Details

analyze451.0ms (6.4%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
8.0ms	34×	body	2048	valid
4.0ms	23×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	24×	body	128	nan
0.0ms	9×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify469.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (300.0ms)

Iter	Nodes	Cost
0	1706	24
1	1706	24

prune6.0ms (0.1%)

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: 33.7b

Counts

2 → 2

Compiler

Compiled 82 to 67 computations (18.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
0.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite39.0ms (0.6%)

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 3 a) c)))) (.f64 3 a))
10.0ms	(+.f64 (neg.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series506.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
122.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5343	1836

prune623.0ms (8.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	72	12	84

Merged error: 7.1b

Counts

84 → 12

Compiler

Compiled 12098 to 8827 computations (27% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.1b	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
10.4b	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite67.0ms (0.9%)

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 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
16.0ms	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
11.0ms	(-.f64 (neg.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)))

series948.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
304.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
140.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4938	3955
1	4938	3955

prune455.0ms (6.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	138	11	149

Merged error: 7.1b

Counts

149 → 11

Compiler

Compiled 9693 to 6493 computations (33% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (.f64 1 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) c)))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64_1837`
16×	`div-exp_binary64_1850`
14×	`add-sqr-sqrt_binary64_1821`
13×	`add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799`
12×	`prod-exp_binary64_1848`
11×	`1-exp_binary64_1843`
10×	`add-log-exp_binary64_1838`
9×	`add-cube-cbrt_binary64_1834`
8×	`pow1_binary64_1860`
7×	`sqrt-prod_binary64_1815` `cancel-sign-sub-inv_binary64_1765`
5×	`rec-exp_binary64_1849`
4×	`cbrt-undiv_binary64_1833`
3×	`associate-/l*_binary64_1744` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `times-frac_binary64_1805`
2×	`sqrt-div_binary64_1816` `sub-neg_binary64_1792` `pow-flip_binary64_1873` `difference-of-squares_binary64_1768` `cbrt-unprod_binary64_1832` `distribute-lft-out--_binary64_1751`
1×	`clear-num_binary64_1798` `neg-sub0_binary64_1794` `frac-2neg_binary64_1810` `associate-/r_binary64_1743` `pow1/2_binary64_1879` `associate-r/_binary64_1741` `associate-/r/_binary64_1745` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `neg-log_binary64_1892` `rem-sqrt-square_binary64_1812` `distribute-rgt-neg-in_binary64_1757` `associate--l-_binary64_1737` `inv-pow_binary64_1884`

Counts

4 → 89

Calls

4 calls:

16.0ms	(/.f64 1 (.f64 1 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) c)))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series575.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

273.0ms	(/.f64 1 (.f64 1 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) c)))
126.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5049	2231

prune197.0ms (2.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	100	12	112

Merged error: 7.1b

Counts

112 → 12

Compiler

Compiled 4052 to 2729 computations (32.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1821`
12×	`*-un-lft-identity_binary64_1799`
10×	`pow1_binary64_1860` `add-log-exp_binary64_1838`
9×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
8×	`add-cube-cbrt_binary64_1834`
7×	`sqrt-prod_binary64_1815` `cancel-sign-sub-inv_binary64_1765`
3×	`prod-exp_binary64_1848` `diff-log_binary64_1891` `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` `difference-of-squares_binary64_1768` `distribute-lft-out--_binary64_1751`
1×	`neg-sub0_binary64_1794` `associate-l_binary64_1740` `pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `*-commutative_binary64_1730` `neg-log_binary64_1892` `rem-sqrt-square_binary64_1812` `distribute-rgt-neg-in_binary64_1757` `associate--l-_binary64_1737`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series332.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
29.0ms	(.f64 (.f64 3 a) c)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5791	1426

prune137.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	2	7	9
Picked	1	0	1
Done	1	1	2
Total	81	11	92

Merged error: 7.1b

Counts

92 → 11

Compiler

Compiled 2766 to 1794 computations (35.1% saved)

regimes263.0ms (3.7%)

Compiler: Compiled 1020 to 831 computations (18.5% saved)

bsearch88.0ms (1.2%)

Steps

Iters	Range		Point
7	5.660586254752312e+90	1.2519979933934522e+93	7.178750185064038e+92
7	-5.258493096485131e-266	-3.2234018866166593e-267	-1.566285583643343e-266
7	-5.334360280276333e+52	-5.908223480446143e+50	-5.212113506128886e+52

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	91
1	143	91

end0.0ms (0%)

sample1.4s (20.4%)

Algorithm

1×

intervals

Results

288.0ms	1124×	body	2048	valid
276.0ms	5203×	body	128	valid
144.0ms	720×	body	1024	valid
132.0ms	414×	body	4096	valid
56.0ms	373×	body	512	valid
36.0ms	674×	body	128	nan
21.0ms	402×	body	128	invalid
17.0ms	166×	body	256	valid

Compiler

Compiled 301 to 235 computations (21.9% saved)

Details

analyze451.0ms (6.4%)

sample38.0ms (0.5%)

simplify469.0ms (6.7%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite39.0ms (0.6%)

series506.0ms (7.2%)

simplify56.0ms (0.8%)

prune623.0ms (8.9%)

localize12.0ms (0.2%)

rewrite67.0ms (0.9%)

series948.0ms (13.5%)

simplify81.0ms (1.1%)

prune455.0ms (6.5%)

localize13.0ms (0.2%)

rewrite48.0ms (0.7%)

series575.0ms (8.2%)

simplify66.0ms (0.9%)

prune197.0ms (2.8%)

localize11.0ms (0.2%)

rewrite33.0ms (0.5%)

series332.0ms (4.7%)

simplify69.0ms (1%)

prune137.0ms (2%)

regimes263.0ms (3.7%)

bsearch88.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.4%)

Profiling