Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample26.0ms (1.1%)

Algorithm

1×

intervals

Results

5.0ms	175×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	34×	body	640	valid
4.0ms	26×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify67.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5002	13

prune10.0ms (0.4%)

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: 19.1b

Counts

2 → 1

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0))
2.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0)) 1.0)

rewrite33.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 65

Calls

2 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0)) 1.0)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0))

series23.0ms (1%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0)) 1.0)
9.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0))

simplify51.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5370	1005

prune115.0ms (4.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 18.2b

Counts

72 → 10

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)

rewrite66.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
24×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64`

Counts

4 → 108

Calls

4 calls:

32.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0))

series45.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
14.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0))

simplify31.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4978	1670
1	4978	1670

prune199.0ms (8.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Merged error: 3.8b

Counts

130 → 10

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
0.0b	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0))
2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)
2.0b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))

rewrite55.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64` `exp-prod_binary64`
9×	`add-log-exp_binary64`
7×	`log-pow_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`log-prod_binary64`
3×	`sub-neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
2×	`diff-log_binary64` `associate-/r/_binary64` `rem-exp-log_binary64` `exp-diff_binary64` `exp-sum_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 88

Calls

4 calls:

15.0ms	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0))
15.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))

series51.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0))
14.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))

simplify51.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4966	1131
1	4966	1131

prune161.0ms (6.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Merged error: 3.8b

Counts

110 → 10

localize17.0ms (0.7%)

Local error

Found 4 expressions with local error:

2.0b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))
7.1b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
7.1b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
7.1b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))

rewrite45.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64`
63×	`cbrt-prod_binary64`
46×	`times-frac_binary64`
38×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
27×	`distribute-lft-out_binary64`
7×	`log-pow_binary64`
6×	`associate-/r/_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-div_binary64` `flip3-+_binary64` `pow1/3_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `distribute-lft-out--_binary64` `log-div_binary64`

Counts

4 → 110

Calls

4 calls:

15.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))
10.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))

series95.0ms (4%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
26.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
26.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
14.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))

simplify68.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4930	1719
1	4930	1719

prune241.0ms (10.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Merged error: 3.8b

Counts

132 → 8

regimes126.0ms (5.3%)

Accuracy

Total 3.1b remaining (49.4%)

Threshold costs 0b (0%)

bsearch20.0ms (0.8%)

Steps

Iters	Range		Point
11	11.147105962075988	1.2795261915093277e+22	828658772.7005112

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	260	44
1	260	44

end0.0ms (0%)

sample718.0ms (30.5%)

Algorithm

1×

intervals

Results

183.0ms	5836×	body	80	valid
132.0ms	8000×	pre	80	true
128.0ms	847×	body	1280	valid
86.0ms	733×	body	640	valid
39.0ms	414×	body	320	valid
10.0ms	170×	body	160	valid

Details

analyze3.0ms (0.1%)

sample26.0ms (1.1%)

simplify67.0ms (2.8%)

prune10.0ms (0.4%)

localize8.0ms (0.3%)

rewrite33.0ms (1.4%)

series23.0ms (1%)

simplify51.0ms (2.2%)

prune115.0ms (4.9%)

localize12.0ms (0.5%)

rewrite66.0ms (2.8%)

series45.0ms (1.9%)

simplify31.0ms (1.3%)

prune199.0ms (8.4%)

localize15.0ms (0.6%)

rewrite55.0ms (2.3%)

series51.0ms (2.2%)

simplify51.0ms (2.2%)

prune161.0ms (6.8%)

localize17.0ms (0.7%)

rewrite45.0ms (1.9%)

series95.0ms (4%)

simplify68.0ms (2.9%)

prune241.0ms (10.2%)

regimes126.0ms (5.3%)

bsearch20.0ms (0.8%)

simplify7.0ms (0.3%)

end0.0ms (0%)

sample718.0ms (30.5%)

Profiling