Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample34.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify220.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5050	41

prune6.0ms (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

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite101.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`pow1_binary64_1844`
43×	`add-exp-log_binary64_1821`
40×	`add-sqr-sqrt_binary64_1805`
39×	`add-cbrt-cube_binary64_1819`
36×	`associate-l_binary64_1724`
31×	`times-frac_binary64_1789`
29×	`*-un-lft-identity_binary64_1783`
27×	`add-cube-cbrt_binary64_1818`
22×	`prod-exp_binary64_1832`
21×	`pow-plus_binary64_1846` `pow-prod-up_binary64_1853`
20×	`cbrt-unprod_binary64_1816`
14×	`associate-*l/_binary64_1726` `sqrt-prod_binary64_1799`
13×	`pow-prod-down_binary64_1854`
12×	`frac-add_binary64_1791`
7×	`associate-r_binary64_1723`
6×	`associate-*r/_binary64_1725` `flip-+_binary64_1757` `frac-times_binary64_1793` `flip3-+_binary64_1786`
5×	`div-exp_binary64_1834` `unswap-sqr_binary64_1751`
4×	`pow-sqr_binary64_1756` `cbrt-undiv_binary64_1817` `add-log-exp_binary64_1822` `pow2_binary64_1864`
3×	`*-commutative_binary64_1714`
2×	`pow3_binary64_1866` `div-inv_binary64_1780`
1×	`distribute-lft-in_binary64_1732` `1-exp_binary64_1827` `pow1/2_binary64_1863` `distribute-rgt-in_binary64_1733` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

4 → 150

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
14.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
11.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series380.0ms (8.2%)

Counts

4 → 10

Calls

4 calls:

310.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
39.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
31.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4958	4756
1	4958	4756

prune442.0ms (9.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Error

Counts

162 → 4

Compiler

Compiled 9989 to 4588 computations (54.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 x 6))
0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1805`
30×	`associate-r_binary64_1723`
23×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
20×	`times-frac_binary64_1789`
19×	`add-exp-log_binary64_1821`
16×	`add-cbrt-cube_binary64_1819`
13×	`sqrt-prod_binary64_1799`
12×	`pow1_binary64_1844`
9×	`associate-l_binary64_1724`
8×	`prod-exp_binary64_1832`
7×	`unswap-sqr_binary64_1751`
6×	`cbrt-unprod_binary64_1816`
4×	`unpow-prod-down_binary64_1862` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
3×	`*-commutative_binary64_1714`
2×	`sqr-pow_binary64_1755`
1×	`associate-*r/_binary64_1725` `div-inv_binary64_1780` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 99

Calls

4 calls:

24.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/21 (pow.f64 x 6))
1.0ms	(sqrt.f64 PI.f64)

series119.0ms (2.6%)

Counts

4 → 10

Calls

4 calls:

65.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
37.0ms	(*.f64 1/21 (pow.f64 x 6))
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5054	2532

prune204.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	110	3	113

Error

Counts

113 → 3

Compiler

Compiled 3846 to 2599 computations (32.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 6) 1/21)
0.1b	(.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 (pow.f64 x 4) 1/5))))) (/.f64 1 (sqrt.f64 PI.f64)))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64_1821`
29×	`add-sqr-sqrt_binary64_1805`
26×	`associate-r_binary64_1723`
23×	`add-cbrt-cube_binary64_1819`
22×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
18×	`prod-exp_binary64_1832` `times-frac_binary64_1789`
15×	`pow1_binary64_1844`
12×	`sqrt-prod_binary64_1799`
11×	`associate-l_binary64_1724`
10×	`cbrt-unprod_binary64_1816`
6×	`pow-prod-down_binary64_1854`
5×	`associate-*r/_binary64_1725`
4×	`unpow-prod-down_binary64_1862` `div-exp_binary64_1834` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`*-commutative_binary64_1714`
2×	`sqr-pow_binary64_1755` `1-exp_binary64_1827` `flip-+_binary64_1757` `associate-*l/_binary64_1726` `cbrt-undiv_binary64_1817` `frac-times_binary64_1793` `flip3-+_binary64_1786` `rec-exp_binary64_1833`
1×	`un-div-inv_binary64_1781` `div-inv_binary64_1780` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 108

Calls

4 calls:

24.0ms	(.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 (pow.f64 x 4) 1/5))))) (/.f64 1 (sqrt.f64 PI.f64)))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 6) 1/21)
1.0ms	(sqrt.f64 PI.f64)

series117.0ms (2.5%)

Counts

4 → 10

Calls

4 calls:

70.0ms	(.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 (pow.f64 x 4) 1/5))))) (/.f64 1 (sqrt.f64 PI.f64)))
29.0ms	(*.f64 (pow.f64 x 6) 1/21)
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4933	2891
1	4933	2891

prune208.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	3	121

Error

Counts

121 → 3

Compiler

Compiled 3928 to 2677 computations (31.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 6) 1/21)
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1805`
19×	`add-exp-log_binary64_1821`
16×	`add-cbrt-cube_binary64_1819`
13×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`associate-l_binary64_1724` `pow1_binary64_1844`
9×	`sqrt-prod_binary64_1799`
7×	`prod-exp_binary64_1832`
6×	`associate-/r*_binary64_1727` `times-frac_binary64_1789`
5×	`cbrt-unprod_binary64_1816`
4×	`unpow-prod-down_binary64_1862` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822` `associate-r_binary64_1723`
3×	`pow-prod-down_binary64_1854`
2×	`associate-r/_binary64_1725` `associate-/l/_binary64_1730` `sqr-pow_binary64_1755` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `div-exp_binary64_1834`
1×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `div-inv_binary64_1780` `pow1/2_binary64_1863` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 86

Calls

4 calls:

17.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
7.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 6) 1/21)
1.0ms	(sqrt.f64 PI.f64)

series116.0ms (2.5%)

Counts

4 → 10

Calls

4 calls:

68.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
30.0ms	(*.f64 (pow.f64 x 6) 1/21)
18.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4995	1906
1	4995	1906

prune142.0ms (3.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	96	3	99

Error

Counts

99 → 3

Compiler

Compiled 2953 to 1977 computations (33.1% saved)

regimes336.0ms (7.2%)

Accuracy

Total 0.1b remaining (99.4%)

Threshold costs 0.1b (99.4%)

Compiler

Compiled 4709 to 3338 computations (29.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	44
1	34	44

end0.0ms (0%)

sample1.7s (36%)

Algorithm

1×

intervals

Results

738.0ms	8000×	body	128	valid
98.0ms	8000×	pre	128	true

Compiler

Compiled 929 to 672 computations (27.7% saved)

Details

analyze6.0ms (0.1%)

sample34.0ms (0.7%)

simplify220.0ms (4.7%)

prune6.0ms (0.1%)

localize25.0ms (0.5%)

rewrite101.0ms (2.2%)

series380.0ms (8.2%)

simplify94.0ms (2%)

prune442.0ms (9.5%)

localize17.0ms (0.4%)

rewrite51.0ms (1.1%)

series119.0ms (2.6%)

simplify69.0ms (1.5%)

prune204.0ms (4.4%)

localize18.0ms (0.4%)

rewrite54.0ms (1.2%)

series117.0ms (2.5%)

simplify93.0ms (2%)

prune208.0ms (4.5%)

localize16.0ms (0.4%)

rewrite40.0ms (0.9%)

series116.0ms (2.5%)

simplify63.0ms (1.4%)

prune142.0ms (3.1%)

regimes336.0ms (7.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (36%)

Profiling