Details

sample29.0ms

Algorithm

intervals

Results

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

simplify40.0ms

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

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: 54.5b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.9b	(/ (/ (* (* 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))
46.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

98716×	`*-un-lft-identity`
45662×	`distribute-lft-out`
39648×	`times-frac`
39111×	`associate-l`
26851×	`add-sqr-sqrt`
13479×	`swap-sqr`
12215×	`associate-r`
7974×	`distribute-lft-out--`
7374×	`add-cube-cbrt`
6645×	`difference-of-squares`
4800×	`unswap-sqr`
3290×	`*-commutative`
1384×	`associate-/l*`
130×	`associate-/r/`
115×	`flip3-+` `flip-+`
108×	`associate-/r*`
102×	`associate-/l/`
76×	`frac-times`
61×	`add-exp-log` `add-cbrt-cube`
58×	`associate-*r/`
38×	`associate-*l/`
22×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
17×	`div-inv`
16×	`associate-+r+`
14×	`+-commutative`
12×	`associate-+l+`
11×	`pow1`
4×	`pow-prod-down` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`flip3--` `flip--`

Counts

4 → 21570

Calls

4 calls:

9.0ms	(* i (+ (+ alpha beta) i))
31.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
659.0ms	(/ (/ (* (* 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))
88.0ms	(/ (* (* 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:

23.0ms	(* i (+ (+ alpha beta) i))
114.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
781.0ms	(/ (/ (* (* 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))
186.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify7.8s

Algorithm

egg-herbie

Counts

21582 → 21582

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	5001	740831

prune6.4s

Filtered

21582 candidates to 1479 candidates (93.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	21571	11	21582
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21572	11	21583

Merged error: 32.7b

Counts

21583 → 11

localize19.0ms

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))))
32.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite7.9s

Algorithm

rewrite-expression-head

Rules

55741×	`*-un-lft-identity`
27540×	`distribute-lft-out`
19501×	`times-frac`
19277×	`associate-/l*`
14682×	`associate-l`
12267×	`frac-times`
9647×	`add-sqr-sqrt`
7045×	`add-cube-cbrt`
5477×	`associate-/l/`
4396×	`associate-r`
3765×	`associate-/r*`
1265×	`distribute-lft-out--`
783×	`unswap-sqr`
769×	`*-commutative`
528×	`associate-/r/`
506×	`difference-of-squares`
495×	`flip3-+` `flip-+`
466×	`clear-num`
464×	`frac-2neg`
265×	`associate-*r/`
264×	`div-inv`
253×	`sqrt-prod`
141×	`associate-*l/`
70×	`add-exp-log` `add-cbrt-cube`
33×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
8×	`un-div-inv`
6×	`pow1`
4×	`add-log-exp`
2×	`flip3--` `flip--`
1×	`pow-prod-down`

Counts

4 → 14808

Calls

4 calls:

63.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
5.1s	(* (/ (/ (* 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))))
25.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
31.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.9s

Counts

4 → 12

Calls

4 calls:

334.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.4s	(* (/ (/ (* 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))))
93.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
125.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify5.1s

Algorithm

egg-herbie

Counts

14820 → 14820

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	5001	536076

prune9.0s

Filtered

14820 candidates to 2023 candidates (86.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	14813	7	14820
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	14822	9	14831

Merged error: 32.7b

Counts

14831 → 9

localize19.0ms

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 (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
0.1b	(/ (* i (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))))
33.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite10.1s

Algorithm

rewrite-expression-head

Rules

205196×	`*-un-lft-identity`
113930×	`times-frac`
96365×	`distribute-lft-out`
55536×	`associate-r`
43018×	`associate-l`
37222×	`add-sqr-sqrt`
20868×	`add-cube-cbrt`
16240×	`distribute-lft-out--`
6496×	`difference-of-squares`
3248×	`sqrt-prod`
2501×	`associate-/r/`
1310×	`unswap-sqr`
1222×	`div-inv`
1187×	`flip3-+` `flip-+`
798×	`associate-/l*`
626×	`*-commutative`
191×	`associate-*r/`
178×	`associate-/l/`
129×	`associate-/r*`
74×	`add-exp-log` `add-cbrt-cube`
59×	`flip3--` `flip--`
34×	`frac-times`
32×	`cbrt-undiv` `div-exp`
22×	`un-div-inv`
20×	`prod-exp` `cbrt-unprod`
16×	`clear-num`
11×	`frac-2neg`
6×	`pow1`
4×	`add-log-exp`
2×	`associate-*l/`
1×	`pow-prod-down`

Counts

4 → 33964

Calls

4 calls:

63.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
165.0ms	(* i (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
954.0ms	(/ (* i (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))))
32.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.3s

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
368.0ms	(* i (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
2.4s	(/ (* i (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))))
134.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify14.8s

Algorithm

egg-herbie

Counts

33976 → 33976

Iterations

Useful iterations: 0 (196.0ms)

Iter	Nodes	Cost
0	5002	1547888

prune11.4s

Filtered

33976 candidates to 2262 candidates (93.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	33974	2	33976
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	33978	7	33985

Merged error: 2.6b

Counts

33985 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
0.0b	(/ (* i (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))))
0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

47370×	`*-un-lft-identity`
24350×	`distribute-lft-out`
21137×	`times-frac`
13956×	`associate-r`
12266×	`associate-l`
7814×	`add-sqr-sqrt`
3780×	`distribute-lft-out--`
3760×	`add-cube-cbrt`
1512×	`difference-of-squares`
756×	`sqrt-prod`
473×	`associate-/r/`
412×	`unswap-sqr`
253×	`associate-/l*`
208×	`div-inv`
206×	`*-commutative`
194×	`flip3-+` `flip-+`
111×	`associate-/r*`
90×	`associate-*r/`
68×	`frac-times`
58×	`flip3--` `flip--` `associate-/l/`
52×	`add-exp-log` `add-cbrt-cube`
36×	`un-div-inv`
18×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
14×	`clear-num`
10×	`frac-2neg`
8×	`pow1`
4×	`associate-*l/` `add-log-exp`
2×	`pow-prod-down`

Counts

4 → 8885

Calls

4 calls:

79.0ms	(* i (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
304.0ms	(/ (* i (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))))
16.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
46.0ms	(* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* i (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
496.0ms	(/ (* i (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))))
66.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
203.0ms	(* (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))

simplify3.5s

Algorithm

egg-herbie

Counts

8897 → 8897

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5001	312883

prune3.8s

Filtered

8897 candidates to 787 candidates (91.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	8893	4	8897
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	8895	9	8904

Merged error: 2.6b

Counts

8904 → 9

regimes175.0ms

Accuracy

44.9% (8.8b remaining)

Error of 10.8b against oracle of 2.0b and baseline of 18.0b

bsearch63.0ms

Steps

Iters	Range		Point
6	3.0135278463849936e+133	3.1429806752022023e+134	2.9980560932417817e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	74
1	56	74

end0.0ms

sample682.0ms

Algorithm

intervals

Results

360.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true