Details

sample27.0ms

Algorithm

intervals

Results

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

simplify82.0ms

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

prune6.0ms

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: 4.9b

Counts

2 → 1

localize12.0ms

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))
4.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 463

Calls

4 calls:

8.0ms	(+ (+ alpha beta) (* beta alpha))
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
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)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ alpha beta) (* beta alpha))
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms	(/ (/ (/ (+ (+ (+ 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))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify144.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune866.0ms

Filtered

475 candidates to 280 candidates (58.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	467	8	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	468	8	476

Merged error: 1.6b

Counts

476 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.2b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
4.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite837.0ms

Algorithm

rewrite-expression-head

Rules

13728×	`times-frac`
8082×	`*-un-lft-identity`
5318×	`add-sqr-sqrt` `add-cube-cbrt`
4110×	`sqrt-prod`
1382×	`distribute-lft-out`
826×	`associate-/l*`
550×	`associate-/r/`
276×	`flip3-+` `flip-+`
275×	`div-inv`
88×	`sqrt-div`
34×	`add-exp-log` `add-cbrt-cube`
20×	`cbrt-undiv` `div-exp`
19×	`associate-/r*`
5×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4482

Calls

4 calls:

193.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
56.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
143.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
211.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
83.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Algorithm

egg-herbie

Counts

4494 → 4494

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5001	193430

prune9.1s

Filtered

4494 candidates to 2122 candidates (47.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	4493	1	4494
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	4494	8	4502

Merged error: 1.6b

Counts

4502 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(* (+ alpha beta) (+ alpha beta))
2.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
4.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
145×	`*-un-lft-identity`
87×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
29×	`distribute-lft-out`
25×	`associate-/l*`
19×	`difference-of-squares`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
11×	`pow1` `associate-/r*`
8×	`div-inv`
6×	`swap-sqr`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`frac-times` `associate-r` `associate-l` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `associate-r/` `associate-l/` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `div-sub` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 222

Calls

4 calls:

13.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
8.0ms	(* (+ alpha beta) (+ alpha beta))
24.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
19.0ms	(* (+ alpha beta) (+ alpha beta))
158.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
70.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1039	4291
1	5002	4105

prune539.0ms

Filtered

234 candidates to 163 candidates (69.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	234	8	242

Merged error: 1.6b

Counts

242 → 8

localize14.0ms

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))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.0b	(* (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))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
4.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

1508×	`times-frac`
1074×	`*-un-lft-identity`
671×	`add-sqr-sqrt`
612×	`add-cube-cbrt`
520×	`sqrt-prod`
282×	`associate-r`
231×	`distribute-lft-out`
82×	`associate-/r/`
77×	`associate-/l*`
43×	`flip3-+` `flip-+`
41×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-l`
15×	`unswap-sqr`
10×	`associate-/r*`
8×	`cbrt-undiv` `div-exp`
6×	`pow1`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
2×	`sqrt-div`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 772

Calls

4 calls:

37.0ms	(/ (/ (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))
148.0ms	(* (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))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

449.0ms	(/ (/ (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))
154.0ms	(* (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))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
76.0ms	(/ (+ (+ (+ 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)))

simplify246.0ms

Algorithm

egg-herbie

Counts

784 → 784

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2241	23777
1	5001	23307

prune1.8s

Filtered

784 candidates to 468 candidates (59.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	784	0	784
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	784	8	792

Merged error: 1.6b

Counts

792 → 8

regimes76.0ms

Accuracy

52.8% (1.2b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.7b

bsearch19.0ms

Steps

Iters	Range		Point
3	4.71915148139575e+161	6.486415991369088e+161	5.271421640762418e+161

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	23
1	27	23

end0.0ms

sample626.0ms

Algorithm

intervals

Results

348.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true

Details

sample27.0ms

simplify82.0ms

prune6.0ms

localize12.0ms

rewrite107.0ms

series382.0ms

simplify144.0ms

prune866.0ms

localize14.0ms

rewrite837.0ms

series595.0ms

simplify1.7s

prune9.1s

localize16.0ms

rewrite70.0ms

series291.0ms

simplify71.0ms

prune539.0ms

localize14.0ms

rewrite278.0ms

series759.0ms

simplify246.0ms

prune1.8s

regimes76.0ms

bsearch19.0ms

simplify1.0ms

end0.0ms

sample626.0ms

Profiling