Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 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: 53.2b

Counts

2 → 1

localize14.0ms

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))))
34.5b	(/ (/ (* (* 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))
46.0b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite98.0ms

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:

12.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
40.0ms	(/ (/ (* (* 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:

57.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
109.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
743.0ms	(/ (/ (* (* 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))
195.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify84.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1249	5670
1	5001	5161

prune580.0ms

Filtered

212 candidates to 143 candidates (67.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	8	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	8	213

Merged error: 31.8b

Counts

213 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* 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))))
32.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-exp-log` `add-cbrt-cube`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 364

Calls

4 calls:

24.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
110.0ms	(* (/ (/ (* 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)))

series2.9s

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.3s	(* (/ (/ (* 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))))
89.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
129.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify130.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1683	10749
1	5001	9903

prune1.1s

Filtered

376 candidates to 246 candidates (65.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	371	5	376
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	376	8	384

Merged error: 31.8b

Counts

384 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
48×	`*-un-lft-identity`
42×	`associate-l`
39×	`add-sqr-sqrt`
38×	`cbrt-undiv` `div-exp`
29×	`prod-exp` `cbrt-unprod`
28×	`add-cube-cbrt`
14×	`associate-/r/`
12×	`associate-r`
9×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`pow1`
7×	`sqrt-prod` `div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r/` `associate-/r`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`frac-times` `flip3--` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--`

Counts

4 → 155

Calls

4 calls:

56.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* 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)))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
4.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series2.5s

Counts

4 → 12

Calls

4 calls:

2.3s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
90.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
60.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
54.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify71.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1076	4950
1	5001	3682

prune486.0ms

Filtered

167 candidates to 108 candidates (64.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	167	8	175

Merged error: 31.8b

Counts

175 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

28.2b	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`cbrt-undiv` `sqrt-div` `div-exp`
7×	`flip3-+` `times-frac` `associate-/r*` `flip-+` `associate-/l/`
6×	`pow1` `sqrt-prod`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-*r/` `associate-/r/` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`
1×	`associate-*l/`

Counts

4 → 89

Calls

4 calls:

28.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
13.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
4.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series954.0ms

Counts

4 → 12

Calls

4 calls:

747.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
92.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
59.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
55.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify86.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	638	1492
1	3554	1275
2	5003	1273

prune345.0ms

Filtered

101 candidates to 76 candidates (75.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 31.8b

Counts

109 → 8

regimes140.0ms

Accuracy

24.4% (2.8b remaining)

Error of 36.6b against oracle of 33.9b and baseline of 37.5b

bsearch47.0ms

Steps

Iters	Range		Point
6	3.169913242419009e+181	3.967418286213429e+182	4.600403367912247e+181

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	29
1	33	29

end0.0ms

sample679.0ms

Algorithm

intervals

Results

360.0ms	8000×	body	80	valid
131.0ms	8000×	pre	80	true