Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	205×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	18×	body	1280	valid
4.0ms	20×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	7×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

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: 24.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.8b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

5.0ms	(+ (+ alpha beta) (* 2.0 i))
19.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* 2.0 i))
223.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
262.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	701	1981
1	3980	1865
2	5002	1865

prune347.0ms

Filtered

136 candidates to 101 candidates (74.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	126	10	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	10	137

Merged error: 5.0b

Counts

137 → 10

localize13.0ms

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)))
1.4b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite112.0ms

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:

19.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
41.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series734.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
75.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
224.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
274.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune650.0ms

Filtered

307 candidates to 199 candidates (64.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	308	9	317

Merged error: 5.0b

Counts

317 → 9

localize20.0ms

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)))
1.4b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite113.0ms

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:

26.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
12.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
38.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series847.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
78.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
228.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
272.0ms	(+ (* (+ 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

prune546.0ms

Filtered

203 candidates to 133 candidates (65.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	6	203
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	203	9	212

Merged error: 5.0b

Counts

212 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

8.4b	(+ (* (* (+ alpha beta) (* (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
14.6b	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.6b	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.6b	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

432×	`times-frac`
376×	`*-un-lft-identity`
270×	`cbrt-prod`
250×	`add-sqr-sqrt`
178×	`add-cube-cbrt`
63×	`distribute-lft-out`
36×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/r/`
16×	`flip3-+` `flip-+`
15×	`div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `pow1/3`
1×	`+-commutative` `sum-log`

Counts

4 → 308

Calls

4 calls:

79.0ms	(+ (* (* (+ alpha beta) (* (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
26.0ms	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
20.0ms	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
20.0ms	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series2.1s

Counts

4 → 12

Calls

4 calls:

315.0ms	(+ (* (* (+ alpha beta) (* (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
590.0ms	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
583.0ms	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
589.0ms	(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	833	8126
1	2959	7843
2	5001	7822

prune1.2s

Filtered

320 candidates to 210 candidates (65.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	319	10	329

Merged error: 5.0b

Counts

329 → 10

regimes295.0ms

Accuracy

73.1% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 12.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	46
1	56	46

end0.0ms

sample995.0ms

Algorithm

intervals

Results

311.0ms	6378×	body	80	valid
172.0ms	8000×	pre	80	true
134.0ms	508×	body	1280	valid
115.0ms	580×	body	640	valid
52.0ms	350×	body	320	valid
18.0ms	184×	body	160	valid