Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	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

prune3.0ms

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: 4.2b

Counts

2 → 1

localize12.0ms

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))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite113.0ms

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)))
39.0ms	(/ (/ (/ (+ (+ (+ 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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ 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)))
22.0ms	(/ (/ (/ (+ (+ (+ 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))
19.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify141.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.3s

Filtered

281 candidates to 477 candidates (-69.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	469	8	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	470	8	478

Merged error: 1.2b

Counts

478 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.3b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite824.0ms

Algorithm

rewrite-expression-head

Rules

10323×	`times-frac`
6511×	`*-un-lft-identity`
3883×	`add-sqr-sqrt`
3881×	`add-cube-cbrt`
2904×	`sqrt-prod`
1315×	`distribute-lft-out`
591×	`associate-/l*`
239×	`associate-/r/`
216×	`sqrt-div`
127×	`div-inv`
115×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
11×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 3044

Calls

4 calls:

163.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series119.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
77.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.2s

Algorithm

egg-herbie

Counts

3056 → 3056

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5001	141011

prune19.4s

Filtered

1366 candidates to 3056 candidates (-123.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	3056	0	3056
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	3056	8	3064

Merged error: 1.2b

Counts

3064 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.7b	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

309×	`times-frac`
212×	`*-un-lft-identity`
187×	`sqrt-prod`
174×	`add-sqr-sqrt`
164×	`add-cube-cbrt`
27×	`associate-/l*`
24×	`distribute-lft-out`
18×	`sqrt-div`
16×	`flip3-+` `associate-/r/` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`div-inv`
7×	`associate-l`
6×	`associate-r` `associate-/r*`
4×	`frac-times` `sqrt-pow1` `pow1/2` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`frac-2neg` `sqrt-unprod` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 283

Calls

4 calls:

24.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
16.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 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))

series60.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
9.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify136.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	1110	6694
1	4663	6363
2	5002	6349

prune1.1s

Filtered

166 candidates to 295 candidates (-77.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	295	8	303

Merged error: 1.2b

Counts

303 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.4b	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

3939×	`times-frac`
2530×	`*-un-lft-identity`
1518×	`add-sqr-sqrt` `add-cube-cbrt`
506×	`distribute-lft-out`
311×	`associate-/r*`
186×	`associate-/r/`
96×	`div-inv`
92×	`flip3-+` `flip-+`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/l*`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1462

Calls

4 calls:

20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
42.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
22.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify476.0ms

Algorithm

egg-herbie

Counts

1474 → 1474

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	3694	48037
1	5001	46600

prune7.3s

Filtered

758 candidates to 1474 candidates (-94.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1473	1	1474
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	1474	8	1482

Merged error: 1.2b

Counts

1482 → 8

regimes128.0ms

Accuracy

55.6% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 4.0b

bsearch20.0ms

Steps

Iters	Range		Point
8	1.5253966904648332e+160	3.9133746645344376e+163	1.680186211472593e+160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms

sample809.0ms

Algorithm

intervals

Results

471.0ms	8000×	body	80	valid
119.0ms	8000×	pre	80	true

Details

sample32.0ms

simplify80.0ms

prune3.0ms

localize12.0ms

rewrite113.0ms

series63.0ms

simplify141.0ms

prune1.3s

localize14.0ms

rewrite824.0ms

series119.0ms

simplify1.2s

prune19.4s

localize19.0ms

rewrite71.0ms

series60.0ms

simplify136.0ms

prune1.1s

localize13.0ms

rewrite303.0ms

series96.0ms

simplify476.0ms

prune7.3s

regimes128.0ms

bsearch20.0ms

simplify1.0ms

end0.0ms

sample809.0ms

Profiling