Details

sample34.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune14.0ms

Filtered

1 candidates to 1 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: 2.3b

Counts

2 → 2

localize13.0ms

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))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite124.0ms

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:

6.0ms	(+ (+ alpha beta) (* beta alpha))
26.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 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))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
23.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
30.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify360.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5048	23442

prune1.3s

Filtered

286 candidates to 475 candidates (-66.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	467	8	475
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	469	8	477

Merged error: 0.5b

Counts

477 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
0.1b	(/ (/ (/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.2b	(/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

5314×	`times-frac`
4304×	`*-un-lft-identity`
1925×	`add-sqr-sqrt` `add-cube-cbrt`
1314×	`distribute-lft-out`
345×	`associate-/l*`
158×	`associate-/r/`
89×	`div-inv`
70×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
38×	`associate-/r*`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1835

Calls

4 calls:

35.0ms	(/ (/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
18.0ms	(/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
95.0ms	(/ (/ (/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
25.0ms	(/ (/ (/ 1 (/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
17.0ms	(/ (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify651.0ms

Algorithm

egg-herbie

Counts

1847 → 1847

Iterations

Useful iterations: 0 (182.0ms)

Iter	Nodes	Cost
0	4992	104248
1	4992	104248

prune6.7s

Filtered

690 candidates to 1847 candidates (-167.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1846	1	1847
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	1848	7	1855

Merged error: 0.0b

Counts

1855 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
0.2b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
2.1b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
2.1b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
64×	`times-frac`
60×	`sqrt-prod`
54×	`distribute-lft-out`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
16×	`associate-/l*`
8×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `flip3-+` `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 → 154

Calls

4 calls:

14.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
17.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
8.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
51.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
10.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
10.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4920	3974
1	4920	3974

prune347.0ms

Filtered

98 candidates to 166 candidates (-69.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	166	7	173

Merged error: 0.0b

Counts

173 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (/ (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
2.5b	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
2.5b	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
2.5b	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
38×	`associate-r`
36×	`cbrt-prod`
34×	`times-frac`
30×	`cbrt-div`
29×	`add-sqr-sqrt` `distribute-lft-out`
24×	`add-cube-cbrt`
16×	`add-exp-log` `frac-times` `flip3-+` `flip-+`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 122

Calls

4 calls:

39.0ms	(* (* (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (/ (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
8.0ms	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (* (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))) (/ (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
16.0ms	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
20.0ms	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
16.0ms	(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5491	3908

prune368.0ms

Filtered

94 candidates to 134 candidates (-42.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	134	7	141

Merged error: 0.0b

Counts

141 → 7

regimes125.0ms

Accuracy

64.8% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 3.5b

bsearch18.0ms

Steps

Iters	Range		Point
7	7.177480459497802e+164	8.235032861842214e+166	7.300544338572419e+164

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	74
1	43	74

end0.0ms

sample910.0ms

Algorithm

intervals

Results

531.0ms	8000×	body	80	valid
131.0ms	8000×	pre	80	true

Details

sample34.0ms

simplify98.0ms

prune14.0ms

localize13.0ms

rewrite124.0ms

series71.0ms

simplify360.0ms

prune1.3s

localize19.0ms

rewrite412.0ms

series83.0ms

simplify651.0ms

prune6.7s

localize18.0ms

rewrite53.0ms

series119.0ms

simplify68.0ms

prune347.0ms

localize25.0ms

rewrite69.0ms

series66.0ms

simplify54.0ms

prune368.0ms

regimes125.0ms

bsearch18.0ms

simplify1.0ms

end0.0ms

sample910.0ms

Profiling