Details

analyze2.0ms (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)

sample18.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	49×	body	1024	valid
4.0ms	143×	body	128	valid
3.0ms	39×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify100.0ms (3.6%)

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

Error

27.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_1799`
14×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
6×	`cancel-sign-sub-inv_binary64_1749`
5×	`add-cube-cbrt_binary64_1818`
4×	`difference-of-squares_binary64_1752` `add-log-exp_binary64_1822`
3×	`distribute-lft-out--_binary64_1735` `pow1_binary64_1844`
2×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800`
1×	`flip3--_binary64_1787` `flip-+_binary64_1757` `pow1/2_binary64_1863` `diff-log_binary64_1875` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series51.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

37.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify75.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune49.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Error

0.1b

Counts

47 → 3

Compiler

Compiled 690 to 454 computations (34.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1783`
24×	`sqrt-prod_binary64_1799`
21×	`distribute-lft-out_binary64_1734`
18×	`times-frac_binary64_1789`
16×	`add-sqr-sqrt_binary64_1805`
15×	`add-cube-cbrt_binary64_1818`
7×	`add-exp-log_binary64_1821`
6×	`associate-/r*_binary64_1727`
5×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822` `pow1_binary64_1844`
3×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786`
2×	`associate-/r/_binary64_1729` `sqrt-div_binary64_1800` `div-exp_binary64_1834`
1×	`+-commutative_binary64_1713` `inv-pow_binary64_1868` `1-exp_binary64_1827` `div-inv_binary64_1780` `pow-flip_binary64_1857` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series69.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

33.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
22.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify59.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune94.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Error

0.0b

Counts

87 → 8

Compiler

Compiled 1481 to 1051 computations (29% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite81.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64_1799`
74×	`*-un-lft-identity_binary64_1783`
37×	`pow1_binary64_1844`
32×	`add-sqr-sqrt_binary64_1805` `distribute-lft-out_binary64_1734`
28×	`sqrt-div_binary64_1800`
18×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
17×	`add-exp-log_binary64_1821`
16×	`add-cube-cbrt_binary64_1818`
15×	`swap-sqr_binary64_1750`
14×	`flip-+_binary64_1757` `pow-flip_binary64_1857` `flip3-+_binary64_1786`
11×	`add-cbrt-cube_binary64_1819`
10×	`pow-prod-up_binary64_1853`
9×	`associate-l_binary64_1724` `associate-r_binary64_1723`
8×	`associate-/r/_binary64_1729` `frac-times_binary64_1793`
6×	`pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
4×	`associate-r/_binary64_1725` `prod-exp_binary64_1832` `associate-l/_binary64_1726` `div-exp_binary64_1834` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `times-frac_binary64_1789`
2×	`cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `pow-plus_binary64_1846` `cbrt-undiv_binary64_1817` `rec-exp_binary64_1833` `pow2_binary64_1864`
1×	`inv-pow_binary64_1868` `sqrt-unprod_binary64_1803` `div-inv_binary64_1780` `associate-/r_binary64_1727` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `rem-square-sqrt_binary64_1795` `clear-num_binary64_1782` `sqr-abs_binary64_1798`

Counts

4 → 155

Calls

4 calls:

25.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
24.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series139.0ms (5%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
39.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
32.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
24.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify80.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4900	3040
1	4900	3040

prune200.0ms (7.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	167	8	175

Error

0.0b

Counts

175 → 8

Compiler

Compiled 3647 to 2565 computations (29.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.3b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite46.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_1783`
36×	`sqrt-prod_binary64_1799`
33×	`distribute-lft-out_binary64_1734`
12×	`add-sqr-sqrt_binary64_1805` `pow1_binary64_1844`
10×	`swap-sqr_binary64_1750`
9×	`add-cube-cbrt_binary64_1818` `flip-+_binary64_1757` `flip3-+_binary64_1786`
8×	`add-log-exp_binary64_1822`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`frac-times_binary64_1793`
2×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `associate-l/_binary64_1726` `sqrt-div_binary64_1800` `sum-log_binary64_1874`
1×	`distribute-lft-in_binary64_1732` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `pow1/2_binary64_1863` `pow-sqr_binary64_1756` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796` `pow2_binary64_1864`

Counts

4 → 92

Calls

4 calls:

19.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series93.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
26.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
23.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
13.0ms	(sqrt.f64 (+.f64 1 x))

simplify68.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4916	1965
1	4916	1965

prune120.0ms (4.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	103	9	112

Error

0.0b

Counts

112 → 9

Compiler

Compiled 2307 to 1580 computations (31.5% saved)

regimes119.0ms (4.3%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Compiler

Compiled 1318 to 1073 computations (18.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.2s (44%)

Algorithm

1×

intervals

Results

204.0ms	2049×	body	1024	valid
117.0ms	4246×	body	128	valid
74.0ms	987×	body	512	valid
31.0ms	214×	body	2048	valid
25.0ms	504×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 631 to 516 computations (18.2% saved)

Details

analyze2.0ms (0.1%)

sample18.0ms (0.7%)

simplify100.0ms (3.6%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite15.0ms (0.5%)

series51.0ms (1.8%)

simplify75.0ms (2.7%)

prune49.0ms (1.8%)

localize6.0ms (0.2%)

rewrite26.0ms (0.9%)

series69.0ms (2.5%)

simplify59.0ms (2.1%)

prune94.0ms (3.4%)

localize9.0ms (0.3%)

rewrite81.0ms (2.9%)

series139.0ms (5%)

simplify80.0ms (2.9%)

prune200.0ms (7.3%)

localize10.0ms (0.3%)

rewrite46.0ms (1.7%)

series93.0ms (3.4%)

simplify68.0ms (2.5%)

prune120.0ms (4.4%)

regimes119.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (44%)

Profiling