Details

sample585.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 94.134521%

Results

12.0ms	208×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify52.0ms

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

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 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

2.0b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

18.9b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

19.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

28.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

14.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

82.0ms

(+ (/ (/ (* (+ 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)))

simplify95.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5001	1789

prune251.0ms

Filtered

89 candidates to 120 candidates (-34.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 4.7b

Counts

121 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite109.0ms

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:

21.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
36.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series347.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
212.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
83.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune586.0ms

Filtered

200 candidates to 307 candidates (-53.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	300	7	307
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	305	12	317

Merged error: 4.7b

Counts

317 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.2b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
152×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
90×	`associate-r`
76×	`add-cube-cbrt`
22×	`distribute-lft-out`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `associate-/r/`
10×	`flip3-+` `flip-+`
6×	`pow1` `div-inv` `add-log-exp`
5×	`associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-l`
3×	`unpow-prod-down` `cube-prod` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `frac-times` `cbrt-div` `associate-*l/` `associate-/l/`
1×	`+-commutative` `cube-mult` `flip3--` `frac-2neg` `pow1/3` `unpow3` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 191

Calls

4 calls:

28.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
36.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
14.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
63.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
82.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	970	2869
1	5001	2778

prune429.0ms

Filtered

133 candidates to 203 candidates (-52.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	204	11	215

Merged error: 4.7b

Counts

215 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.1b	(- 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.4b	(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

294×	`times-frac`
260×	`*-un-lft-identity`
188×	`add-sqr-sqrt`
180×	`associate-r`
122×	`add-cube-cbrt`
45×	`distribute-lft-out`
24×	`distribute-lft-out--` `difference-of-squares`
22×	`add-exp-log` `add-cbrt-cube`
20×	`associate-/r/`
15×	`flip3-+` `flip-+`
10×	`div-inv`
8×	`pow1` `associate-l` `add-log-exp`
6×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`frac-times` `associate-*l/`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `sum-cubes` `flip--`

Counts

4 → 259

Calls

4 calls:

36.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
39.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.0ms	(- 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
10.0ms	(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))

series3.0s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
65.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
57.0ms	(- 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
2.8s	(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	909	3916
1	5002	3708

prune1.4s

Filtered

175 candidates to 271 candidates (-54.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	269	2	271
Fresh	1	8	9
Picked	1	0	1
Done	1	0	1
Total	272	10	282

Merged error: 4.7b

Counts

282 → 10

regimes522.0ms

Accuracy

75.5% (1.6b remaining)

Error of 7.4b against oracle of 5.8b and baseline of 12.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	114
1	70	114

end0.0ms

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 94.134521%

Results

367.0ms	6342×	body	80	valid
172.0ms	8000×	pre	80	true
144.0ms	526×	body	1280	valid
119.0ms	549×	body	640	valid
64.0ms	371×	body	320	valid
23.0ms	212×	body	160	valid

Details

sample585.0ms

simplify52.0ms

prune3.0ms

localize16.0ms

rewrite65.0ms

series163.0ms

simplify95.0ms

prune251.0ms

localize15.0ms

rewrite109.0ms

series347.0ms

simplify72.0ms

prune586.0ms

localize18.0ms

rewrite109.0ms

series240.0ms

simplify53.0ms

prune429.0ms

localize22.0ms

rewrite104.0ms

series3.0s

simplify65.0ms

prune1.4s

regimes522.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling