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)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	67×	body	1024	valid
4.0ms	140×	body	128	valid
2.0ms	25×	body	512	valid
1.0ms	11×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify169.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune5.0ms (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: 29.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_1815`
14×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
6×	`cancel-sign-sub-inv_binary64_1765`
5×	`add-cube-cbrt_binary64_1834`
4×	`add-log-exp_binary64_1838` `difference-of-squares_binary64_1768`
3×	`pow1_binary64_1860` `distribute-lft-out--_binary64_1751`
2×	`sqrt-div_binary64_1816` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `distribute-lft-out_binary64_1750`
1×	`sub-neg_binary64_1792` `pow1/2_binary64_1879` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `sqrt-pow1_binary64_1817` `flip3-+_binary64_1802` `rem-sqrt-square_binary64_1812` `flip-+_binary64_1773`

Counts

2 → 40

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series102.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

75.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5005	794

prune74.0ms (2%)

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

Merged error: 0.1b

Counts

47 → 3

Compiler

Compiled 1029 to 725 computations (29.5% saved)

localize7.0ms (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)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1799`
24×	`sqrt-prod_binary64_1815`
21×	`distribute-lft-out_binary64_1750`
18×	`times-frac_binary64_1805`
16×	`add-sqr-sqrt_binary64_1821`
15×	`add-cube-cbrt_binary64_1834`
7×	`add-exp-log_binary64_1837`
6×	`associate-/r*_binary64_1743`
5×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835`
3×	`associate-/l*_binary64_1744` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`sqrt-div_binary64_1816` `div-exp_binary64_1850` `associate-/r/_binary64_1745`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812` `inv-pow_binary64_1884`

Counts

3 → 75

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series135.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
44.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
30.0ms	(sqrt.f64 (+.f64 x 1))

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4944	1516
1	4944	1516

prune189.0ms (5.1%)

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

Merged error: 0.0b

Counts

87 → 8

Compiler

Compiled 3028 to 2316 computations (23.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite68.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_1815`
70×	`add-sqr-sqrt_binary64_1821`
46×	`*-un-lft-identity_binary64_1799`
40×	`sqrt-pow1_binary64_1817`
32×	`pow1_binary64_1860` `sqrt-div_binary64_1816`
28×	`add-cube-cbrt_binary64_1834`
20×	`pow1/2_binary64_1879`
18×	`swap-sqr_binary64_1766`
12×	`rem-sqrt-square_binary64_1812`
10×	`associate-l_binary64_1740` `add-exp-log_binary64_1837` `associate-r_binary64_1739`
9×	`unswap-sqr_binary64_1767` `times-frac_binary64_1805` `pow-prod-up_binary64_1869` `flip3-+_binary64_1802` `flip-+_binary64_1773`
8×	`add-cbrt-cube_binary64_1835` `distribute-lft-out_binary64_1750`
5×	`pow-sqr_binary64_1772` `pow-prod-down_binary64_1870`
4×	`sqr-abs_binary64_1814` `add-log-exp_binary64_1838` `frac-times_binary64_1809`
3×	`associate-/l_binary64_1744` `associate-/r_binary64_1743`
2×	`div-exp_binary64_1850` `associate-r/_binary64_1741` `associate-/r/_binary64_1745` `associate-l/_binary64_1742`
1×	`pow2_binary64_1880` `clear-num_binary64_1798` `prod-exp_binary64_1848` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `div-inv_binary64_1796` `rem-square-sqrt_binary64_1811` `pow-plus_binary64_1862` `inv-pow_binary64_1884`

Counts

4 → 169

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
19.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series181.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
41.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
40.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
31.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4969	2509
1	4969	2509

prune439.0ms (11.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	180	9	189

Merged error: 0.0b

Counts

189 → 9

Compiler

Compiled 4147 to 3152 computations (24% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
18×	`add-cube-cbrt_binary64_1834`
13×	`cbrt-prod_binary64_1830`
10×	`add-exp-log_binary64_1837` `associate-r_binary64_1739`
9×	`sqrt-prod_binary64_1815` `times-frac_binary64_1805`
8×	`add-cbrt-cube_binary64_1835`
7×	`pow1_binary64_1860`
6×	`cbrt-div_binary64_1831`
4×	`add-log-exp_binary64_1838` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`associate-/l_binary64_1744` `unswap-sqr_binary64_1767` `associate-/r_binary64_1743` `associate-l_binary64_1740` `distribute-lft-out_binary64_1750`
2×	`sqrt-div_binary64_1816` `div-exp_binary64_1850` `pow1/3_binary64_1881` `associate-*r/_binary64_1741` `associate-/r/_binary64_1745`
1×	`clear-num_binary64_1798` `prod-exp_binary64_1848` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `inv-pow_binary64_1884`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
4.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series767.0ms (20.5%)

Counts

4 → 12

Calls

4 calls:

584.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
85.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
49.0ms	(cbrt.f64 (+.f64 1 x))
48.0ms	(cbrt.f64 (+.f64 1 x))

simplify92.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4869	3063
1	4869	3063

prune241.0ms (6.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

Compiler

Compiled 4284 to 3375 computations (21.2% saved)

regimes51.0ms (1.4%)

Compiler: Compiled 552 to 454 computations (17.8% 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%)

sample877.0ms (23.5%)

Algorithm

1×

intervals

Results

220.0ms	2039×	body	1024	valid
125.0ms	4318×	body	128	valid
75.0ms	941×	body	512	valid
29.0ms	223×	body	2048	valid
25.0ms	479×	body	256	valid

Compiler

Compiled 294 to 244 computations (17% saved)

Details

analyze3.0ms (0.1%)

sample20.0ms (0.5%)

simplify169.0ms (4.5%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite17.0ms (0.5%)

series102.0ms (2.7%)

simplify63.0ms (1.7%)

prune74.0ms (2%)

localize7.0ms (0.2%)

rewrite31.0ms (0.8%)

series135.0ms (3.6%)

simplify68.0ms (1.8%)

prune189.0ms (5.1%)

localize12.0ms (0.3%)

rewrite68.0ms (1.8%)

series181.0ms (4.8%)

simplify71.0ms (1.9%)

prune439.0ms (11.8%)

localize11.0ms (0.3%)

rewrite38.0ms (1%)

series767.0ms (20.5%)

simplify92.0ms (2.5%)

prune241.0ms (6.4%)

regimes51.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample877.0ms (23.5%)

Profiling