Details

analyze458.0ms (5.6%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	173×	body	128	valid
7.0ms	24×	body	1024	valid
7.0ms	27×	body	2048	valid
4.0ms	12×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	6×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify234.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

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: 31.7b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.8b	(-.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))))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_1799`
10×	`add-log-exp_binary64_1838`
9×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
8×	`add-sqr-sqrt_binary64_1821`
7×	`add-cube-cbrt_binary64_1834`
6×	`distribute-lft-out_binary64_1750`
5×	`pow1_binary64_1860` `associate-/l*_binary64_1744` `times-frac_binary64_1805`
3×	`sqrt-prod_binary64_1815` `distribute-rgt-neg-in_binary64_1757`
2×	`sqrt-div_binary64_1816` `sum-log_binary64_1890` `div-exp_binary64_1850` `neg-sub0_binary64_1794` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-undiv_binary64_1833` `associate-/l/_binary64_1746` `flip3-+_binary64_1802` `associate-+l-_binary64_1734` `flip-+_binary64_1773`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `clear-num_binary64_1798` `+-commutative_binary64_1729` `prod-exp_binary64_1848` `frac-2neg_binary64_1810` `associate-/r*_binary64_1743` `pow1/2_binary64_1879` `diff-log_binary64_1891` `cbrt-unprod_binary64_1832` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `neg-log_binary64_1892` `cancel-sign-sub-inv_binary64_1765` `rem-sqrt-square_binary64_1812`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.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)))

series551.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
128.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5290	1826

prune356.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.6b

Counts

83 → 8

Compiler

Compiled 6836 to 4815 computations (29.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.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))
9.6b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite67.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
34×	`add-sqr-sqrt_binary64_1821` `times-frac_binary64_1805`
33×	`*-un-lft-identity_binary64_1799`
17×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
14×	`associate-/l*_binary64_1744`
13×	`add-cube-cbrt_binary64_1834` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
11×	`sqrt-prod_binary64_1815`
10×	`difference-of-squares_binary64_1768` `distribute-lft-out--_binary64_1751`
8×	`add-log-exp_binary64_1838` `associate-/r*_binary64_1743`
6×	`associate-/r/_binary64_1745` `cancel-sign-sub-inv_binary64_1765`
5×	`pow1_binary64_1860` `flip--_binary64_1774` `flip3--_binary64_1803` `distribute-rgt-neg-in_binary64_1757`
4×	`div-inv_binary64_1796`
2×	`sqrt-div_binary64_1816` `clear-num_binary64_1798` `frac-2neg_binary64_1810` `diff-log_binary64_1891`
1×	`sub-neg_binary64_1792` `neg-sub0_binary64_1794` `pow1/2_binary64_1879` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `neg-log_binary64_1892` `rem-sqrt-square_binary64_1812` `associate--l-_binary64_1737`

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))
15.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
13.0ms	(-.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)))

series990.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

421.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
318.0ms	(/.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))
136.0ms	(-.f64 (neg.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)))

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4940	4228
1	4940	4228

prune346.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	136	9	145

Merged error: 5.5b

Counts

145 → 9

Compiler

Compiled 7412 to 4782 computations (35.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.4b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.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))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
17×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
14×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
12×	`add-sqr-sqrt_binary64_1821`
11×	`*-un-lft-identity_binary64_1799`
10×	`add-log-exp_binary64_1838`
7×	`add-cube-cbrt_binary64_1834` `sqrt-prod_binary64_1815` `cancel-sign-sub-inv_binary64_1765`
5×	`pow1_binary64_1860`
3×	`diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803`
2×	`sqrt-div_binary64_1816` `sub-neg_binary64_1792` `difference-of-squares_binary64_1768` `distribute-lft-out--_binary64_1751`
1×	`clear-num_binary64_1798` `neg-sub0_binary64_1794` `associate-/l_binary64_1744` `frac-2neg_binary64_1810` `associate-/r_binary64_1743` `pow1/2_binary64_1879` `associate-*r/_binary64_1741` `times-frac_binary64_1805` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `neg-log_binary64_1892` `rem-sqrt-square_binary64_1812` `distribute-rgt-neg-in_binary64_1757` `associate--l-_binary64_1737`

Counts

4 → 84

Calls

4 calls:

22.0ms	(/.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))
10.0ms	(-.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series637.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

