Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	78×	body	1024	valid
4.0ms	125×	body	128	valid
2.0ms	30×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify177.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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: 31.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1821` `sqrt-prod_binary64_1815`
10×	`*-un-lft-identity_binary64_1799`
6×	`cancel-sign-sub-inv_binary64_1765`
4×	`difference-of-squares_binary64_1768`
3×	`add-cube-cbrt_binary64_1834` `add-log-exp_binary64_1838` `distribute-lft-out--_binary64_1751`
1×	`pow1_binary64_1860` `sub-neg_binary64_1792` `diff-log_binary64_1891` `flip--_binary64_1774` `add-cbrt-cube_binary64_1835` `flip3--_binary64_1803` `add-exp-log_binary64_1837` `distribute-lft-out_binary64_1750`

Counts

1 → 24

Calls

1 calls:

10.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series72.0ms (1.7%)

Counts

1 → 3

Calls

1 calls:

72.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4918	539
1	4918	539

prune57.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.1b

Counts

28 → 2

Compiler

Compiled 695 to 509 computations (26.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_1799`
20×	`sqrt-prod_binary64_1815` `distribute-lft-out_binary64_1750`
18×	`times-frac_binary64_1805`
13×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
6×	`associate-/r*_binary64_1743` `add-exp-log_binary64_1837`
4×	`add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835`
3×	`pow1_binary64_1860` `associate-/l*_binary64_1744`
2×	`div-exp_binary64_1850` `associate-/r/_binary64_1745` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796` `inv-pow_binary64_1884`

Counts

2 → 59

Calls

2 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series104.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

63.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
41.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4900	1269
1	4900	1269

prune155.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	61	6	67

Merged error: 0.0b

Counts

67 → 6

Compiler

Compiled 2547 to 1951 computations (23.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite128.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_1799`
290×	`sqrt-prod_binary64_1815`
172×	`times-frac_binary64_1805`
144×	`add-sqr-sqrt_binary64_1821`
116×	`distribute-lft-out_binary64_1750`
88×	`add-cube-cbrt_binary64_1834`
43×	`swap-sqr_binary64_1766`
31×	`pow1_binary64_1860`
27×	`associate-l_binary64_1740` `sqrt-pow1_binary64_1817` `associate-r_binary64_1739`
16×	`unswap-sqr_binary64_1767`
14×	`associate-/r/_binary64_1745` `add-exp-log_binary64_1837`
12×	`associate-/r*_binary64_1743`
11×	`pow-flip_binary64_1873` `inv-pow_binary64_1884`
10×	`add-cbrt-cube_binary64_1835`
9×	`pow1/2_binary64_1879` `pow-prod-up_binary64_1869` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`
7×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`associate-/l*_binary64_1744`
5×	`sqrt-div_binary64_1816` `pow-sqr_binary64_1772` `pow-prod-down_binary64_1870`
4×	`div-exp_binary64_1850` `add-log-exp_binary64_1838`
3×	`sqr-abs_binary64_1814`
2×	`clear-num_binary64_1798` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833`
1×	`pow2_binary64_1880` `prod-exp_binary64_1848` `associate-r/_binary64_1741` `cbrt-unprod_binary64_1832` `-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `rem-square-sqrt_binary64_1811` `pow-plus_binary64_1862` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 281

Calls

4 calls:

46.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
16.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series293.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
67.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
65.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
57.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify129.0ms (3%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4932	6672
1	4932	6672

prune550.0ms (12.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	292	7	299

Merged error: 0.0b

Counts

299 → 7

Compiler

Compiled 9066 to 6746 computations (25.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

rewrite196.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

266×	`sqrt-prod_binary64_1815`
213×	`*-un-lft-identity_binary64_1799`
147×	`times-frac_binary64_1805`
142×	`add-sqr-sqrt_binary64_1821`
78×	`add-cube-cbrt_binary64_1834`
68×	`distribute-lft-out_binary64_1750`
63×	`associate-l_binary64_1740`
58×	`sqrt-pow1_binary64_1817`
41×	`pow1_binary64_1860`
37×	`associate-r_binary64_1739`
35×	`pow-flip_binary64_1873`
24×	`unswap-sqr_binary64_1767`
22×	`sqrt-div_binary64_1816`
21×	`pow-prod-up_binary64_1869`
19×	`add-exp-log_binary64_1837`
16×	`pow1/2_binary64_1879` `pow-prod-down_binary64_1870`
15×	`associate-/r*_binary64_1743` `add-cbrt-cube_binary64_1835`
13×	`inv-pow_binary64_1884`
10×	`associate-/r/_binary64_1745`
6×	`associate-/l_binary64_1744` `associate-r/_binary64_1741` `frac-times_binary64_1809`
5×	`div-inv_binary64_1796` `flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`div-exp_binary64_1850` `add-log-exp_binary64_1838` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `associate-*l/_binary64_1742`
3×	`sqrt-unprod_binary64_1819`
2×	`clear-num_binary64_1798` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `*-commutative_binary64_1730` `pow3_binary64_1882`

Counts

4 → 287

Calls

4 calls:

59.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
57.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series363.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
101.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
72.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
52.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify131.0ms (3%)

Algorithm

1×	egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4925	9963
1	4925	9963

prune924.0ms (21.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	299	7	306

Merged error: 0.0b

Counts

306 → 7

Compiler

Compiled 12985 to 9734 computations (25% saved)

regimes36.0ms (0.8%)

Compiler: Compiled 336 to 268 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample775.0ms (18%)

Algorithm

1×

intervals

Results

208.0ms	2043×	body	1024	valid
123.0ms	4236×	body	128	valid
78.0ms	1000×	body	512	valid
36.0ms	228×	body	2048	valid
25.0ms	493×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 186 to 151 computations (18.8% saved)

Details

analyze3.0ms (0.1%)

sample21.0ms (0.5%)

simplify177.0ms (4.1%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite12.0ms (0.3%)

series72.0ms (1.7%)

simplify56.0ms (1.3%)

prune57.0ms (1.3%)

localize8.0ms (0.2%)

rewrite25.0ms (0.6%)

series104.0ms (2.4%)

simplify63.0ms (1.5%)

prune155.0ms (3.6%)

localize11.0ms (0.2%)

rewrite128.0ms (3%)

series293.0ms (6.8%)

simplify129.0ms (3%)

prune550.0ms (12.8%)

localize13.0ms (0.3%)

rewrite196.0ms (4.5%)

series363.0ms (8.4%)

simplify131.0ms (3%)

prune924.0ms (21.5%)

regimes36.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample775.0ms (18%)

Profiling