Details

analyze123.0ms

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

sample41.0ms

Algorithm

intervals

Results

11.0ms	197×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	22×	body	640	valid
5.0ms	18×	body	1280	valid
1.0ms	9×	body	320	valid
1.0ms	10×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5446	29

prune11.0ms

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: 18.9b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
2.0b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
4.0b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
16.6b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite78.0ms

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:

14.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
24.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
20.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
16.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
66.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
86.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
38.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5522	3306

prune279.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	7	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 7.1b

Counts

134 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.3b	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
2.0b	(* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
4.0b	(+ (* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
45×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
30×	`associate-l`
27×	`times-frac`
24×	`prod-exp`
20×	`add-cube-cbrt`
19×	`div-exp`
17×	`associate-r`
12×	`associate-/r/`
11×	`pow1`
10×	`cbrt-unprod`
9×	`cbrt-undiv` `flip3-+` `flip-+` `distribute-lft-out`
8×	`frac-times`
7×	`associate-*r/`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`associate-*l/`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow-prod-down` `div-inv` `associate-/l*` `unswap-sqr`
2×	`pow-flip` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*` `sum-log` `un-div-inv` `flip--` `inv-pow`

Counts

4 → 147

Calls

4 calls:

19.0ms	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
18.0ms	(/ 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)))))))
25.0ms	(+ (* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
41.0ms	(/ 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)))))))
86.0ms	(+ (* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5057	3746

prune267.0ms

Filtered

104 candidates to 159 candidates (-52.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	157	9	166

Merged error: 7.1b

Counts

166 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
0.5b	(* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
2.0b	(* (+ alpha beta) (/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))))
7.6b	(+ (* (+ alpha beta) (/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))) 1.0)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-exp-log`
72×	`sqrt-div`
50×	`frac-times`
48×	`prod-exp`
47×	`add-cbrt-cube`
39×	`flip3-+` `flip-+`
34×	`associate-/r/`
32×	`associate-r`
26×	`associate-*l/`
25×	`associate-*r/`
23×	`div-exp`
20×	`cbrt-unprod`
18×	`*-un-lft-identity`
17×	`pow1`
13×	`add-sqr-sqrt`
11×	`cbrt-undiv` `add-cube-cbrt`
8×	`rec-exp` `1-exp`
7×	`pow-prod-down`
6×	`times-frac` `add-log-exp`
5×	`associate-l` `sqrt-prod`
4×	`distribute-lft-out`
3×	`pow-flip` `associate-/l*`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

29.0ms	(/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
28.0ms	(* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
43.0ms	(* (+ alpha beta) (/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))))
35.0ms	(+ (* (+ alpha beta) (/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))) 1.0)

series827.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
45.0ms	(* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
443.0ms	(* (+ alpha beta) (/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))))
230.0ms	(+ (* (+ alpha beta) (/ 1 (* (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))) 1.0)

simplify105.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4977	5623
1	4977	5623

prune415.0ms

Filtered

119 candidates to 181 candidates (-52.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	183	7	190

Merged error: 7.1b

Counts

190 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
0.6b	(/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
2.0b	(* (+ alpha beta) (* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))))
7.2b	(+ (* (+ alpha beta) (* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) 1.0)

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-exp-log`
74×	`add-cbrt-cube`
70×	`*-un-lft-identity`
57×	`prod-exp` `cbrt-unprod`
55×	`associate-r`
54×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-undiv` `cbrt-prod` `div-exp` `sqrt-prod`
19×	`distribute-lft-out`
18×	`pow1`
17×	`associate-*r/`
12×	`frac-times`
9×	`pow-prod-down`
8×	`flip3-+` `flip-+`
7×	`associate-*l/` `associate-/r/`
6×	`sqrt-div` `associate-/l*` `add-log-exp`
5×	`associate-l`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log`

Counts

4 → 182

Calls

4 calls:

46.0ms	(* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
19.0ms	(/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
41.0ms	(* (+ alpha beta) (* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))))
39.0ms	(+ (* (+ alpha beta) (* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
43.0ms	(/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
64.0ms	(* (+ alpha beta) (* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))))
87.0ms	(+ (* (+ alpha beta) (* (* (cbrt 1) (/ (cbrt 1) (* (/ (+ alpha (+ beta (* 2.0 i))) (- beta alpha)) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (cbrt 1) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) 1.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4977	6161
1	4977	6161

prune402.0ms

Filtered

108 candidates to 194 candidates (-79.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	194	7	201

Merged error: 7.1b

Counts

201 → 7

regimes283.0ms

Accuracy

-16.3% (7.8b remaining)

Error of 13.7b against oracle of 5.9b and baseline of 12.6b

bsearch45.0ms

Steps

Iters	Range		Point
8	1.0550893536374179e-199	4.240892736400285e-195	1.0861756241842032e-199
7	3.1911492208882756e-221	4.432434280686067e-219	4.3536151651021257e-219

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	80
1	83	80

end0.0ms

sample1.1s

Algorithm

intervals

Results

357.0ms	6328×	body	80	valid
171.0ms	8000×	pre	80	true
147.0ms	511×	body	1280	valid
131.0ms	602×	body	640	valid
60.0ms	344×	body	320	valid
24.0ms	215×	body	160	valid

Details

analyze123.0ms

sample41.0ms

simplify43.0ms

prune11.0ms

localize15.0ms

rewrite78.0ms

series210.0ms

simplify47.0ms

prune279.0ms

localize17.0ms

rewrite95.0ms

series223.0ms

simplify80.0ms

prune267.0ms

localize26.0ms

rewrite144.0ms

series827.0ms

simplify105.0ms

prune415.0ms

localize23.0ms

rewrite155.0ms

series233.0ms

simplify87.0ms

prune402.0ms

regimes283.0ms

bsearch45.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling