Details

analyze131.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.1%)

Algorithm

1×

intervals

Results

12.0ms	206×	body	128	valid
5.0ms	256×	pre	128	true
4.0ms	16×	body	1024	valid
3.0ms	17×	body	512	valid
2.0ms	15×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify163.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5371	43

prune6.0ms (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

Error

25.0b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

2.7b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

20.7b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite317.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

12.4b

Rules

54×	`times-frac_binary64_1789`
47×	`*-un-lft-identity_binary64_1783`
25×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805`
17×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
14×	`associate-/r/_binary64_1729`
11×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out_binary64_1734`
10×	`associate-/l*_binary64_1728`
9×	`associate-/l/_binary64_1730`
7×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `div-inv_binary64_1780` `associate-/r*_binary64_1727`
5×	`add-log-exp_binary64_1822`
4×	`frac-times_binary64_1793`
3×	`pow1_binary64_1844` `flip3--_binary64_1787` `flip--_binary64_1758`
2×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-l/_binary64_1726` `associate-r/_binary64_1725`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

3 → 111

Calls

3 calls:

35.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

22.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

16.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 5370 to 2710 computations (49.5% saved)

series3.8s (8.1%)

Error

0.2b

Counts

3 → 77

Calls

3 calls:

1.8s

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

1.2s

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

241.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 17696 to 13715 computations (22.5% saved)

simplify134.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5040	15635

prune680.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	3	189

Error

0.0b

Counts

189 → 3

Compiler

Compiled 12438 to 7160 computations (42.4% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
2.7b	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite319.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`*-un-lft-identity_binary64_1783`
45×	`add-sqr-sqrt_binary64_1805`
35×	`times-frac_binary64_1789`
26×	`add-cube-cbrt_binary64_1818`
21×	`associate-r_binary64_1723`
20×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
8×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
7×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `associate-/l/_binary64_1730` `associate-/r*_binary64_1727`
6×	`add-log-exp_binary64_1822` `pow1_binary64_1844` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-/r/_binary64_1729` `associate-/l*_binary64_1728`
4×	`distribute-lft-out_binary64_1734` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `frac-times_binary64_1793` `associate-l/_binary64_1726` `associate-l*_binary64_1724`
3×	`div-inv_binary64_1780`
2×	`unswap-sqr_binary64_1751` `associate-*r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713` `pow-prod-down_binary64_1854` `*-commutative_binary64_1714` `div-sub_binary64_1788` `flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 129

Calls

4 calls:

29.0ms	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
27.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
19.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 5642 to 2885 computations (48.9% saved)

series4.0s (8.7%)

Error

0.0b

Counts

4 → 98

Calls

4 calls:

1.8s	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.2s	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
236.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
216.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 20076 to 15443 computations (23.1% saved)

simplify134.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5009	15312

prune903.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	226	4	230

Error

Counts

230 → 4

Compiler

Compiled 13659 to 8058 computations (41% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
0.8b	(-.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))
2.7b	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3))

rewrite1.0s (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

78×	`*-un-lft-identity_binary64_1783`
57×	`add-sqr-sqrt_binary64_1805`
52×	`associate-r_binary64_1723`
47×	`times-frac_binary64_1789`
28×	`add-cube-cbrt_binary64_1818`
16×	`distribute-lft-out_binary64_1734`
14×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
11×	`cancel-sign-sub-inv_binary64_1749`
10×	`difference-of-squares_binary64_1752`
9×	`distribute-lft-out--_binary64_1735`
8×	`add-log-exp_binary64_1822` `pow1_binary64_1844` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-l_binary64_1724`
6×	`associate-/r/_binary64_1729`
4×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `associate-*l/_binary64_1726`
3×	`div-inv_binary64_1780`
2×	`pow-prod-down_binary64_1854` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-r/_binary64_1725` `-commutative_binary64_1714`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713` `diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758`

Counts

4 → 137

Calls

4 calls:

27.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
21.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
19.0ms	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3))
15.0ms	(-.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))

Compiler

Compiled 17389 to 9851 computations (43.3% saved)

series26.3s (56.7%)

Error

Counts

4 → 83

Calls

4 calls:

22.5s	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3))
2.3s	(-.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))
313.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
225.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))

Compiler

Compiled 37706 to 25524 computations (32.3% saved)

simplify134.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5179	13462

prune2.5s (5.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	220	4	224

Error

Counts

224 → 4

Compiler

Compiled 30255 to 17415 computations (42.4% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 (.f64 i 4) (+.f64 2 (.f64 beta 2))) alpha)

rewrite48.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `times-frac_binary64_1789` `*-un-lft-identity_binary64_1783`
3×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`associate-/l/_binary64_1730`
1×	`pow1_binary64_1844` `div-exp_binary64_1834` `add-log-exp_binary64_1822` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `flip3-+_binary64_1786` `flip-+_binary64_1757`

Counts

1 → 29

Calls

1 calls:

9.0ms

(/.f64 (+.f64 (*.f64 i 4) (+.f64 2 (*.f64 beta 2))) alpha)

Compiler

Compiled 739 to 567 computations (23.3% saved)

series208.0ms (0.4%)

Error

Counts

1 → 15

Calls

1 calls:

196.0ms

(/.f64 (+.f64 (*.f64 i 4) (+.f64 2 (*.f64 beta 2))) alpha)

Compiler

Compiled 551 to 471 computations (14.5% saved)

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4931	958
1	4931	958

prune46.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	44	4	48

Error

Counts

48 → 4

Compiler

Compiled 862 to 638 computations (26% saved)

regimes2.0s (4.3%)

Accuracy

Total 1.3b remaining (91%)

Threshold costs 0b (0%)

Compiler

Compiled 26685 to 18519 computations (30.6% saved)

bsearch6.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	113
1	56	113

end0.0ms (0%)

sample3.3s (7.1%)

Algorithm

1×

intervals

Results

383.0ms	6488×	body	128	valid
185.0ms	8000×	pre	128	true
156.0ms	634×	body	1024	valid
94.0ms	550×	body	512	valid
39.0ms	279×	body	256	valid
14.0ms	49×	body	2048	valid

Compiler

Compiled 3401 to 2367 computations (30.4% saved)

Details

analyze131.0ms (0.3%)

sample40.0ms (0.1%)

simplify163.0ms (0.4%)

prune6.0ms (0%)

localize12.0ms (0%)

rewrite317.0ms (0.7%)

series3.8s (8.1%)

simplify134.0ms (0.3%)

prune680.0ms (1.5%)

localize14.0ms (0%)

rewrite319.0ms (0.7%)

series4.0s (8.7%)

simplify134.0ms (0.3%)

prune903.0ms (2%)

localize23.0ms (0%)

rewrite1.0s (2.2%)

series26.3s (56.7%)

simplify134.0ms (0.3%)

prune2.5s (5.4%)

localize8.0ms (0%)

rewrite48.0ms (0.1%)

series208.0ms (0.4%)

simplify83.0ms (0.2%)

prune46.0ms (0.1%)

regimes2.0s (4.3%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (7.1%)

Profiling