Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	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

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: 54.8b

Counts

2 → 1

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))))
35.5b	(/ (/ (* (* 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))
46.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite5.4s

Algorithm

rewrite-expression-head

Rules

98841×	`*-un-lft-identity`
45731×	`distribute-lft-out`
39648×	`times-frac`
39139×	`associate-l`
26853×	`add-sqr-sqrt`
13506×	`swap-sqr`
12217×	`associate-r`
7974×	`distribute-lft-out--`
7376×	`add-cube-cbrt`
6645×	`difference-of-squares`
4800×	`unswap-sqr`
3290×	`*-commutative`
1384×	`associate-/l*`
130×	`associate-/r/`
120×	`flip3-+` `flip-+`
108×	`associate-/r*`
102×	`associate-/l/`
80×	`frac-times`
61×	`add-exp-log` `add-cbrt-cube`
58×	`associate-*r/`
40×	`associate-*l/`
22×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
17×	`div-inv`
16×	`pow1` `associate-+r+`
14×	`+-commutative`
12×	`associate-+l+`
4×	`pow-prod-down` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 21613

Calls

4 calls:

22.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
41.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
694.0ms	(/ (/ (* (* 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))
91.0ms	(/ (* (* 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:

54.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
103.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
749.0ms	(/ (/ (* (* 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))
177.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify7.4s

Algorithm

egg-herbie

Counts

21625 → 21625

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5001	741328

prune7.0s

Filtered

21625 candidates to 1485 candidates (6.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	21618	7	21625
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21619	7	21626

Merged error: 33.9b

Counts

21626 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
34.0b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

6619×	`*-un-lft-identity`
3419×	`distribute-lft-out`
2950×	`times-frac`
1338×	`associate-l`
1083×	`add-sqr-sqrt`
715×	`add-cube-cbrt`
360×	`associate-r`
280×	`distribute-lft-out--`
201×	`associate-/l*`
112×	`difference-of-squares`
72×	`*-commutative` `unswap-sqr`
56×	`sqrt-prod`
53×	`associate-/l/`
48×	`associate-/r/`
46×	`associate-/r*`
27×	`flip3-+` `flip-+`
25×	`add-exp-log` `add-cbrt-cube`
24×	`div-inv`
11×	`cbrt-undiv` `div-exp`
6×	`frac-2neg` `clear-num`
4×	`pow1` `associate-*r/` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`
1×	`flip3--` `flip--`

Counts

4 → 1854

Calls

4 calls:

67.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
61.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
27.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
31.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
329.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
84.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
118.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify380.0ms

Algorithm

egg-herbie

Counts

1866 → 1866

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1755	37572
1	5001	37289

prune1.6s

Filtered

1866 candidates to 355 candidates (19.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1862	4	1866
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	1865	8	1873

Merged error: 33.9b

Counts

1873 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ i (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.5b	(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

487×	`*-un-lft-identity`
234×	`distribute-lft-out`
189×	`times-frac`
138×	`add-sqr-sqrt`
137×	`sqrt-prod`
135×	`associate-l`
98×	`add-cube-cbrt`
50×	`associate-r`
47×	`associate-/r*`
26×	`sqrt-div`
20×	`unswap-sqr`
16×	`flip3-+` `flip-+`
15×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
12×	`associate-/r/`
8×	`pow1` `frac-times`
5×	`*-commutative`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `div-inv`
2×	`sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`
1×	`sqrt-unprod`

Counts

4 → 352

Calls

4 calls:

35.0ms	(/ i (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
18.0ms	(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
33.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
30.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.5s

Counts

4 → 12

Calls

4 calls:

806.0ms	(/ i (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
162.0ms	(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
427.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
116.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify158.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	1085	5449
1	4683	5261
2	5001	5103

prune951.0ms

Filtered

364 candidates to 160 candidates (44.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	361	3	364
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	363	9	372

Merged error: 2.2b

Counts

372 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ (+ alpha beta) (* 2.0 i)))
0.3b	(/ i (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.5b	(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

338×	`*-un-lft-identity`
160×	`distribute-lft-out`
144×	`sqrt-prod`
140×	`times-frac`
124×	`add-sqr-sqrt`
89×	`associate-l`
83×	`add-cube-cbrt`
50×	`associate-r`
40×	`associate-/r*`
28×	`sqrt-div`
20×	`unswap-sqr`
15×	`flip3-+` `flip-+`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`pow1`
8×	`frac-times` `associate-/l*`
5×	`*-commutative`
4×	`associate-r/` `associate-l/` `add-log-exp`
3×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`rem-sqrt-square` `sqrt-unprod`

Counts

4 → 292

Calls

4 calls:

9.0ms	(sqrt (+ (+ alpha beta) (* 2.0 i)))
36.0ms	(/ i (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
23.0ms	(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
28.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i))))

series1.5s

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (+ (+ alpha beta) (* 2.0 i)))
803.0ms	(/ i (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
148.0ms	(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
435.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 i))))

simplify120.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	968	4569
1	3942	4401
2	5001	4236

prune887.0ms

Filtered

304 candidates to 146 candidates (48.0%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	294	10	304
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	296	17	313

Merged error: 1.8b

Counts

313 → 17

regimes366.0ms

Accuracy

24% (9.2b remaining)

Error of 11.2b against oracle of 2.0b and baseline of 14.1b

bsearch79.0ms

Steps

Iters	Range		Point
7	1.6286324200346649e+131	6.079544634243233e+132	3.0431262076792387e+131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	84
1	59	84

end0.0ms

sample691.0ms

Algorithm

intervals

Results

374.0ms	8000×	body	80	valid
125.0ms	8000×	pre	80	true