Details

sample31.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	26
1	283	26
2	1620	26
3	5003	26

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.0b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.1b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

13.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
41.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
25.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
105.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
740.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
176.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify78.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1249	5670
1	5001	5161

prune627.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

264×	`times-frac`
191×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
110×	`add-cube-cbrt`
96×	`associate-r`
74×	`add-exp-log` `add-cbrt-cube`
42×	`associate-l`
40×	`associate-/r/`
35×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
21×	`flip3-+` `flip-+`
20×	`div-inv`
19×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
15×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/l*`
10×	`associate-/r*`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 304

Calls

4 calls:

21.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
106.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
13.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts

4 → 12

Calls

4 calls:

259.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
88.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
250.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify102.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1581	8513
1	5001	7655

prune976.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
35.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

389×	`sqrt-prod`
365×	`add-sqr-sqrt`
327×	`times-frac`
213×	`*-un-lft-identity`
137×	`add-cube-cbrt`
114×	`difference-of-squares`
38×	`distribute-lft-out--`
32×	`associate-/r/`
25×	`associate-/l*`
20×	`associate-/r*`
18×	`flip3-+` `flip-+`
16×	`div-inv`
15×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l/`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
2×	`associate-*r/`
1×	`flip3--` `sqrt-div` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 329

Calls

4 calls:

26.0ms	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
14.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
13.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.8s

Counts

4 → 12

Calls

4 calls:

4.4s	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
89.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
119.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
121.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify166.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1015	10069
1	4314	9572
2	5002	9518

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 34.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (+ (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
0.1b	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
36.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

517×	`sqrt-prod`
468×	`times-frac`
430×	`add-sqr-sqrt`
354×	`*-un-lft-identity`
202×	`add-cube-cbrt`
114×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-/l*`
38×	`distribute-lft-out` `distribute-lft-out--`
23×	`flip3-+` `flip-+`
22×	`associate-/r*` `div-inv`
12×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l/`
4×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `add-log-exp`
2×	`sqrt-div`
1×	`flip3--` `flip--`

Counts

4 → 432

Calls

4 calls:

23.0ms	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (+ (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
31.0ms	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
13.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series9.0s

Counts

4 → 12

Calls

4 calls:

4.2s	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (+ (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
4.6s	(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (sqrt (+ (+ alpha beta) (* 2.0 i))) (sqrt (sqrt 1.0))))
116.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
118.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify182.0ms

Algorithm

egg-herbie

Counts

444 → 444

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1074	13986
1	3760	13325
2	5002	13215

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 34.1b

regimes150.0ms

Accuracy

27.7% (2.7b remaining)

Error of 36.7b against oracle of 34.0b and baseline of 37.7b

bsearch85.0ms

Steps

Iters	Range		Point
10	3.0666942791070792e+181	2.7115522405940807e+194	3.4412066338811634e+181

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	51
1	43	51

end0.0ms

sample670.0ms

Algorithm

intervals

Results

357.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true