Details

sample23.0ms

Algorithm

intervals

Results

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

simplify79.0ms

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

29629×	`*-un-lft-identity`
17765×	`distribute-lft-out`
11948×	`times-frac`
4330×	`associate-l`
2249×	`add-sqr-sqrt` `add-cube-cbrt`
588×	`associate-/l*`
168×	`associate-/r/`
138×	`associate-/l/`
88×	`flip3-+` `flip-+`
84×	`div-inv`
43×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`frac-2neg` `clear-num`
4×	`pow1`
3×	`sum-log`
2×	`+-commutative` `associate-+l+`

Counts

4 → 4722

Calls

4 calls:

56.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
9.0ms	(+ (+ alpha beta) (* beta alpha))
193.0ms	(/ (/ (/ (+ (+ (+ 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))
28.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(+ (+ alpha beta) (* beta alpha))
148.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify1.2s

Algorithm

egg-herbie

Counts

4734 → 4734

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1605	115829
1	5001	114691

prune1.3s

Filtered

4734 candidates to 310 candidates (6.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	4727	7	4734
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	4728	7	4735

Merged error: 0.7b

Counts

4735 → 7

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))))
0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite406.0ms

Algorithm

rewrite-expression-head

Rules

5246×	`*-un-lft-identity`
3074×	`distribute-lft-out`
1882×	`times-frac`
880×	`sqrt-prod`
808×	`associate-l`
438×	`add-sqr-sqrt`
426×	`add-cube-cbrt`
184×	`sqrt-div`
156×	`associate-/l*`
48×	`associate-/l/`
42×	`associate-/r*`
40×	`associate-/r/`
24×	`flip3-+` `flip-+`
20×	`div-inv`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `rem-sqrt-square` `frac-2neg` `clear-num`
4×	`add-log-exp`
2×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-exp`

Counts

4 → 1262

Calls

4 calls:

85.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
89.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
183.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
71.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify279.0ms

Algorithm

egg-herbie

Counts

1274 → 1274

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	740	24070
1	2711	23142
2	5001	22258

prune872.0ms

Filtered

1274 candidates to 200 candidates (15.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1272	2	1274
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	1274	7	1281

Merged error: 0.7b

Counts

1281 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
12.2b	(sqrt (* (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

631×	`*-un-lft-identity`
370×	`distribute-lft-out`
196×	`sqrt-prod`
137×	`times-frac`
97×	`associate-l`
83×	`sqrt-div` `associate-r`
79×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
46×	`frac-times`
40×	`associate-/r*`
34×	`associate-/l*`
32×	`flip3-+` `flip-+`
23×	`associate-*r/`
9×	`pow1`
8×	`associate-/l/`
6×	`add-exp-log` `rem-sqrt-square` `un-div-inv` `add-cbrt-cube` `unswap-sqr`
5×	`clear-num`
4×	`frac-2neg` `sqrt-pow1` `associate-/r/` `add-log-exp`
3×	`pow1/2`
2×	`associate-*l/` `div-inv`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative`

Counts

4 → 316

Calls

4 calls:

11.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
12.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
24.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
70.0ms	(sqrt (* (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))))

series415.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
247.0ms	(sqrt (* (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))))

simplify155.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	863	5635
1	4432	5531
2	5001	5328

prune673.0ms

Filtered

328 candidates to 121 candidates (36.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	328	7	335

Merged error: 0.7b

Counts

335 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

944×	`*-un-lft-identity`
568×	`distribute-lft-out`
224×	`times-frac`
136×	`associate-l`
72×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`associate-/l*`
28×	`associate-/r*`
12×	`add-exp-log` `add-cbrt-cube`
8×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
4×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

4 → 348

Calls

4 calls:

25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
30.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
26.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
26.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	237	4120
1	1042	3976
2	5002	3972

prune725.0ms

Filtered

360 candidates to 112 candidates (31.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	360	7	367

Merged error: 0.7b

Counts

367 → 7

regimes80.0ms

Accuracy

40.5% (1.6b remaining)

Error of 2.8b against oracle of 1.2b and baseline of 3.9b

bsearch55.0ms

Steps

Iters	Range		Point
6	4.909214320538352e+91	3.7507584931071266e+92	7.929088531646719e+91

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	56
1	49	56

end0.0ms

sample557.0ms

Algorithm

intervals

Results

313.0ms	8000×	body	80	valid
99.0ms	8000×	pre	80	true