Details

analyze124.0ms

Algorithm

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

sample39.0ms

Algorithm

intervals

Results

11.0ms	207×	body	80	valid
8.0ms	256×	pre	80	true
4.0ms	16×	body	1280	valid
4.0ms	18×	body	640	valid
1.0ms	10×	body	160	valid
1.0ms	5×	body	320	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5446	29

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 20.1b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.6b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
3.9b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
19.0b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
22×	`associate-r`
21×	`add-sqr-sqrt` `flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r/`
14×	`frac-times`
11×	`add-cube-cbrt`
10×	`times-frac`
8×	`pow1` `associate-l` `associate-*l/`
7×	`associate-*r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`distribute-lft-out` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow-prod-down` `*-commutative` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-sub` `clear-num` `associate-/r*` `sum-log` `flip--`

Counts

4 → 120

Calls

4 calls:

13.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
21.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
22.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
15.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
62.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
82.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
41.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5522	3306

prune276.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	9	134

Merged error: 6.1b

Counts

134 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
1.6b	(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
3.9b	(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

123×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
69×	`times-frac`
60×	`add-exp-log`
37×	`distribute-lft-out`
36×	`add-cube-cbrt` `add-cbrt-cube`
32×	`associate-r`
25×	`prod-exp`
22×	`associate-l`
17×	`div-exp`
13×	`cbrt-unprod`
11×	`pow1` `distribute-lft-out--` `difference-of-squares`
10×	`frac-times`
9×	`cbrt-undiv`
8×	`flip3-+` `flip-+`
7×	`associate-*r/`
6×	`associate-*l/` `associate-/r/` `add-log-exp` `unswap-sqr`
5×	`associate-/r` `associate-/l`
4×	`rec-exp` `1-exp` `pow-prod-down`
3×	`div-inv`
2×	`*-commutative` `associate-/l/`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `clear-num` `sum-log` `flip--`

Counts

4 → 182

Calls

4 calls:

10.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
30.0ms	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
21.0ms	(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
24.0ms	(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
37.0ms	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
64.0ms	(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
83.0ms	(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5143	4381

prune296.0ms

Filtered

120 candidates to 194 candidates (-61.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Merged error: 6.1b

Counts

203 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
0.0b	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
2.2b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
86×	`times-frac`
80×	`add-sqr-sqrt`
51×	`distribute-lft-out`
46×	`add-cube-cbrt`
31×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`associate-/r` `associate-/l`
8×	`associate-/r/`
6×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `flip3--` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip--`

Counts

4 → 180

Calls

4 calls:

10.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
8.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
28.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
22.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

series153.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
13.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
65.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
58.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5223	4158

prune284.0ms

Filtered

122 candidates to 192 candidates (-57.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	192	10	202

Merged error: 6.1b

Counts

202 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
0.1b	(pow (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 3)
1.7b	(- (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
2.1b	(+ (pow (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 3) (pow 1.0 3))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
47×	`add-sqr-sqrt`
45×	`times-frac`
31×	`associate-r`
29×	`add-exp-log` `add-cbrt-cube`
25×	`add-cube-cbrt`
24×	`distribute-lft-out`
22×	`associate-l`
9×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`pow-exp` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`
4×	`associate-/r/` `unswap-sqr`
3×	`cube-div` `pow-unpow` `flip3-+` `flip-+`
2×	`frac-times` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `div-inv`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `diff-log` `unpow3` `cube-prod` `sum-log` `sum-cubes` `*-commutative` `flip--` `sqr-pow`

Counts

4 → 132

Calls

4 calls:

32.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
20.0ms	(pow (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 3)
20.0ms	(- (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
11.0ms	(+ (pow (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 3) (pow 1.0 3))

series5.6s

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
1.7s	(pow (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 3)
84.0ms	(- (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
3.7s	(+ (pow (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 3) (pow 1.0 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5626	3763

prune420.0ms

Filtered

94 candidates to 144 candidates (-53.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	144	10	154

Merged error: 6.1b

Counts

154 → 10

regimes345.0ms

Accuracy

-0.8% (6.6b remaining)

Error of 12.3b against oracle of 5.7b and baseline of 12.3b

bsearch84.0ms

Steps

Iters	Range	Point
8	4.1326161653523833e+254	2.884289509810265e+257	4.175868241327161e+254
4	1.7877789436177205e+130	3.2296999959417845e+130	3.1711913126916907e+130
9	2.4914058638208025e+68	1.2548492583473907e+75	7.360326372640298e+74

Iters

Range

Point

4.1326161653523833e+254

2.884289509810265e+257

4.175868241327161e+254

1.7877789436177205e+130

3.2296999959417845e+130

3.1711913126916907e+130

2.4914058638208025e+68

1.2548492583473907e+75

7.360326372640298e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	61
1	86	61

end0.0ms

sample1.1s

Algorithm

intervals

Results

367.0ms	6362×	body	80	valid
171.0ms	8000×	pre	80	true
164.0ms	557×	body	1280	valid
121.0ms	541×	body	640	valid
57.0ms	339×	body	320	valid
22.0ms	201×	body	160	valid

Details

analyze124.0ms

sample39.0ms

simplify43.0ms

prune12.0ms

localize16.0ms

rewrite75.0ms

series207.0ms

simplify48.0ms

prune276.0ms

localize20.0ms

rewrite93.0ms

series202.0ms

simplify71.0ms

prune296.0ms

localize16.0ms

rewrite76.0ms

series153.0ms

simplify62.0ms

prune284.0ms

localize26.0ms

rewrite88.0ms

series5.6s

simplify60.0ms

prune420.0ms

regimes345.0ms

bsearch84.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling