Details

analyze138.0ms (2.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify235.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5070	43

prune4.0ms (0.1%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.4b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64_1860` `add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
14×	`add-cbrt-cube_binary64_1835`
10×	`add-cube-cbrt_binary64_1834` `associate-r_binary64_1739`
6×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `add-log-exp_binary64_1838` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870` `cancel-sign-sub-inv_binary64_1765`
4×	`associate-*r/_binary64_1741`
3×	`pow-unpow_binary64_1876` `unpow-prod-down_binary64_1878`
2×	`sub-neg_binary64_1792` `unswap-sqr_binary64_1767` `associate-l_binary64_1740` `difference-of-squares_binary64_1768` `associate-+r+_binary64_1731` `*-commutative_binary64_1730` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `unpow2_binary64_1864` `pow-to-exp_binary64_1868` `flip--_binary64_1774` `flip3--_binary64_1803` `pow-exp_binary64_1867` `sqr-pow_binary64_1771` `pow-pow_binary64_1871` `distribute-lft-out_binary64_1750` `distribute-lft-out--_binary64_1751`

Counts

4 → 87

Calls

4 calls:

11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series303.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
74.0ms	(.f64 (.f64 a a) (-.f64 1 a))
49.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
48.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify60.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5074	1789

prune204.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	2	100

Merged error: 0.0b

Counts

100 → 2

Compiler

Compiled 4809 to 2590 computations (46.1% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
1.4b	(.f64 (.f64 b b) (+.f64 3 a))
2.8b	(.f64 (.f64 b b) (*.f64 a a))

rewrite84.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_1860`
32×	`associate-*r/_binary64_1741`
26×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
20×	`pow-prod-down_binary64_1870` `frac-add_binary64_1807`
14×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `flip3-+_binary64_1802` `flip-+_binary64_1773`
13×	`add-sqr-sqrt_binary64_1821` `add-log-exp_binary64_1838` `*-un-lft-identity_binary64_1799`
11×	`associate-r_binary64_1739`
8×	`add-cube-cbrt_binary64_1834`
6×	`sum-log_binary64_1890` `distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `cancel-sign-sub-inv_binary64_1765`
5×	`flip--_binary64_1774` `flip3--_binary64_1803`
4×	`pow-prod-up_binary64_1869` `pow-plus_binary64_1862`
3×	`unswap-sqr_binary64_1767` `associate-l_binary64_1740` `*-commutative_binary64_1730`
2×	`pow2_binary64_1880` `pow-sqr_binary64_1772` `sub-neg_binary64_1792` `difference-of-squares_binary64_1768` `associate-+r+_binary64_1731`
1×	`+-commutative_binary64_1729` `distribute-lft-out_binary64_1750` `distribute-lft-out--_binary64_1751` `associate-+l+_binary64_1732`

Counts

4 → 113

Calls

4 calls:

31.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
13.0ms	(.f64 (.f64 b b) (*.f64 a a))
11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series303.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
71.0ms	(.f64 (.f64 a a) (-.f64 1 a))
50.0ms	(.f64 (.f64 b b) (+.f64 3 a))
45.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify102.0ms (2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4942	4559
1	4942	4559

prune297.0ms (5.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Merged error: 0.0b

Counts

127 → 2

Compiler

Compiled 6527 to 3838 computations (41.2% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (pow.f64 (.f64 b a) 2))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.1b	(pow.f64 (*.f64 b a) 2)
1.4b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_1837`
20×	`add-sqr-sqrt_binary64_1821`
17×	`pow1_binary64_1860`
16×	`add-cbrt-cube_binary64_1835` `-un-lft-identity_binary64_1799` `associate-r*_binary64_1739`
12×	`prod-exp_binary64_1848`
11×	`add-cube-cbrt_binary64_1834`
7×	`cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
6×	`cancel-sign-sub-inv_binary64_1765`
5×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `unswap-sqr_binary64_1767` `associate-l_binary64_1740`
4×	`add-log-exp_binary64_1838` `associate-*r/_binary64_1741` `pow-exp_binary64_1867`
3×	`pow-unpow_binary64_1876` `unpow2_binary64_1864` `sqr-pow_binary64_1771` `*-commutative_binary64_1730`
2×	`sub-neg_binary64_1792` `pow-to-exp_binary64_1868` `unpow-prod-down_binary64_1878` `difference-of-squares_binary64_1768` `pow-pow_binary64_1871`
1×	`flip--_binary64_1774` `flip3--_binary64_1803` `distribute-lft-out_binary64_1750` `flip3-+_binary64_1802` `distribute-lft-out--_binary64_1751` `flip-+_binary64_1773`

