 (.f64 3 a) c)

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4939	1210
1	4939	1210

prune99.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	10	71

Merged error: 12.6b

Counts

71 → 10

Compiler

Compiled 1735 to 1059 computations (39% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.7b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.1b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite54.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
22×	`times-frac_binary64_1431`
21×	`*-un-lft-identity_binary64_1425`
17×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
13×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
12×	`add-sqr-sqrt_binary64_1446`
11×	`add-cube-cbrt_binary64_1457` `associate-/l*_binary64_1372`
6×	`associate-/r/_binary64_1373` `add-log-exp_binary64_1461`
5×	`associate-/r*_binary64_1371` `distribute-lft-out_binary64_1378` `pow1_binary64_1483`
4×	`flip3-+_binary64_1428` `div-inv_binary64_1422` `flip-+_binary64_1399`
3×	`sqrt-prod_binary64_1440`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `sqrt-div_binary64_1441`
1×	`flip--_binary64_1400` `pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `sum-log_binary64_1513` `+-commutative_binary64_1357` `associate-/l/_binary64_1374` `rem-sqrt-square_binary64_1438` `flip3--_binary64_1429`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series889.0ms (16.2%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
287.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5403	3147

prune169.0ms (3.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	101	13	114
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	106	18	124

Merged error: 7.5b

Counts

124 → 18

Compiler

Compiled 3520 to 2188 computations (37.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 3 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_1483`
9×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`add-log-exp_binary64_1461` `*-un-lft-identity_binary64_1425`
7×	`add-sqr-sqrt_binary64_1446`
6×	`add-cube-cbrt_binary64_1457`
3×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-r_binary64_1367` `sqrt-prod_binary64_1440` `pow-prod-down_binary64_1493`
2×	`flip--_binary64_1400` `sqrt-div_binary64_1441` `flip3--_binary64_1429`
1×	`diff-log_binary64_1514` `associate-l_binary64_1368` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `distribute-lft-out_binary64_1378` `sqrt-pow1_binary64_1442` `sum-log_binary64_1513` `flip-+_binary64_1399` `+-commutative_binary64_1357` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 56

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series328.0ms (6%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
26.0ms	(.f64 (.f64 3 a) c)

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4879	1119
1	4879	1119

prune97.0ms (1.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	5	11	16
Picked	1	0	1
Done	0	1	1
Total	71	15	86

Merged error: 6.8b

Counts

86 → 15

Compiler

Compiled 2034 to 1375 computations (32.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 3 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_1483`
9×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`add-log-exp_binary64_1461` `*-un-lft-identity_binary64_1425`
7×	`add-sqr-sqrt_binary64_1446`
6×	`add-cube-cbrt_binary64_1457`
3×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-r_binary64_1367` `sqrt-prod_binary64_1440` `pow-prod-down_binary64_1493`
2×	`flip--_binary64_1400` `sqrt-div_binary64_1441` `flip3--_binary64_1429`
1×	`diff-log_binary64_1514` `associate-l_binary64_1368` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `distribute-lft-out_binary64_1378` `sqrt-pow1_binary64_1442` `sum-log_binary64_1513` `flip-+_binary64_1399` `+-commutative_binary64_1357` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 56

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
6.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series341.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
70.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
27.0ms	(.f64 (.f64 3 a) c)

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4879	1119
1	4879	1119

prune71.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	69	14	83

Merged error: 6.8b

Counts

83 → 14

Compiler

Compiled 1571 to 986 computations (37.2% saved)

regimes218.0ms (4%)

Compiler: Compiled 1304 to 1032 computations (20.9% saved)

bsearch118.0ms (2.2%)

Steps

Iters	Range	Point
9	7.133955408180205e+122	8.618933981254862e+131	3.2493324446871104e+131
9	2.2570946147804535e-182	5.99349766551832e-173	8.969766515049942e-182
8	-9.73333868460494e+156	-4.49823275505298e+152	-1.3249665758399062e+154

Iters

Range

Point

7.133955408180205e+122

8.618933981254862e+131

3.2493324446871104e+131

2.2570946147804535e-182

5.99349766551832e-173

8.969766515049942e-182

-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	143	171
1	143	171

end0.0ms (0%)

sample1.5s (26.9%)

Algorithm

1×

intervals

Results

265.0ms	5220×	body	128	valid
263.0ms	1093×	body	2048	valid
138.0ms	717×	body	1024	valid
119.0ms	398×	body	4096	valid
52.0ms	376×	body	512	valid
31.0ms	661×	body	128	nan
22.0ms	360×	body	128	invalid
18.0ms	196×	body	256	valid

Compiler

Compiled 454 to 341 computations (24.9% saved)

Details

analyze438.0ms (8%)

sample38.0ms (0.7%)

simplify422.0ms (7.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite29.0ms (0.5%)

series345.0ms (6.3%)

simplify56.0ms (1%)

prune99.0ms (1.8%)

localize14.0ms (0.2%)

rewrite54.0ms (1%)

series889.0ms (16.2%)

simplify57.0ms (1%)

prune169.0ms (3.1%)

localize16.0ms (0.3%)

rewrite27.0ms (0.5%)

series328.0ms (6%)

simplify59.0ms (1.1%)

prune97.0ms (1.8%)

localize12.0ms (0.2%)

rewrite28.0ms (0.5%)

series341.0ms (6.2%)

simplify59.0ms (1.1%)

prune71.0ms (1.3%)

regimes218.0ms (4%)

bsearch118.0ms (2.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (26.9%)

Profiling