Details

sample27.0ms

Algorithm

intervals

Results

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

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

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: 3.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
38.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify149.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune894.0ms

Filtered

477 candidates to 281 candidates (58.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	468	9	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	9	478

Merged error: 1.1b

Counts

478 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.0b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
65×	`*-un-lft-identity`
54×	`add-exp-log`
49×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
18×	`associate-/r/`
15×	`associate-r`
14×	`cbrt-undiv`
13×	`flip3-+` `flip-+` `associate-/l*`
12×	`prod-exp`
11×	`distribute-lft-out`
10×	`associate-/r*`
9×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 181

Calls

4 calls:

7.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
22.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

simplify131.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	800	3242
1	4722	2900
2	5001	2894

prune352.0ms

Filtered

193 candidates to 129 candidates (66.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	193	9	202

Merged error: 1.1b

Counts

202 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

22.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series409.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394

prune378.0ms

Filtered

171 candidates to 99 candidates (57.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	171	9	180

Merged error: 1.1b

Counts

180 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.2b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.2b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.2b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
424×	`*-un-lft-identity`
375×	`add-sqr-sqrt`
279×	`cbrt-prod`
244×	`add-cube-cbrt`
194×	`associate-l`
114×	`associate-r`
90×	`distribute-lft-out`
40×	`add-exp-log`
28×	`add-cbrt-cube` `unswap-sqr`
25×	`associate-/r/`
20×	`cbrt-div`
18×	`cbrt-undiv` `div-exp`
15×	`flip3-+` `flip-+`
13×	`div-inv`
9×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`pow1/3`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 408

Calls

4 calls:

299.0ms	(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
12.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify146.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1780	13514
1	5001	13084

prune1.2s

Filtered

420 candidates to 314 candidates (74.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	420	0	420
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	420	9	429

Merged error: 1.1b

Counts

429 → 9

regimes77.0ms

Accuracy

56.7% (1.0b remaining)

Error of 2.2b against oracle of 1.2b and baseline of 3.6b

bsearch63.0ms

Steps

Iters	Range		Point
9	4.876217483973988e+170	4.033142460877422e+176	9.218170999579248e+170

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample629.0ms

Algorithm

intervals

Results

361.0ms	8000×	body	80	valid
123.0ms	8000×	pre	80	true