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

6.0ms	188×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	23×	body	1280	valid
3.0ms	22×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	8×	body	160	valid

simplify323.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	5019	19

prune2.0ms

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: 15.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.6b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite31.0ms

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:

10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series74.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
44.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify84.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	6089	1488

prune83.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 15.1b

Counts

72 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
2.6b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

35.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
30.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series179.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
46.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
30.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
49.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify134.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4867	4058
1	4867	4058

prune163.0ms

Filtered

100 candidates to 135 candidates (-35.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Merged error: 2.4b

Counts

147 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
0.1b	(/.f64 (+.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) (-.f64 beta (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
2.5b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
5.6b	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
27×	`unpow-prod-down_binary64` `cube-prod_binary64`
26×	`add-cube-cbrt_binary64`
23×	`associate-*r/_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`distribute-lft-out_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`associate-/l/_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
10×	`pow1_binary64` `frac-add_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-sqr-1_binary64` `prod-exp_binary64` `flip--_binary64`
5×	`associate-*l/_binary64`
4×	`cbrt-undiv_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`rem-cube-cbrt_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `sub-neg_binary64` `associate-+r-_binary64` `diff-log_binary64` `associate-r_binary64` `pow-pow_binary64` `cube-div_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 163

Calls

4 calls:

10.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
44.0ms	(/.f64 (+.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) (-.f64 beta (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
24.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
25.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
311.0ms	(/.f64 (+.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) (-.f64 beta (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
89.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
80.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

simplify90.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5045	7636

prune487.0ms

Filtered

107 candidates to 175 candidates (-63.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	175	8	183

Merged error: 2.4b

Counts

183 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 beta)
2.3b	(.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) (cbrt.f64 beta))
2.5b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
3.5b	(.f64 (.f64 (cbrt.f64 beta) (cbrt.f64 beta)) (.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) (cbrt.f64 beta)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`pow1_binary64`
28×	`add-cbrt-cube_binary64`
27×	`cbrt-unprod_binary64` `prod-exp_binary64`
18×	`pow-prod-down_binary64`
15×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64` `associate-*l/_binary64`
9×	`associate-*r/_binary64`
7×	`associate-r_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `difference-of-sqr-1_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `times-frac_binary64` `cbrt-prod_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`cbrt-undiv_binary64` `sqr-pow_binary64` `div-exp_binary64`
2×	`associate-l_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 106

Calls

4 calls:

1.0ms	(cbrt.f64 beta)
27.0ms	(.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) (cbrt.f64 beta))
28.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
34.0ms	(.f64 (.f64 (cbrt.f64 beta) (cbrt.f64 beta)) (.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) (cbrt.f64 beta)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt.f64 beta)
170.0ms	(.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) (cbrt.f64 beta))
83.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
86.0ms	(.f64 (.f64 (cbrt.f64 beta) (cbrt.f64 beta)) (.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) (cbrt.f64 beta)))

simplify116.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5049	3060

prune205.0ms

Filtered

68 candidates to 118 candidates (-73.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 2.4b

Counts

126 → 8

regimes82.0ms

Accuracy

75.7% (3.1b remaining)

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

bsearch20.0ms

Steps

Iters	Range		Point
6	677671856594.3629	6754296772797.5625	1192146593148.475

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	346	149
1	346	149

end0.0ms

sample727.0ms

Algorithm

intervals

Results

188.0ms	5839×	body	80	valid
128.0ms	8000×	pre	80	true
128.0ms	829×	body	1280	valid
87.0ms	722×	body	640	valid
36.0ms	398×	body	320	valid
13.0ms	212×	body	160	valid

Details

analyze3.0ms

sample25.0ms

simplify323.0ms

prune2.0ms

localize8.0ms

rewrite31.0ms

series74.0ms

simplify84.0ms

prune83.0ms

localize12.0ms

rewrite93.0ms

series179.0ms

simplify134.0ms

prune163.0ms

localize22.0ms

rewrite111.0ms

series534.0ms

simplify90.0ms

prune487.0ms

localize33.0ms

rewrite96.0ms

series424.0ms

simplify116.0ms

prune205.0ms

regimes82.0ms

bsearch20.0ms

simplify9.0ms

end0.0ms

sample727.0ms

Profiling