Details

analyze461.0ms (6.6%)

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

10.0ms	34×	body	2048	valid
9.0ms	171×	body	128	valid
5.0ms	28×	body	1024	valid
4.0ms	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)

simplify242.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 34.4b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1821`
10×	`pow1_binary64_1860`
9×	`add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
8×	`add-log-exp_binary64_1838`
7×	`add-cube-cbrt_binary64_1834`
4×	`sqrt-prod_binary64_1815` `cancel-sign-sub-inv_binary64_1765`
3×	`prod-exp_binary64_1848` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870` `associate-r_binary64_1739`
2×	`sqrt-div_binary64_1816` `sub-neg_binary64_1792` `diff-log_binary64_1891` `difference-of-squares_binary64_1768`
1×	`associate-l_binary64_1740` `pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `*-commutative_binary64_1730` `rem-sqrt-square_binary64_1812` `distribute-lft-out--_binary64_1751`

Counts

4 → 62

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
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))

series368.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
129.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
33.0ms	(.f64 (.f64 4 a) c)

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4883	1223
1	4883	1223

prune277.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	9	75

Merged error: 12.9b

Counts

75 → 9

Compiler

Compiled 5188 to 3621 computations (30.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.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)))

rewrite57.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
22×	`times-frac_binary64_1805`
21×	`*-un-lft-identity_binary64_1799`
17×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
13×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
12×	`add-sqr-sqrt_binary64_1821`
11×	`add-cube-cbrt_binary64_1834` `associate-/l*_binary64_1744`
6×	`add-log-exp_binary64_1838` `associate-/r/_binary64_1745`
5×	`pow1_binary64_1860` `associate-/r*_binary64_1743` `distribute-lft-out_binary64_1750`
4×	`div-inv_binary64_1796` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`sqrt-prod_binary64_1815`
2×	`sqrt-div_binary64_1816` `clear-num_binary64_1798` `frac-2neg_binary64_1810`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `pow1/2_binary64_1879` `flip--_binary64_1774` `flip3--_binary64_1803` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`

Counts

4 → 102

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.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)))

series954.0ms (13.6%)

Counts

4 → 12

Calls

4 calls:

373.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
317.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
132.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5005	3121

prune667.0ms (9.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 8.2b

Counts

123 → 9

Compiler

Compiled 8832 to 6188 computations (29.9% 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 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)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_1860`
9×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
8×	`add-log-exp_binary64_1838` `*-un-lft-identity_binary64_1799`
7×	`add-sqr-sqrt_binary64_1821`
6×	`add-cube-cbrt_binary64_1834`
3×	`prod-exp_binary64_1848` `sqrt-prod_binary64_1815` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870` `associate-r_binary64_1739`
2×	`sqrt-div_binary64_1816` `flip--_binary64_1774` `flip3--_binary64_1803`
1×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `+-commutative_binary64_1729` `associate-l_binary64_1740` `pow1/2_binary64_1879` `diff-log_binary64_1891` `sqrt-pow1_binary64_1817` `*-commutative_binary64_1730` `distribute-lft-out_binary64_1750` `flip3-+_binary64_1802` `cancel-sign-sub-inv_binary64_1765` `rem-sqrt-square_binary64_1812` `flip-+_binary64_1773`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+.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))

series345.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.0ms	(.f64 (.f64 4 a) c)

simplify88.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4908	1123
1	4908	1123

prune111.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 7.2b

Counts

78 → 6

Compiler

Compiled 2213 to 1498 computations (32.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite72.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_1805`
74×	`*-un-lft-identity_binary64_1799`
53×	`add-sqr-sqrt_binary64_1821`
52×	`add-cube-cbrt_binary64_1834`
45×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
32×	`associate-/l*_binary64_1744`
23×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
14×	`div-inv_binary64_1796`
11×	`distribute-lft-out_binary64_1750`
9×	`associate-/r*_binary64_1743`
7×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
6×	`add-log-exp_binary64_1838`
5×	`pow1_binary64_1860`
3×	`sqrt-prod_binary64_1815` `associate-/r/_binary64_1745`
2×	`sqrt-div_binary64_1816` `clear-num_binary64_1798` `frac-2neg_binary64_1810`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `pow1/2_binary64_1879` `flip--_binary64_1774` `flip3--_binary64_1803` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `flip3-+_binary64_1802` `rem-sqrt-square_binary64_1812` `flip-+_binary64_1773`

Counts

4 → 165

Calls

4 calls:

24.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
14.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
7.0ms	(+.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)))

series1000.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

407.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
350.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify100.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5065	6019

prune282.0ms (4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	175	8	183

Merged error: 7.2b

Counts

183 → 8

Compiler

Compiled 5937 to 3573 computations (39.8% saved)

regimes147.0ms (2.1%)

Compiler: Compiled 402 to 345 computations (14.2% saved)

bsearch109.0ms (1.6%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.525835260688754e+121
9	2.173626231849138e-227	1.6620553427918547e-219	7.131198222427231e-227
8	-1.6407368404235515e+56	-3.3624292403433257e+53	-1.6236541306877014e+56

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.525835260688754e+121

2.173626231849138e-227

1.6620553427918547e-219

7.131198222427231e-227

-1.6407368404235515e+56

-3.3624292403433257e+53

-1.6236541306877014e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	122	104
1	122	104

end0.0ms (0%)

sample1.4s (20%)

Algorithm

1×

intervals

Results

282.0ms	5258×	body	128	valid
276.0ms	1104×	body	2048	valid
133.0ms	682×	body	1024	valid
125.0ms	398×	body	4096	valid
54.0ms	372×	body	512	valid
32.0ms	662×	body	128	nan
22.0ms	360×	body	128	invalid
19.0ms	186×	body	256	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

Details

analyze461.0ms (6.6%)

sample41.0ms (0.6%)

simplify242.0ms (3.5%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite30.0ms (0.4%)

series368.0ms (5.3%)

simplify79.0ms (1.1%)

prune277.0ms (4%)

localize15.0ms (0.2%)

rewrite57.0ms (0.8%)

series954.0ms (13.6%)

simplify80.0ms (1.1%)

prune667.0ms (9.5%)

localize13.0ms (0.2%)

rewrite28.0ms (0.4%)

series345.0ms (4.9%)

simplify88.0ms (1.3%)

prune111.0ms (1.6%)

localize16.0ms (0.2%)

rewrite72.0ms (1%)

series1000.0ms (14.3%)

simplify100.0ms (1.4%)

prune282.0ms (4%)

regimes147.0ms (2.1%)

bsearch109.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20%)

Profiling