Counts

4 → 99

Calls

4 calls:

11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(.f64 2 (pow.f64 (.f64 b a) 2))
4.0ms	(pow.f64 (*.f64 b a) 2)

series219.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (.f64 a a) (-.f64 1 a))
50.0ms	(.f64 (.f64 b b) (+.f64 3 a))
48.0ms	(.f64 2 (pow.f64 (.f64 b a) 2))
44.0ms	(pow.f64 (*.f64 b a) 2)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5261	1191

prune396.0ms (7.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	111	2	113

Merged error: 0.0b

Counts

113 → 2

Compiler

Compiled 4296 to 2740 computations (36.2% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
0.3b	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)
1.4b	(.f64 (.f64 b b) (+.f64 3 a))
31.8b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1799`
14×	`add-sqr-sqrt_binary64_1821`
13×	`add-cube-cbrt_binary64_1834`
12×	`cbrt-prod_binary64_1830`
11×	`pow1_binary64_1860` `add-exp-log_binary64_1837`
10×	`add-cbrt-cube_binary64_1835`
9×	`unpow-prod-down_binary64_1878`
6×	`pow-unpow_binary64_1876` `cube-prod_binary64_1827`
4×	`add-log-exp_binary64_1838` `cube-div_binary64_1828` `associate-r_binary64_1739`
3×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `sqr-pow_binary64_1771` `pow-prod-down_binary64_1870` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`cube-mult_binary64_1829` `pow-to-exp_binary64_1868` `associate-*r/_binary64_1741` `unpow3_binary64_1865` `pow-exp_binary64_1867` `pow-pow_binary64_1871` `cbrt-div_binary64_1831`
1×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `rem-cbrt-cube_binary64_1823` `pow1/3_binary64_1881` `unpow2_binary64_1864` `unswap-sqr_binary64_1767` `associate-l_binary64_1740` `*-commutative_binary64_1730` `distribute-lft-out_binary64_1750` `rem-cube-cbrt_binary64_1822`

Counts

4 → 90

Calls

4 calls:

12.0ms	(.f64 (.f64 b b) (+.f64 3 a))
11.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
9.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))
6.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)

series1.4s (27.6%)

Counts

4 → 12

Calls

4 calls:

1.2s	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
141.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))
48.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)
47.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4876	3619
1	4876	3619

prune174.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	102	2	104

Merged error: 0.0b

Counts

104 → 2

Compiler

Compiled 4333 to 2319 computations (46.5% saved)

regimes31.0ms (0.6%)

Compiler: Compiled 211 to 161 computations (23.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	52
1	54	52

end0.0ms (0%)

sample814.0ms (15.8%)

Algorithm

1×

intervals

Results

526.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 132 to 98 computations (25.8% saved)

Details

analyze138.0ms (2.7%)

sample28.0ms (0.5%)

simplify235.0ms (4.5%)

prune4.0ms (0.1%)

localize19.0ms (0.4%)

rewrite46.0ms (0.9%)

series303.0ms (5.9%)

simplify60.0ms (1.2%)

prune204.0ms (3.9%)

localize20.0ms (0.4%)

rewrite84.0ms (1.6%)

series303.0ms (5.9%)

simplify102.0ms (2%)

prune297.0ms (5.7%)

localize26.0ms (0.5%)

rewrite43.0ms (0.8%)

series219.0ms (4.2%)

simplify52.0ms (1%)

prune396.0ms (7.7%)

localize19.0ms (0.4%)

rewrite50.0ms (1%)

series1.4s (27.6%)

simplify71.0ms (1.4%)

prune174.0ms (3.4%)

regimes31.0ms (0.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample814.0ms (15.8%)

Profiling