Details

sample26.0ms

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

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

rewrite121.0ms

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)))
40.0ms	(/ (/ (/ (+ (+ (+ 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)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
134.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify150.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune891.0ms

Filtered

477 candidates to 281 candidates (58.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	471	7	478

Merged error: 0.9b

Counts

478 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.1b	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

1659×	`times-frac`
1185×	`*-un-lft-identity`
689×	`add-sqr-sqrt` `add-cube-cbrt`
672×	`cbrt-prod`
306×	`unpow-prod-down` `cube-prod`
248×	`distribute-lft-out`
145×	`associate-/l*`
82×	`associate-/r/`
42×	`flip3-+` `flip-+`
41×	`div-inv`
17×	`cube-mult` `unpow3` `sqr-pow`
14×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-div` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 869

Calls

4 calls:

61.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))

series506.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
205.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
71.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))

simplify280.0ms

Algorithm

egg-herbie

Counts

881 → 881

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1984	26584
1	5001	26211

prune1.3s

Filtered

881 candidates to 328 candidates (37.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	880	1	881
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	881	7	888

Merged error: 0.9b

Counts

888 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.2b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
54×	`times-frac`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
13×	`add-log-exp`
12×	`distribute-lft-out`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `sum-log`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*` `div-inv`
3×	`associate-r` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 143

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
15.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
27.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify116.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	732	2482
1	3919	2257
2	5002	2257

prune317.0ms

Filtered

155 candidates to 113 candidates (72.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	155	7	162

Merged error: 0.9b

Counts

162 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.8b	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite744.0ms

Algorithm

rewrite-expression-head

Rules

3553×	`times-frac`
2088×	`*-un-lft-identity`
1654×	`add-sqr-sqrt`
1436×	`add-cube-cbrt`
1370×	`sqrt-prod`
615×	`associate-r`
326×	`distribute-lft-out`
126×	`associate-/r/`
87×	`associate-/l*`
65×	`flip3-+` `flip-+`
63×	`div-inv`
55×	`associate-l`
45×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
22×	`cbrt-undiv` `div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-/r*`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 1497

Calls

4 calls:

55.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
500.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series646.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
148.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
56.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify519.0ms

Algorithm

egg-herbie

Counts

1509 → 1509

Iterations

Useful iterations: 1 (78.0ms)

Iter	Nodes	Cost
0	4302	53952
1	5001	52369

prune2.7s

Filtered

1509 candidates to 628 candidates (41.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1509	0	1509
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1509	7	1516

Merged error: 0.9b

Counts

1516 → 7

regimes75.0ms

Accuracy

46.3% (1.5b remaining)

Error of 2.6b against oracle of 1.1b and baseline of 3.9b

bsearch61.0ms

Steps

Iters	Range		Point
8	2.587619639749337e+192	3.794403629647689e+196	1.0654652534436594e+193

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	33
1	40	33

end0.0ms

sample654.0ms

Algorithm

intervals

Results

366.0ms	8000×	body	80	valid
130.0ms	8000×	pre	80	true