Details

analyze118.0ms

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

sample37.0ms

Algorithm

intervals

Results

11.0ms	201×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
4.0ms	21×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4904	27
1	4904	27

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: 12.6b

Counts

2 → 2

localize14.0ms

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))
1.2b	(+ (/ (- 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)))

rewrite68.0ms

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))
18.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
22.0ms	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
18.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
27.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
95.0ms	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
192.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

simplify37.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5268	2806

prune256.0ms

Filtered

100 candidates to 126 candidates (-26.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Merged error: 12.2b

Counts

128 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
1.0b	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
1.2b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
1.9b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

rewrite76.0ms

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:

17.0ms	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
16.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
22.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
17.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
77.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
60.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
78.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

simplify38.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5060	2791

prune315.0ms

Filtered

93 candidates to 113 candidates (-21.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 5.6b

Counts

123 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
1.2b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
1.9b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
20.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
18.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt beta)
21.0ms	(cbrt beta)
60.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
77.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5187	1315

prune186.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 5.6b

Counts

87 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
1.2b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
1.7b	(log (exp (/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))))
1.9b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/r/`
18×	`flip3-+` `flip-+`
16×	`log-pow`
15×	`exp-prod`
14×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`frac-times`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`associate-r/` `associate-l/` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`log-prod` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 98

Calls

4 calls:

17.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
20.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
5.0ms	(log (exp (/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))))
18.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
60.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
78.0ms	(log (exp (/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))))
77.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

simplify34.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5024	2623

prune284.0ms

Filtered

90 candidates to 110 candidates (-22.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 5.6b

Counts

121 → 11

regimes360.0ms

Accuracy

21.7% (5.3b remaining)

Error of 11.0b against oracle of 5.7b and baseline of 12.5b

bsearch499.0ms

Steps

Iters	Range	Point
8	4.284254530945478e+185	1.1173591088725841e+188	8.880827712970242e+187
7	3.9929842956734625e+155	8.786271007115093e+156	4.0300115290250407e+155
7	8.427111193330525e+129	8.675194731271743e+131	8.117678325149238e+131

Iters

Range

Point

4.284254530945478e+185

1.1173591088725841e+188

8.880827712970242e+187

3.9929842956734625e+155

8.786271007115093e+156

4.0300115290250407e+155

8.427111193330525e+129

8.675194731271743e+131

8.117678325149238e+131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	189
1	75	189

end0.0ms

analyze117.0ms

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

353.0ms	6337×	body	80	valid
173.0ms	8000×	pre	80	true
155.0ms	546×	body	1280	valid
122.0ms	560×	body	640	valid
58.0ms	362×	body	320	valid
21.0ms	195×	body	160	valid

Details

analyze118.0ms

sample37.0ms

simplify64.0ms

prune12.0ms

localize14.0ms

rewrite68.0ms

series324.0ms

simplify37.0ms

prune256.0ms

localize22.0ms

rewrite76.0ms

series241.0ms

simplify38.0ms

prune315.0ms

localize25.0ms

rewrite42.0ms

series179.0ms

simplify50.0ms

prune186.0ms

localize24.0ms

rewrite64.0ms

series292.0ms

simplify34.0ms

prune284.0ms

regimes360.0ms

bsearch499.0ms

simplify2.0ms

end0.0ms

analyze117.0ms

sample1.1s

Profiling