Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 3.9b

Counts

2 → 1

localize16.0ms

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:

11.0ms	(+ (+ (+ 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)))
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)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ (+ 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)))
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))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify145.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune897.0ms

Filtered

477 candidates to 281 candidates (58.9%)

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: 1.3b

Counts

478 → 8

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)))

rewrite121.0ms

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))
23.0ms	(/ (/ (+ (+ (+ 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)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms	(/ (/ (/ (+ (+ (+ 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)))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify163.0ms

Algorithm

egg-herbie

Counts

540 → 540

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1632	15099
1	5001	14543

prune854.0ms

Filtered

540 candidates to 283 candidates (52.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	540	0	540
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	540	8	548

Merged error: 1.3b

Counts

548 → 8

localize22.0ms

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) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.9b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

297×	`times-frac`
216×	`*-un-lft-identity`
161×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
78×	`associate-l`
38×	`distribute-lft-out`
37×	`difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r/`
25×	`associate-/l*`
18×	`associate-r`
14×	`cbrt-undiv` `div-exp` `div-inv`
13×	`flip3-+` `flip-+`
11×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`frac-times` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 308

Calls

4 calls:

13.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
61.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
26.0ms	(/ (/ (+ (+ (+ 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)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
213.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
157.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify101.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1417	7781
1	5001	7281

prune785.0ms

Filtered

320 candidates to 239 candidates (74.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	320	8	328

Merged error: 1.3b

Counts

328 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.4b	(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`cbrt-prod`
14×	`cbrt-div`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`associate-/r/`
7×	`times-frac` `associate-/l*`
6×	`add-cbrt-cube`
5×	`distribute-lft-out`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
23.0ms	(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
59.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
296.0ms	(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	586	1440
1	2082	1369
2	5001	1345

prune349.0ms

Filtered

93 candidates to 81 candidates (87.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Merged error: 1.3b

Counts

101 → 8

regimes83.0ms

Accuracy

58% (1.2b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.9b

bsearch36.0ms

Steps

Iters	Range		Point
5	4.926746269158418e+161	1.3231883097255524e+162	1.303850468869263e+162

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	17
1	27	17

end0.0ms

sample534.0ms

Algorithm

intervals

Results

299.0ms	8000×	body	80	valid
98.0ms	8000×	pre	80	true