317.0ms	(/.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))
139.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	2283
1	4957	2283

prune140.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	96	9	105

Merged error: 5.5b

Counts

105 → 9

Compiler

Compiled 3060 to 1889 computations (38.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.4b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite138.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

834×	`times-frac_binary64_1805`
487×	`add-sqr-sqrt_binary64_1821`
486×	`*-un-lft-identity_binary64_1799`
338×	`add-cube-cbrt_binary64_1834`
86×	`associate-/r*_binary64_1743`
74×	`difference-of-squares_binary64_1768` `distribute-lft-out--_binary64_1751`
43×	`sqrt-prod_binary64_1815`
37×	`distribute-rgt-neg-in_binary64_1757`
29×	`associate-/r/_binary64_1745`
25×	`add-exp-log_binary64_1837`
17×	`div-inv_binary64_1796`
15×	`div-exp_binary64_1850` `flip--_binary64_1774` `flip3--_binary64_1803`
13×	`add-cbrt-cube_binary64_1835`
10×	`add-log-exp_binary64_1838`
7×	`cancel-sign-sub-inv_binary64_1765`
6×	`pow1_binary64_1860` `cbrt-undiv_binary64_1833`
3×	`associate-/l*_binary64_1744` `rec-exp_binary64_1849` `1-exp_binary64_1843` `diff-log_binary64_1891`
2×	`sqrt-div_binary64_1816` `sub-neg_binary64_1792`
1×	`clear-num_binary64_1798` `neg-sub0_binary64_1794` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `pow-flip_binary64_1873` `sqrt-pow1_binary64_1817` `neg-log_binary64_1892` `rem-sqrt-square_binary64_1812` `associate--l-_binary64_1737` `inv-pow_binary64_1884`

Counts

4 → 422

Calls

4 calls:

31.0ms	(/.f64 1 (/.f64 1/2 (/.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series681.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
117.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify218.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4942	19878
1	4942	19878

prune1.2s (15%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	435	8	443

Merged error: 5.5b

Counts

443 → 8

Compiler

Compiled 17326 to 10508 computations (39.4% saved)

regimes154.0ms (1.9%)

Compiler: Compiled 744 to 586 computations (21.2% saved)

bsearch94.0ms (1.1%)

Steps

Iters	Range	Point
7	5.299135082393502e+130	9.634242899973525e+131	1.341209881992474e+131
7	-5.258493096485131e-266	-8.912885875042921e-268	-2.038598643446564e-267
8	-8.039036545206531e+90	-9.901707510965063e+86	-7.1093208455340995e+90

Iters

Range

Point

5.299135082393502e+130

9.634242899973525e+131

1.341209881992474e+131

-5.258493096485131e-266

-8.912885875042921e-268

-2.038598643446564e-267

-8.039036545206531e+90

-9.901707510965063e+86

-7.1093208455340995e+90

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	84
1	120	84

end0.0ms (0%)

sample1.4s (17.6%)

Algorithm

1×

intervals

Results

284.0ms	5240×	body	128	valid
278.0ms	1101×	body	2048	valid
142.0ms	701×	body	1024	valid
130.0ms	415×	body	4096	valid
53.0ms	363×	body	512	valid
40.0ms	675×	body	128	nan
24.0ms	404×	body	128	invalid
18.0ms	180×	body	256	valid

Compiler

Compiled 292 to 217 computations (25.7% saved)

Details

analyze458.0ms (5.6%)

sample41.0ms (0.5%)

simplify234.0ms (2.9%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

rewrite39.0ms (0.5%)

series551.0ms (6.8%)

simplify58.0ms (0.7%)

prune356.0ms (4.4%)

localize13.0ms (0.2%)

rewrite67.0ms (0.8%)

series990.0ms (12.1%)

simplify106.0ms (1.3%)

prune346.0ms (4.2%)

localize14.0ms (0.2%)

rewrite52.0ms (0.6%)

series637.0ms (7.8%)

simplify74.0ms (0.9%)

prune140.0ms (1.7%)

localize16.0ms (0.2%)

rewrite138.0ms (1.7%)

series681.0ms (8.3%)

simplify218.0ms (2.7%)

prune1.2s (15%)

regimes154.0ms (1.9%)

bsearch94.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (17.6%)

Profiling