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

sample29.0ms

Algorithm

intervals

Results

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

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune12.0ms

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: 3.6b

Counts

2 → 2

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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

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)
23.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms	(/ (/ (/ (+ (+ (+ 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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
29.0ms	(/ (/ (/ (+ (+ (+ 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))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify187.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune1.4s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	472	7	479

Merged error: 0.7b

Counts

479 → 7

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 3.0)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 524

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
24.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify164.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5040	24742

prune1.4s

Filtered

286 candidates to 536 candidates (-87.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	530	6	536
Fresh	6	0	6
Picked	0	1	1
Done	0	0	0
Total	536	7	543

Merged error: 0.7b

Counts

543 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ alpha (+ beta 3.0))))
0.5b	(/ 1 (sqrt (+ alpha (+ beta (* 1.0 2.0)))))
0.7b	(pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)
15.4b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

1720×	`*-un-lft-identity`
1269×	`times-frac`
752×	`distribute-lft-out`
583×	`add-sqr-sqrt`
536×	`associate-r`
427×	`add-cube-cbrt`
310×	`sqrt-prod`
234×	`unpow-prod-down` `cube-prod`
83×	`add-exp-log`
43×	`div-exp`
40×	`unswap-sqr`
37×	`sqr-pow`
32×	`cube-mult` `unpow3`
30×	`add-cbrt-cube`
27×	`associate-l` `associate-/r*`
20×	`prod-exp`
18×	`sqrt-div` `associate-/r/`
14×	`cube-div`
11×	`cbrt-undiv` `flip3-+` `flip-+`
10×	`pow1`
9×	`div-inv`
8×	`associate-/l*`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow` `pow-flip` `pow-pow`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `sqrt-pow2` `inv-pow` `rem-cube-cbrt`

Counts

4 → 871

Calls

4 calls:

257.0ms	(* (/ 1 (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ alpha (+ beta 3.0))))
7.0ms	(/ 1 (sqrt (+ alpha (+ beta (* 1.0 2.0)))))
6.0ms	(pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)
21.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3))

series98.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (/ 1 (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ alpha (+ beta 3.0))))
12.0ms	(/ 1 (sqrt (+ alpha (+ beta (* 1.0 2.0)))))
29.0ms	(pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)
35.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3))

simplify181.0ms

Algorithm

egg-herbie

Counts

883 → 883

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5046	25094

prune1.2s

Filtered

238 candidates to 883 candidates (-271.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	883	0	883
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	883	7	890

Merged error: 0.7b

Counts

890 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
0.0b	(* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
1.3b	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
3.4b	(/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

145×	`*-un-lft-identity`
68×	`distribute-lft-out`
54×	`add-exp-log` `times-frac`
36×	`add-sqr-sqrt`
35×	`associate-l`
34×	`frac-times` `add-cbrt-cube`
31×	`add-cube-cbrt`
29×	`flip3-+` `flip-+`
24×	`associate-*r/`
22×	`prod-exp`
21×	`associate-/r/`
17×	`pow1`
14×	`div-exp`
12×	`cbrt-unprod`
11×	`associate-*l/`
8×	`cbrt-undiv` `associate-/l*`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-flip` `div-inv`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`inv-pow`

Counts

4 → 204

Calls

4 calls:

25.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
21.0ms	(* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
30.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
14.0ms	(/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
22.0ms	(* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
22.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
20.0ms	(/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5476	5992

prune306.0ms

Filtered

122 candidates to 216 candidates (-77.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	216	7	223

Merged error: 0.2b

Counts

223 → 7

regimes107.0ms

Accuracy

70% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.4b

bsearch16.0ms

Steps

Iters	Range		Point
7	1.9289726800519353e+161	1.094688825943062e+163	6.370230282252863e+161

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	54
1	43	54

end0.0ms

sample811.0ms

Algorithm

intervals

Results

536.0ms	8000×	body	80	valid
132.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample29.0ms

simplify116.0ms

prune12.0ms

localize12.0ms

rewrite112.0ms

series64.0ms

simplify187.0ms

prune1.4s

localize13.0ms

rewrite117.0ms

series62.0ms

simplify164.0ms

prune1.4s

localize20.0ms

rewrite372.0ms

series98.0ms

simplify181.0ms

prune1.2s

localize16.0ms

rewrite98.0ms

series106.0ms

simplify62.0ms

prune306.0ms

regimes107.0ms

bsearch16.0ms

simplify1.0ms

end0.0ms

sample811.0ms

Profiling