Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	199×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	20×	body	1280	valid
4.0ms	18×	body	640	valid
2.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 24.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.5b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
48×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
12×	`flip3-+` `flip-+`
11×	`distribute-lft-out` `add-log-exp`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
4×	`pow1` `frac-times` `sum-log`
3×	`flip3--` `flip--`
2×	`+-commutative` `frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-+l+`

Counts

4 → 124

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* 2.0 i))
19.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
27.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* 2.0 i))
63.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
85.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify99.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	701	1981
1	3980	1865
2	5002	1865

prune266.0ms

Filtered

136 candidates to 101 candidates (25.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Merged error: 3.5b

Counts

137 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
18.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
24.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
39.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
41.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
84.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
64.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune555.0ms

Filtered

307 candidates to 200 candidates (34.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	305	2	307
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	309	6	315

Merged error: 3.5b

Counts

315 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.8b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.8b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
7.9b	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 101

Calls

4 calls:

8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
62.0ms	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series327.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
77.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
76.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
97.0ms	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	360	1874
1	1194	1757
2	5002	1749

prune408.0ms

Filtered

113 candidates to 93 candidates (17.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	114	5	119

Merged error: 3.5b

Counts

119 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.8b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.8b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
7.9b	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 101

Calls

4 calls:

8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
64.0ms	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series324.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
78.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
77.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
92.0ms	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	360	1874
1	1194	1757
2	5002	1749

prune452.0ms

Filtered

113 candidates to 93 candidates (17.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	112	6	118

Merged error: 3.5b

Counts

118 → 6

regimes383.0ms

Accuracy

74.4% (2.1b remaining)

Error of 8.9b against oracle of 6.7b and baseline of 15.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	60
1	54	60

end0.0ms

sample1.2s

Algorithm

intervals

Results

330.0ms	6000×	body	80	valid
182.0ms	651×	body	1280	valid
179.0ms	8000×	pre	80	true
146.0ms	665×	body	640	valid
79.0ms	461×	body	320	valid
24.0ms	223×	body	160	valid

Details

sample45.0ms

simplify51.0ms

prune3.0ms

localize17.0ms

rewrite69.0ms

series174.0ms

simplify99.0ms

prune266.0ms

localize12.0ms

rewrite110.0ms

series204.0ms

simplify75.0ms

prune555.0ms

localize20.0ms

rewrite90.0ms

series327.0ms

simplify50.0ms

prune408.0ms

localize25.0ms

rewrite92.0ms

series324.0ms

simplify50.0ms

prune452.0ms

regimes383.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling