Details

analyze172.0ms (2.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	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)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	65×	body	1024	valid
7.0ms	129×	body	128	valid
6.0ms	38×	body	512	valid
2.0ms	19×	body	256	valid
1.0ms	5×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (0%)

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

31.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite28.0ms (0.4%)

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:

18.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series79.0ms (1.1%)

Counts

2 → 9

Calls

2 calls:

54.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 170 to 142 computations (16.5% saved)

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune82.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.1b

Counts

50 → 3

Compiler

Compiled 583 to 384 computations (34.1% saved)

localize16.0ms (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)))

rewrite52.0ms (0.7%)

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:

21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series87.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
31.0ms	(sqrt.f64 (+.f64 x 1))
25.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 182 to 168 computations (7.7% saved)

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4911	1227
1	4911	1227

prune159.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Error

0.0b

Counts

90 → 8

Compiler

Compiled 1309 to 958 computations (26.8% saved)

localize19.0ms (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)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite69.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
18×	`add-cube-cbrt_binary64_1818`
13×	`cbrt-prod_binary64_1814`
10×	`add-exp-log_binary64_1821` `associate-r_binary64_1723`
9×	`sqrt-prod_binary64_1799` `times-frac_binary64_1789`
8×	`add-cbrt-cube_binary64_1819`
7×	`pow1_binary64_1844`
6×	`cbrt-div_binary64_1815`
4×	`flip-+_binary64_1757` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
3×	`associate-/l_binary64_1728` `distribute-lft-out_binary64_1734` `associate-/r_binary64_1727` `associate-l_binary64_1724` `unswap-sqr_binary64_1751`
2×	`associate-*r/_binary64_1725` `associate-/r/_binary64_1729` `sqrt-div_binary64_1800` `div-exp_binary64_1834` `pow1/3_binary64_1865`
1×	`inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `1-exp_binary64_1827` `div-inv_binary64_1780` `pow-flip_binary64_1857` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `rec-exp_binary64_1833`

Counts

4 → 90

Calls

4 calls:

25.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
18.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
6.0ms	(cbrt.f64 (+.f64 1 x))
6.0ms	(cbrt.f64 (+.f64 1 x))

series469.0ms (6.2%)

Counts

4 → 30

Calls

4 calls:

175.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
129.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
82.0ms	(cbrt.f64 (+.f64 1 x))
81.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1101 to 969 computations (12% saved)

simplify174.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4840	2640
1	4840	2640

prune301.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Error

0.0b

Counts

128 → 8

Compiler

Compiled 2938 to 2261 computations (23% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite276.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_1783`
700×	`sqrt-prod_binary64_1799`
594×	`times-frac_binary64_1789`
280×	`distribute-lft-out_binary64_1734`
254×	`add-sqr-sqrt_binary64_1805`
252×	`add-cube-cbrt_binary64_1818`
36×	`associate-/l*_binary64_1728`
28×	`sqrt-div_binary64_1800`
24×	`associate-/r/_binary64_1729`
18×	`associate-/r*_binary64_1727`
17×	`add-exp-log_binary64_1821`
14×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
12×	`div-inv_binary64_1780`
11×	`add-cbrt-cube_binary64_1819`
8×	`div-exp_binary64_1834` `pow1_binary64_1844`
4×	`cbrt-undiv_binary64_1817` `add-log-exp_binary64_1822`
3×	`pow-flip_binary64_1857` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
2×	`1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`
1×	`associate-/l/_binary64_1730` `inv-pow_binary64_1868`

Counts

4 → 453

Calls

4 calls:

64.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
23.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series172.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
46.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
43.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
36.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 408 to 368 computations (9.8% saved)

simplify424.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (149.0ms)

Iter	Nodes	Cost
0	4875	14766
1	4875	14766

prune1.4s (19.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	465	8	473

Error

Counts

473 → 8

Compiler

Compiled 11336 to 8340 computations (26.4% saved)

regimes309.0ms (4.1%)

Accuracy

Total 0.2b remaining (96.1%)

Threshold costs 0.2b (96.1%)

Compiler

Compiled 1851 to 1516 computations (18.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample2.9s (38.6%)

Algorithm

1×

intervals

Results

408.0ms	2033×	body	1024	valid
233.0ms	4240×	body	128	valid
160.0ms	1003×	body	512	valid
55.0ms	217×	body	2048	valid
51.0ms	507×	body	256	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 910 to 747 computations (17.9% saved)

Details

analyze172.0ms (2.3%)

sample39.0ms (0.5%)

simplify18.0ms (0.2%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite28.0ms (0.4%)

series79.0ms (1.1%)

simplify70.0ms (0.9%)

prune82.0ms (1.1%)

localize16.0ms (0.2%)

rewrite52.0ms (0.7%)

series87.0ms (1.2%)

simplify137.0ms (1.8%)

prune159.0ms (2.1%)

localize19.0ms (0.3%)

rewrite69.0ms (0.9%)

series469.0ms (6.2%)

simplify174.0ms (2.3%)

prune301.0ms (4%)

localize25.0ms (0.3%)

rewrite276.0ms (3.7%)

series172.0ms (2.3%)

simplify424.0ms (5.6%)

prune1.4s (19.1%)

regimes309.0ms (4.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.9s (38.6%)

Profiling