Details

analyze125.0ms

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

14.0ms	199×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	16×	body	1280	valid
4.0ms	16×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	8×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4904	27
1	4904	27

prune10.0ms

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: 13.5b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
0.1b	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
2.3b	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
2.4b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

7.0ms	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
17.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
25.0ms	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
19.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
28.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
97.0ms	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
195.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

simplify42.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5268	2806

prune268.0ms

Filtered

100 candidates to 126 candidates (-26.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	114	12	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	12	128

Merged error: 12.8b

Counts

128 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
1.2b	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
1.7b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
2.3b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

20.0ms	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
17.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
16.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
20.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

series245.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
78.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
78.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
61.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5060	2791

prune315.0ms

Filtered

93 candidates to 113 candidates (-21.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Merged error: 5.3b

Counts

125 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
1.4b	(/ (* (cbrt beta) (cbrt beta)) (* (/ (+ alpha (+ beta (* 2.0 i))) (cbrt beta)) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
1.7b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
2.3b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
22×	`add-cbrt-cube`
13×	`associate-/r/`
10×	`cbrt-undiv` `div-exp`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
7×	`add-cube-cbrt`
6×	`frac-times` `add-log-exp`
4×	`pow1` `times-frac` `associate-r/` `associate-/l`
3×	`cbrt-prod` `associate-*l/`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

1.0ms	(cbrt beta)
27.0ms	(/ (* (cbrt beta) (cbrt beta)) (* (/ (+ alpha (+ beta (* 2.0 i))) (cbrt beta)) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
17.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
20.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt beta)
82.0ms	(/ (* (cbrt beta) (cbrt beta)) (* (/ (+ alpha (+ beta (* 2.0 i))) (cbrt beta)) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
80.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
61.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4970	1999
1	4970	1999

prune215.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Merged error: 5.3b

Counts

103 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
1.4b	(/ (* (cbrt beta) (cbrt beta)) (* (/ (+ alpha (+ beta (* 2.0 i))) (* (* (cbrt (cbrt beta)) (cbrt (cbrt beta))) (cbrt (cbrt beta)))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
1.7b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
2.3b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
36×	`add-cbrt-cube`
20×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
13×	`associate-/r/`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`flip3-+` `flip-+`
7×	`add-cube-cbrt`
6×	`frac-times` `add-log-exp`
4×	`pow1` `times-frac` `associate-r/` `associate-/l`
3×	`cbrt-prod` `associate-*l/`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt beta)
29.0ms	(/ (* (cbrt beta) (cbrt beta)) (* (/ (+ alpha (+ beta (* 2.0 i))) (* (* (cbrt (cbrt beta)) (cbrt (cbrt beta))) (cbrt (cbrt beta)))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
16.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
20.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt beta)
84.0ms	(/ (* (cbrt beta) (cbrt beta)) (* (/ (+ alpha (+ beta (* 2.0 i))) (* (* (cbrt (cbrt beta)) (cbrt (cbrt beta))) (cbrt (cbrt beta)))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
78.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
62.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4943	2185
1	4943	2185

prune175.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	103	9	112

Merged error: 5.3b

Counts

112 → 9

regimes316.0ms

Accuracy

6.8% (6.5b remaining)

Error of 12.1b against oracle of 5.7b and baseline of 12.6b

bsearch598.0ms

Steps

Iters	Range		Point
8	4.464108673669251e+199	2.830288279233186e+202	5.599357149971467e+201
8	1.1560236775919376e+123	1.0971955860630182e+126	2.6496394980429403e+123
8	1.611392513622717e+37	9.391345661722063e+39	9.293412699166225e+39

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	193
1	81	193

end0.0ms

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

sample1.1s

Algorithm

intervals

Results

360.0ms	6296×	body	80	valid
183.0ms	8000×	pre	80	true
154.0ms	522×	body	1280	valid
134.0ms	602×	body	640	valid
67.0ms	386×	body	320	valid
22.0ms	194×	body	160	valid

Details

analyze125.0ms

sample41.0ms

simplify69.0ms

prune10.0ms

localize15.0ms

rewrite70.0ms

series331.0ms

simplify42.0ms

prune268.0ms

localize26.0ms

rewrite77.0ms

series245.0ms

simplify42.0ms

prune315.0ms

localize31.0ms

rewrite68.0ms

series246.0ms

simplify73.0ms

prune215.0ms

localize34.0ms

rewrite70.0ms

series246.0ms

simplify70.0ms

prune175.0ms

regimes316.0ms

bsearch598.0ms

simplify2.0ms

end0.0ms

analyze124.0ms

sample1.1s

Profiling