Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify78.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

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)
23.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms	(/ (/ (/ (+ (+ (+ 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)))

series383.0ms

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)))
151.0ms	(/ (/ (/ (+ (+ (+ 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))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
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)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
66×	`associate-/r/`
37×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `frac-add` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 528

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
19.0ms	(/ (/ (+ (+ (+ 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)))
18.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (+ alpha beta) (* beta alpha))
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms	(/ (/ (/ (+ (+ (+ 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)))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify154.0ms

Algorithm

egg-herbie

Counts

540 → 540

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1632	15099
1	5001	14543

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`sqrt-div` `associate-/r*`
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` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 176

Calls

4 calls:

15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
16.0ms	(/ (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))

series306.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	325	2980
1	1021	2792
2	4270	2720
3	5001	2720

prune520.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (+ 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)))))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ 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)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite5.4s

Algorithm

rewrite-expression-head

Rules

98889×	`times-frac`
64792×	`*-un-lft-identity`
38820×	`sqrt-prod`
32650×	`add-sqr-sqrt` `add-cube-cbrt`
18119×	`distribute-lft-out`
5246×	`associate-/r/`
2656×	`div-inv`
2597×	`flip3-+` `flip-+`
389×	`associate-/r*`
76×	`associate-/l*`
66×	`sqrt-div`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `frac-add` `clear-num` `add-log-exp`

Counts

4 → 21031

Calls

4 calls:

60.0ms	(/ (+ (+ 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)))))
660.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (+ (+ 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)))))
153.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
74.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify12.4s

Algorithm

egg-herbie

Counts

21043 → 21043

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	16705	1436001

prune1.1m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.4b

regimes126.0ms

Accuracy

61.9% (1.1b remaining)

Error of 2.2b against oracle of 1.2b and baseline of 3.9b

bsearch54.0ms

Steps

Iters	Range		Point
6	3.3069971847189657e+170	3.354978332984879e+171	1.9825795401500267e+171

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	33
1	42	33

end0.0ms

sample543.0ms

Algorithm

intervals

Results

308.0ms	8000×	body	80	valid
91.0ms	8000×	pre	80	true