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 (0.6%)

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)

simplify165.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 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))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_1777` `add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762`
4×	`add-log-exp_binary64_1798` `difference-of-squares_binary64_1731`
3×	`distribute-lft-out--_binary64_1716` `add-cube-cbrt_binary64_1794` `pow1_binary64_1820`
2×	`distribute-lft-out_binary64_1715` `add-cbrt-cube_binary64_1795` `sqrt-div_binary64_1778` `add-exp-log_binary64_1797`
1×	`flip3--_binary64_1766` `rem-sqrt-square_binary64_1775` `diff-log_binary64_1851` `flip3-+_binary64_1765` `flip-+_binary64_1736` `flip--_binary64_1737` `sqrt-pow1_binary64_1779` `sub-neg_binary64_1755` `pow1/2_binary64_1839`

Counts

2 → 34

Calls

2 calls:

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

series94.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify92.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4907	747
1	4907	747

prune46.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

Compiler

Compiled 638 to 424 computations (33.5% 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)))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1762`
24×	`sqrt-prod_binary64_1777`
21×	`distribute-lft-out_binary64_1715`
18×	`times-frac_binary64_1768`
16×	`add-sqr-sqrt_binary64_1783`
15×	`add-cube-cbrt_binary64_1794`
7×	`add-exp-log_binary64_1797`
6×	`associate-/r*_binary64_1708`
5×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `pow1_binary64_1820`
3×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `associate-/l*_binary64_1709`
2×	`associate-/r/_binary64_1710` `div-exp_binary64_1810` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `inv-pow_binary64_1844` `clear-num_binary64_1761` `div-inv_binary64_1759` `+-commutative_binary64_1694` `pow-flip_binary64_1833` `cbrt-undiv_binary64_1793` `sqrt-pow1_binary64_1779` `1-exp_binary64_1803` `rec-exp_binary64_1809` `sum-log_binary64_1850` `pow1/2_binary64_1839`

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

series129.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
44.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify66.0ms (2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5545	1516

prune90.0ms (2.7%)

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 1460 to 1040 computations (28.8% saved)

localize9.0ms (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))))

rewrite65.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`sqrt-prod_binary64_1777`
62×	`add-sqr-sqrt_binary64_1783`
46×	`*-un-lft-identity_binary64_1762`
40×	`sqrt-pow1_binary64_1779`
32×	`sqrt-div_binary64_1778` `pow1_binary64_1820`
28×	`add-cube-cbrt_binary64_1794`
20×	`pow1/2_binary64_1839`
18×	`swap-sqr_binary64_1729`
10×	`add-exp-log_binary64_1797` `associate-l_binary64_1705` `associate-r_binary64_1704`
9×	`times-frac_binary64_1768` `pow-prod-up_binary64_1829` `flip3-+_binary64_1765` `flip-+_binary64_1736` `unswap-sqr_binary64_1730`
8×	`distribute-lft-out_binary64_1715` `add-cbrt-cube_binary64_1795`
5×	`pow-sqr_binary64_1735` `pow-prod-down_binary64_1830`
4×	`rem-sqrt-square_binary64_1775` `frac-times_binary64_1772` `add-log-exp_binary64_1798`
3×	`associate-/r_binary64_1708` `associate-/l_binary64_1709`
2×	`associate-/r/_binary64_1710` `associate-l/_binary64_1707` `div-exp_binary64_1810` `associate-r/_binary64_1706`
1×	`frac-2neg_binary64_1773` `inv-pow_binary64_1844` `prod-exp_binary64_1808` `pow-plus_binary64_1822` `clear-num_binary64_1761` `div-inv_binary64_1759` `pow-flip_binary64_1833` `cbrt-undiv_binary64_1793` `sqrt-unprod_binary64_1781` `cbrt-unprod_binary64_1792` `rem-square-sqrt_binary64_1774` `*-commutative_binary64_1695` `1-exp_binary64_1803` `rec-exp_binary64_1809` `pow2_binary64_1840`

Counts

4 → 165

Calls

4 calls:

22.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
17.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series176.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
45.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
39.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
30.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify83.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5041	2482

prune204.0ms (6.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	176	9	185

Merged error: 0.0b

Counts

185 → 9

Compiler

Compiled 3468 to 2602 computations (25% saved)

localize12.0ms (0.4%)

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))

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762`
18×	`add-cube-cbrt_binary64_1794`
13×	`cbrt-prod_binary64_1790`
10×	`add-exp-log_binary64_1797` `associate-r_binary64_1704`
9×	`times-frac_binary64_1768` `sqrt-prod_binary64_1777`
8×	`add-cbrt-cube_binary64_1795`
7×	`pow1_binary64_1820`
6×	`cbrt-div_binary64_1791`
4×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `add-log-exp_binary64_1798`
3×	`associate-/r_binary64_1708` `unswap-sqr_binary64_1730` `distribute-lft-out_binary64_1715` `associate-/l_binary64_1709` `associate-l_binary64_1705`
2×	`associate-/r/_binary64_1710` `pow1/3_binary64_1841` `div-exp_binary64_1810` `associate-*r/_binary64_1706` `sqrt-div_binary64_1778`
1×	`frac-2neg_binary64_1773` `inv-pow_binary64_1844` `pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `clear-num_binary64_1761` `div-inv_binary64_1759` `pow-flip_binary64_1833` `cbrt-undiv_binary64_1793` `cbrt-unprod_binary64_1792` `*-commutative_binary64_1695` `1-exp_binary64_1803` `rec-exp_binary64_1809`

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)))
9.0ms	(*.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))

series760.0ms (23.2%)

Counts

4 → 12

Calls

4 calls:

589.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
89.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
41.0ms	(cbrt.f64 (+.f64 1 x))
41.0ms	(cbrt.f64 (+.f64 1 x))

simplify56.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5344	3235

prune171.0ms (5.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

Compiler

Compiled 2977 to 2294 computations (22.9% saved)

regimes52.0ms (1.6%)

Compiler: Compiled 568 to 464 computations (18.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample888.0ms (27.1%)

Algorithm

1×

intervals

Results

225.0ms	2039×	body	1024	valid
127.0ms	4318×	body	128	valid
73.0ms	941×	body	512	valid
30.0ms	223×	body	2048	valid
25.0ms	479×	body	256	valid

Compiler

Compiled 302 to 249 computations (17.5% saved)

Details

analyze3.0ms (0.1%)

sample20.0ms (0.6%)

simplify165.0ms (5%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series94.0ms (2.9%)

simplify92.0ms (2.8%)

prune46.0ms (1.4%)

localize6.0ms (0.2%)

rewrite31.0ms (0.9%)

series129.0ms (3.9%)

simplify66.0ms (2%)

prune90.0ms (2.7%)

localize9.0ms (0.3%)

rewrite65.0ms (2%)

series176.0ms (5.4%)

simplify83.0ms (2.5%)

prune204.0ms (6.2%)

localize12.0ms (0.4%)

rewrite36.0ms (1.1%)

series760.0ms (23.2%)

simplify56.0ms (1.7%)

prune171.0ms (5.2%)

regimes52.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample888.0ms (27.1%)

Profiling