Details

sample27.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	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

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: 5.6b

Counts

2 → 1

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))
5.3b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite119.0ms

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)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
42.0ms	(/ (/ (/ (+ (+ (+ 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)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 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))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify149.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune891.0ms

Filtered

477 candidates to 281 candidates (58.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	468	9	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	9	478

Merged error: 1.5b

Counts

478 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt` `sqrt-prod`
38×	`add-cube-cbrt`
14×	`associate-/l*`
10×	`distribute-lft-out`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
6×	`pow1` `flip3-+` `associate-/r*` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

17.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series463.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
183.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	341	1840
1	1212	1736
2	5001	1712

prune318.0ms

Filtered

138 candidates to 94 candidates (68.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Merged error: 1.5b

Counts

147 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) 3)
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0b	(cbrt (pow (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) 3))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
84×	`times-frac`
66×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
60×	`cbrt-prod`
56×	`sqrt-prod`
54×	`unpow-prod-down` `cube-prod`
14×	`distribute-lft-out`
8×	`associate-/r/`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+`
4×	`sqrt-div` `div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 176

Calls

4 calls:

16.0ms	(pow (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) 3)
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
21.0ms	(cbrt (pow (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) 3))

series935.0ms

Counts

4 → 12

Calls

4 calls:

658.0ms	(pow (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) 3)
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
184.0ms	(cbrt (pow (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) 3))

simplify88.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	681	3056
1	2880	2765
2	5001	2679

prune313.0ms

Filtered

188 candidates to 83 candidates (44.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	188	8	196

Merged error: 1.5b

Counts

196 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
0.1b	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
5.2b	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
5.3b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

1659×	`times-frac`
1185×	`*-un-lft-identity`
689×	`add-sqr-sqrt` `add-cube-cbrt`
672×	`cbrt-prod`
306×	`unpow-prod-down` `cube-prod`
248×	`distribute-lft-out`
145×	`associate-/l*`
82×	`associate-/r/`
42×	`flip3-+` `flip-+`
41×	`div-inv`
17×	`cube-mult` `unpow3` `sqr-pow`
14×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-div` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 869

Calls

4 calls:

15.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
61.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
144.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
74.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify283.0ms

Algorithm

egg-herbie

Counts

881 → 881

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1984	26584
1	5001	26211

prune1.1s

Filtered

881 candidates to 328 candidates (37.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	881	0	881
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	881	8	889

Merged error: 1.5b

Counts

889 → 8

regimes86.0ms

Accuracy

51% (1.4b remaining)

Error of 2.4b against oracle of 1.1b and baseline of 3.8b

bsearch65.0ms

Steps

Iters	Range		Point
9	1.007730983848284e+158	5.015723311903944e+163	4.202347054500846e+160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample636.0ms

Algorithm

intervals

Results

355.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true