Details

analyze129.0ms

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

12.0ms	207×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	23×	body	640	valid
5.0ms	16×	body	1280	valid
1.0ms	6×	body	160	valid
1.0ms	4×	body	320	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

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: 21.0b

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)))))
2.6b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
2.7b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
20.4b	(/ (- 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:

13.0ms	(* (+ 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)))))))
21.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
18.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
67.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
87.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
43.0ms	(/ (- 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

prune265.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Merged error: 4.5b

Counts

134 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
0.0b	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
1.3b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite80.0ms

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:

9.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
10.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
30.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
21.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

series164.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
19.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
70.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
60.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5223	4158

prune283.0ms

Filtered

122 candidates to 192 candidates (-57.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	192	5	197

Merged error: 4.5b

Counts

197 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
1.3b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
1.3b	(log (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
70×	`times-frac`
41×	`distribute-lft-out`
38×	`add-cube-cbrt`
31×	`associate-r`
22×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`associate-/r/` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`log-prod` `flip3-+` `prod-exp` `log-pow` `cbrt-unprod` `flip-+` `unswap-sqr`
3×	`exp-prod` `div-inv`
2×	`associate-/l/`
1×	`+-commutative` `frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative` `flip--`

Counts

4 → 156

Calls

4 calls:

11.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
30.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
21.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
25.0ms	(log (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
67.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
61.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
62.0ms	(log (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5269	4042

prune295.0ms

Filtered

107 candidates to 168 candidates (-57.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	166	7	173

Merged error: 4.4b

Counts

173 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
1.3b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
1.3b	(log (sqrt (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0))))
1.3b	(log (sqrt (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

14×	`log-prod`
12×	`log-pow`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `sqrt-pow1` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `exp-prod`
4×	`add-cbrt-cube`
2×	`+-commutative` `flip3-+` `pow1/2` `rem-log-exp` `exp-sum` `sum-log` `flip-+`

Counts

4 → 64

Calls

4 calls:

26.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
22.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
23.0ms	(log (sqrt (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0))))
23.0ms	(log (sqrt (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
61.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
141.0ms	(log (sqrt (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0))))
141.0ms	(log (sqrt (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4969	2526
1	4969	2526

prune252.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	5	5
Picked	0	1	1
Done	1	0	1
Total	76	7	83

Merged error: 4.4b

Counts

83 → 7

regimes284.0ms

Accuracy

14.6% (5.3b remaining)

Error of 11.1b against oracle of 5.9b and baseline of 12.0b

bsearch38.0ms

Steps

Iters	Range		Point
9	1.099029637691782e+117	6.472144571971281e+125	2.0852138065724436e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	87
1	81	87

end0.0ms

sample1.1s

Algorithm

intervals

Results

375.0ms	6398×	body	80	valid
173.0ms	8000×	pre	80	true
145.0ms	491×	body	1280	valid
134.0ms	578×	body	640	valid
59.0ms	335×	body	320	valid
25.0ms	198×	body	160	valid

Details

analyze129.0ms

sample41.0ms

simplify44.0ms

prune11.0ms

localize16.0ms

rewrite78.0ms

series221.0ms

simplify48.0ms

prune265.0ms

localize17.0ms

rewrite80.0ms

series164.0ms

simplify65.0ms

prune283.0ms

localize20.0ms

rewrite94.0ms

series212.0ms

simplify50.0ms

prune295.0ms

localize26.0ms

rewrite95.0ms

series403.0ms

simplify53.0ms

prune252.0ms

regimes284.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling