Details

sample23.0ms

Algorithm

intervals

Results

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

simplify77.0ms

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

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: 4.7b

Counts

2 → 1

localize12.0ms

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)))
0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 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))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite117.0ms

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:

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

series375.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
18.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
145.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify146.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune921.0ms

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: 1.4b

Counts

478 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 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)))
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))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

1471×	`times-frac`
1040×	`*-un-lft-identity`
673×	`add-sqr-sqrt`
627×	`sqrt-prod`
590×	`add-cube-cbrt`
258×	`associate-r`
225×	`distribute-lft-out`
88×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
46×	`flip3-+` `flip-+`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 761

Calls

4 calls:

410.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 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)))
38.0ms	(/ (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))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
19.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 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)))
120.0ms	(/ (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))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify257.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1953	24980
1	5001	24018

prune2.1s

Filtered

773 candidates to 494 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	773	8	781

Merged error: 1.4b

Counts

781 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.2b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

171×	`times-frac`
109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
96×	`add-cube-cbrt`
54×	`add-exp-log`
51×	`associate-r`
34×	`add-cbrt-cube`
26×	`div-exp`
22×	`associate-/r/`
19×	`associate-/l*`
15×	`flip3-+` `flip-+`
14×	`cbrt-undiv`
12×	`div-inv`
10×	`pow1` `prod-exp` `associate-/r*`
6×	`cbrt-unprod` `associate-/l/`
5×	`unswap-sqr`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `distribute-lft-out`
2×	`pow-flip` `associate-*r/` `inv-pow` `pow-div`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 235

Calls

4 calls:

7.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
18.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
31.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
33.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
58.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
157.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
138.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	971	3790
1	5001	3272

prune482.0ms

Filtered

247 candidates to 166 candidates (67.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	247	8	255

Merged error: 1.4b

Counts

255 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
4.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite893.0ms

Algorithm

rewrite-expression-head

Rules

1973×	`times-frac`
1066×	`*-un-lft-identity`
1026×	`add-sqr-sqrt`
779×	`cbrt-prod`
720×	`add-cube-cbrt`
615×	`associate-r`
173×	`distribute-lft-out`
97×	`associate-l`
84×	`add-exp-log`
74×	`associate-/r/`
63×	`unswap-sqr`
44×	`cbrt-undiv` `div-exp`
40×	`flip3-+` `add-cbrt-cube` `flip-+`
37×	`div-inv`
24×	`cbrt-div`
20×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`pow1/3`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 861

Calls

4 calls:

774.0ms	(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
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))

series358.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
60.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify348.0ms

Algorithm

egg-herbie

Counts

873 → 873

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5001	40817

prune3.2s

Filtered

873 candidates to 664 candidates (76.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	873	0	873
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	873	8	881

Merged error: 1.4b

Counts

881 → 8

regimes92.0ms

Accuracy

32% (1.8b remaining)

Error of 3.1b against oracle of 1.2b and baseline of 3.9b

bsearch36.0ms

Steps

Iters	Range		Point
4	4.0135083011877617e+62	6.004551615130244e+62	5.939198602440939e+62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	34
1	42	34

end0.0ms

sample522.0ms

Algorithm

intervals

Results

291.0ms	8000×	body	80	valid
92.0ms	8000×	pre	80	true