Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample50.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune9.0ms

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: 4.1b

Counts

2 → 2

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))
3.8b	(/ (+ (+ (+ 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:

21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
9.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
43.0ms	(/ (/ (/ (+ (+ (+ 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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
22.0ms	(/ (/ (/ (+ (+ (+ 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))
18.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify192.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune1.5s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	471	8	479

Merged error: 1.2b

Counts

479 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
1.6b	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
3.8b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
3.8b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

192×	`*-un-lft-identity`
109×	`times-frac`
80×	`distribute-lft-out`
57×	`sqrt-prod`
55×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
39×	`associate-/l*`
18×	`flip3-+` `flip-+`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-div`
9×	`associate-/r*`
8×	`frac-times`
7×	`associate-l`
6×	`pow1`
5×	`associate-r` `div-inv` `associate-/l/`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative`

Counts

4 → 207

Calls

4 calls:

14.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
31.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
17.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
23.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
15.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5369	6744

prune749.0ms

Filtered

136 candidates to 219 candidates (-61.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	219	8	227

Merged error: 1.2b

Counts

227 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
0.2b	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
1.5b	(* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))))
3.8b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
64×	`add-exp-log`
47×	`times-frac`
42×	`distribute-lft-out`
38×	`add-sqr-sqrt`
34×	`add-cbrt-cube`
31×	`add-cube-cbrt`
30×	`associate-l`
24×	`prod-exp`
21×	`flip3-+` `flip-+`
20×	`div-exp` `associate-r` `associate-/r/`
13×	`frac-times`
11×	`pow1`
10×	`cbrt-undiv` `cbrt-unprod`
8×	`associate-/l*`
7×	`associate-r/` `associate-l/`
6×	`rec-exp` `1-exp`
5×	`associate-/r*`
4×	`div-inv` `add-log-exp`
3×	`pow-prod-down` `unswap-sqr`
2×	`pow-flip` `frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `un-div-inv` `inv-pow`

Counts

4 → 188

Calls

4 calls:

14.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
16.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
37.0ms	(* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))))
15.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
10.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
23.0ms	(* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5388	5425

prune357.0ms

Filtered

118 candidates to 200 candidates (-69.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Merged error: 1.2b

Counts

208 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b	(/ (/ (* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0))))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0))))) (- (+ alpha beta) (* 2.0 1.0)))
19.4b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
82×	`times-frac`
49×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
32×	`distribute-lft-out`
25×	`add-exp-log` `add-cbrt-cube`
21×	`associate-l`
16×	`associate-/r/`
14×	`associate-/l*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
8×	`flip3-+` `flip-+` `div-inv`
7×	`associate-/r*`
6×	`pow1` `sum-log`
4×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
3×	`associate-r` `associate-/l/`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-*r/` `associate--l+` `clear-num` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

9.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
39.0ms	(/ (/ (* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0))))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
32.0ms	(* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0))))) (- (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0)))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
36.0ms	(/ (/ (* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0))))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
25.0ms	(* (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0))))) (- (+ alpha beta) (* 2.0 1.0)))
17.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* 1.0 (* 1.0 (* 2.0 2.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4973	7976
1	4973	7976

prune471.0ms

Filtered

129 candidates to 184 candidates (-42.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	184	8	192

Merged error: 1.2b

Counts

192 → 8

regimes134.0ms

Accuracy

54.1% (1.3b remaining)

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

bsearch22.0ms

Steps

Iters	Range		Point
7	3.622143305497153e+171	2.0699634002714567e+173	9.710938937188406e+171

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	70
1	37	70

end0.0ms

sample1.3s

Algorithm

intervals

Results

460.0ms

8000×

body

valid

Details

analyze3.0ms

sample50.0ms

simplify111.0ms

prune9.0ms

localize12.0ms

rewrite117.0ms

series64.0ms

simplify192.0ms

prune1.5s

localize20.0ms

rewrite85.0ms

series66.0ms

simplify62.0ms

prune749.0ms

localize17.0ms

rewrite89.0ms

series52.0ms

simplify66.0ms

prune357.0ms

localize21.0ms

rewrite109.0ms

series81.0ms

simplify87.0ms

prune471.0ms

regimes134.0ms

bsearch22.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling