Details

analyze816.0ms (12.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	189×	body	128	valid
7.0ms	26×	body	2048	valid
5.0ms	256×	pre	128	true
5.0ms	14×	body	4096	valid
4.0ms	19×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify175.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.4b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.5b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

18.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series204.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

86.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
67.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
50.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4839	1838
1	4839	1838

prune424.0ms (6.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	66	11	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	12	78

Merged error: 13.1b

Counts

78 → 12

Compiler

Compiled 8051 to 5809 computations (27.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
9.0b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64_1815`
30×	`add-sqr-sqrt_binary64_1821`
28×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
27×	`times-frac_binary64_1805`
9×	`associate-/r*_binary64_1743`
8×	`sqrt-div_binary64_1816`
6×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
4×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`associate-/l*_binary64_1744`
2×	`pow1/2_binary64_1879` `associate-/r/_binary64_1745` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `div-exp_binary64_1850` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
4.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))

series359.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
97.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
51.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
46.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4981	2712
1	4981	2712

prune514.0ms (8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	105	13	118

Merged error: 13.1b

Counts

118 → 13

Compiler

Compiled 10591 to 7303 computations (31% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.0b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))))
15.2b	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`cbrt-prod_binary64_1830`
60×	`sqrt-prod_binary64_1815`
54×	`times-frac_binary64_1805`
47×	`add-sqr-sqrt_binary64_1821`
45×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
33×	`unpow-prod-down_binary64_1878` `cube-prod_binary64_1827`
12×	`sqrt-div_binary64_1816`
6×	`pow1_binary64_1860` `add-log-exp_binary64_1838`
5×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`add-cbrt-cube_binary64_1835` `associate-/r/_binary64_1745` `add-exp-log_binary64_1837`
2×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `rem-cbrt-cube_binary64_1823` `cube-mult_binary64_1829` `pow1/3_binary64_1881` `unpow3_binary64_1865` `sqr-pow_binary64_1771` `cube-div_binary64_1828` `cbrt-div_binary64_1831`

Counts

4 → 123

Calls

4 calls:

17.0ms	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
4.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))))

series356.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
97.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))))
55.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5005	4083

prune356.0ms (5.5%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	135	13	148

Merged error: 13.1b

Counts

148 → 13

Compiler

Compiled 7070 to 4717 computations (33.3% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
9.9b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite69.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64_1837`
36×	`prod-exp_binary64_1848`
33×	`associate-l_binary64_1740` `sqrt-prod_binary64_1815`
27×	`add-sqr-sqrt_binary64_1821` `times-frac_binary64_1805`
25×	`add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799`
18×	`div-exp_binary64_1850`
11×	`pow1_binary64_1860`
10×	`cbrt-unprod_binary64_1832`
9×	`rec-exp_binary64_1849` `1-exp_binary64_1843`
8×	`sqrt-div_binary64_1816`
6×	`add-log-exp_binary64_1838`
5×	`cbrt-undiv_binary64_1833`
4×	`associate-*r/_binary64_1741` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`pow-prod-down_binary64_1870`
2×	`un-div-inv_binary64_1797` `pow1/2_binary64_1879` `associate-/r/_binary64_1745` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812` `frac-times_binary64_1809`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `-commutative_binary64_1730` `div-inv_binary64_1796` `associate-l/_binary64_1742` `associate-r_binary64_1739`

Counts

4 → 116

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))))

series272.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))))
84.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
52.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify110.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4918	2952
1	4918	2952

prune347.0ms (5.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	8	9
Picked	0	1	1
Done	1	2	3
Total	128	13	141

Merged error: 13.1b

Counts

141 → 13

Compiler

Compiled 7118 to 4937 computations (30.6% saved)

regimes257.0ms (4%)

Compiler: Compiled 3975 to 2849 computations (28.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms (0%)

sample1.6s (25.4%)

Algorithm

1×

intervals

Results

355.0ms	6106×	body	128	valid
217.0ms	757×	body	2048	valid
160.0ms	8000×	pre	128	true
121.0ms	533×	body	1024	valid
93.0ms	256×	body	4096	valid
42.0ms	240×	body	512	valid
14.0ms	108×	body	256	valid

Compiler

Compiled 602 to 438 computations (27.2% saved)

Details

analyze816.0ms (12.7%)

sample42.0ms (0.6%)

simplify175.0ms (2.7%)

prune3.0ms (0%)

localize12.0ms (0.2%)

rewrite41.0ms (0.6%)

series204.0ms (3.2%)

simplify94.0ms (1.5%)

prune424.0ms (6.6%)

localize15.0ms (0.2%)

rewrite44.0ms (0.7%)

series359.0ms (5.6%)

simplify92.0ms (1.4%)

prune514.0ms (8%)

localize24.0ms (0.4%)

rewrite60.0ms (0.9%)

series356.0ms (5.5%)

simplify86.0ms (1.3%)

prune356.0ms (5.5%)

localize25.0ms (0.4%)

rewrite69.0ms (1.1%)

series272.0ms (4.2%)

simplify110.0ms (1.7%)

prune347.0ms (5.4%)

regimes257.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (25.4%)

Profiling