Details

analyze3.0ms

Algorithm

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

sample25.0ms

Algorithm

intervals

Results

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

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5002	13

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 19.1b

Counts

2 → 1

localize8.0ms

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)

rewrite36.0ms

Algorithm

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:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0))
23.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0)) 1.0)

series23.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5370	1005

prune95.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

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

localize11.0ms

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

Algorithm

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4978	1670
1	4978	1670

prune167.0ms

Filtered

87 candidates to 120 candidates (-37.9%)

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

localize12.0ms

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)))

rewrite59.0ms

Algorithm

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:

9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
18.0ms	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0))
15.0ms	(-.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)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
13.0ms	(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)
14.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4966	1131
1	4966	1131

prune128.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

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

localize16.0ms

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

Algorithm

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:

17.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2.0)) 1.0)))
28.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
25.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
26.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4930	1719
1	4930	1719

prune197.0ms

Filtered

99 candidates to 122 candidates (-23.2%)

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

regimes127.0ms

Accuracy

75.2% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 15.8b

bsearch19.0ms

Steps

Iters	Range		Point
11	11.147105962075988	1.2795261915093277e+22	828658772.7005112

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	260	44
1	260	44

end0.0ms

sample702.0ms

Algorithm

intervals

Results

183.0ms	5836×	body	80	valid
129.0ms	847×	body	1280	valid
122.0ms	8000×	pre	80	true
85.0ms	733×	body	640	valid
41.0ms	414×	body	320	valid
10.0ms	170×	body	160	valid

Details

analyze3.0ms

sample25.0ms

simplify66.0ms

prune5.0ms

localize8.0ms

rewrite36.0ms

series23.0ms

simplify50.0ms

prune95.0ms

localize11.0ms

rewrite66.0ms

series44.0ms

simplify37.0ms

prune167.0ms

localize12.0ms

rewrite59.0ms

series49.0ms

simplify53.0ms

prune128.0ms

localize16.0ms

rewrite45.0ms

series92.0ms

simplify67.0ms

prune197.0ms

regimes127.0ms

bsearch19.0ms

simplify7.0ms

end0.0ms

sample702.0ms

Profiling