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)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms	53×	body	1024	valid
4.0ms	143×	body	128	valid
3.0ms	39×	body	512	valid
1.0ms	6×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify108.0ms (2.3%)

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%)

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

28.0b

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))
2.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.3%)

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:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series57.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

42.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune50.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Error

0.1b

Counts

47 → 4

Compiler

Compiled 709 to 468 computations (34% saved)

localize6.0ms (0.1%)

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

rewrite27.0ms (0.6%)

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:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series73.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

32.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
26.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune97.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Error

0.0b

Counts

88 → 10

Compiler

Compiled 1501 to 1069 computations (28.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.8%)

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:

11.0ms	(/.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))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series425.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
41.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
23.0ms	(cbrt.f64 (+.f64 1 x))
23.0ms	(cbrt.f64 (+.f64 1 x))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4944	3191
1	4944	3191

prune188.0ms (4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	101	11	112

Error

0.0b

Counts

112 → 11

Compiler

Compiled 3193 to 2469 computations (22.7% saved)

localize13.0ms (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)))
0.1b	(/.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))))

rewrite151.0ms (3.2%)

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:

34.0ms	(/.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))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series165.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
43.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
39.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
34.0ms	(/.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))))

simplify235.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4903	17091
1	4903	17091

prune1.1s (23.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	6	3	9
Picked	0	1	1
Done	0	1	1
Total	467	9	476

Error

Counts

476 → 9

Compiler

Compiled 12715 to 9345 computations (26.5% saved)

regimes161.0ms (3.5%)

Accuracy

Total 0.2b remaining (95.9%)

Threshold costs 0.2b (95.9%)

Compiler

Compiled 1796 to 1463 computations (18.5% 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%)

sample1.5s (31.8%)

Algorithm

1×

intervals

Results

203.0ms	1963×	body	1024	valid
118.0ms	4275×	body	128	valid
74.0ms	1008×	body	512	valid
31.0ms	527×	body	256	valid
29.0ms	227×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 888 to 725 computations (18.4% saved)

Details

analyze3.0ms (0.1%)

sample18.0ms (0.4%)

simplify108.0ms (2.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite15.0ms (0.3%)

series57.0ms (1.2%)

simplify77.0ms (1.7%)

prune50.0ms (1.1%)

localize6.0ms (0.1%)

rewrite27.0ms (0.6%)

series73.0ms (1.6%)

simplify57.0ms (1.2%)

prune97.0ms (2.1%)

localize10.0ms (0.2%)

rewrite35.0ms (0.8%)

series425.0ms (9.2%)

simplify79.0ms (1.7%)

prune188.0ms (4%)

localize13.0ms (0.3%)

rewrite151.0ms (3.2%)

series165.0ms (3.6%)

simplify235.0ms (5.1%)

prune1.1s (23.9%)

regimes161.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (31.8%)

Profiling