Details

analyze2.0ms

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

sample26.0ms

Algorithm

intervals

Results

5.0ms	180×	body	80	valid
5.0ms	32×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	28×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	7×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

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: 17.8b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0))
1.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2.0)) 1.0)

rewrite33.0ms

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

series24.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5370	1005

prune101.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 17.0b

Counts

72 → 11

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 beta (+.f64 (+.f64 alpha beta) 2.0))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0))
1.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)

rewrite67.0ms

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:

29.0ms	(-.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))
18.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)

series50.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0))
11.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2.0))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)

simplify33.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4978	1670
1	4978	1670

prune157.0ms

Filtered

87 candidates to 120 candidates (-37.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 3.5b

Counts

131 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

1.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
6.6b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
6.6b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
6.6b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
63×	`cbrt-prod_binary64`
46×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
27×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`pow1_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` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 104

Calls

4 calls:

14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 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)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
30.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
28.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))
28.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4945	1723
1	4945	1723

prune192.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Merged error: 3.5b

Counts

124 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0))
0.1b	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0)))
1.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
4.6b	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
21×	`distribute-lft-out_binary64`
19×	`add-cube-cbrt_binary64`
8×	`log-prod_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`flip3-+_binary64` `exp-sum_binary64` `log-div_binary64` `flip-+_binary64` `exp-prod_binary64`
2×	`associate-/l/_binary64` `log-pow_binary64` `associate-/r/_binary64` `exp-diff_binary64` `div-sub_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-+l-_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0))
21.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0)))
19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
19.0ms	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0))

series64.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0))
14.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0)))
14.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0)
23.0ms	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2.0)) 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6180	1610

prune92.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 3.5b

Counts

118 → 8

regimes149.0ms

Accuracy

76.4% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.2b

bsearch15.0ms

Steps

Iters	Range		Point
9	0.5900090070486723	45029.78694382322	44511.573118962006

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	325	69
1	325	69

end0.0ms

sample719.0ms

Algorithm

intervals

Results

189.0ms	5823×	body	80	valid
127.0ms	8000×	pre	80	true
124.0ms	821×	body	1280	valid
92.0ms	731×	body	640	valid
37.0ms	405×	body	320	valid
13.0ms	220×	body	160	valid

Details

analyze2.0ms

sample26.0ms

simplify68.0ms

prune5.0ms

localize13.0ms

rewrite33.0ms

series24.0ms

simplify56.0ms

prune101.0ms

localize11.0ms

rewrite67.0ms

series50.0ms

simplify33.0ms

prune157.0ms

localize16.0ms

rewrite45.0ms

series101.0ms

simplify85.0ms

prune192.0ms

localize11.0ms

rewrite74.0ms

series64.0ms

simplify63.0ms

prune92.0ms

regimes149.0ms

bsearch15.0ms

simplify8.0ms

end0.0ms

sample719.0ms

Profiling