Details

sample24.0ms

Algorithm

intervals

Results

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

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	33	17
1	122	15
2	598	13
3	4475	13
4	5001	13

prune8.0ms

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: 6.4b

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))
6.0b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

29632×	`*-un-lft-identity`
17766×	`distribute-lft-out`
11948×	`times-frac`
4330×	`associate-l`
2250×	`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` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
3×	`sum-log`
2×	`+-commutative` `associate-+l+`

Counts

4 → 4734

Calls

4 calls:

11.0ms	(+ (+ alpha beta) (* beta alpha))
59.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
457.0ms	(/ (/ (/ (+ (+ (+ 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))
34.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
146.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
156.0ms	(/ (/ (/ (+ (+ (+ 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))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.2s

Algorithm

egg-herbie

Counts

4746 → 4746

Iterations

Useful iterations: 1 (71.0ms)

Iter	Nodes	Cost
0	1618	115851
1	5002	107507

prune1.0s

Filtered

4746 candidates to 327 candidates (93.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	4739	7	4746
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	4741	7	4748

Merged error: 2.1b

Counts

4748 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (- (+ (+ (fma 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))
6.0b	(/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

100031×	`*-un-lft-identity`
55654×	`distribute-lft-out`
50952×	`times-frac`
13760×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12894×	`associate-l`
11507×	`add-sqr-sqrt` `add-cube-cbrt`
2370×	`associate-/l*`
2342×	`neg-mul-1`
385×	`associate-/l/`
168×	`associate-/r/`
152×	`distribute-neg-frac`
88×	`flip3-+` `flip-+`
84×	`div-inv`
76×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
7×	`fma-def`
6×	`associate-+l+` `frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`+-commutative` `neg-sub0`

Counts

4 → 19106

Calls

4 calls:

15.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
120.0ms	(/ (/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
742.0ms	(/ (/ (/ (- (+ (+ (fma 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))
26.0ms	(/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
158.0ms	(/ (/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
161.0ms	(/ (/ (/ (- (+ (+ (fma 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))
85.0ms	(/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))

simplify5.4s

Algorithm

egg-herbie

Counts

19118 → 19118

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5001	512961

prune6.7s

Filtered

19118 candidates to 1703 candidates (91.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19115	3	19118
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	19118	7	19125

Merged error: 2.1b

Counts

19125 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

5257×	`*-un-lft-identity`
2870×	`distribute-lft-out`
2749×	`sqrt-prod`
2480×	`times-frac`
769×	`add-sqr-sqrt`
763×	`add-cube-cbrt`
750×	`associate-l`
138×	`associate-/l*`
34×	`sqrt-div`
30×	`associate-/r*` `associate-/l/`
26×	`associate-/r/`
17×	`flip3-+` `flip-+`
13×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-undiv` `frac-2neg` `clear-num`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 1527

Calls

4 calls:

88.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
32.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
15.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series412.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
110.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
48.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
55.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify402.0ms

Algorithm

egg-herbie

Counts

1539 → 1539

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1078	33611
1	4154	30329
2	5002	30302

prune775.0ms

Filtered

1539 candidates to 197 candidates (87.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1539	0	1539
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	1539	7	1546

Merged error: 2.1b

Counts

1546 → 7

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b

(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) 1) (+ (+ alpha beta) (* 2.0 1.0)))

3.2b

(/ (/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) 1) (+ (+ alpha beta) (* 2.0 1.0))))

6.0b

(/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

29787×	`*-un-lft-identity`
22264×	`times-frac`
13890×	`distribute-lft-out`
8197×	`add-sqr-sqrt`
7484×	`associate-l`
6792×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6377×	`add-cube-cbrt`
1820×	`associate-r`
1156×	`neg-mul-1`
780×	`unswap-sqr`
316×	`associate-/l*`
297×	`div-inv`
260×	`*-commutative`
113×	`associate-/r/`
88×	`associate-/r*`
76×	`distribute-neg-frac`
72×	`flip3-+` `flip-+`
53×	`associate-/l/`
52×	`frac-times`
40×	`add-exp-log`
31×	`add-cbrt-cube`
26×	`associate-*l/`
19×	`div-exp`
13×	`cbrt-undiv`
9×	`frac-2neg` `prod-exp` `clear-num`
6×	`cbrt-unprod`
5×	`pow1`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/`
3×	`expm1-log1p-u` `1-exp` `div-sub` `distribute-frac-neg` `log1p-expm1-u` `add-log-exp`
2×	`neg-sub0`
1×	`pow-prod-down`

Counts

3 → 9568

Calls

3 calls:

39.0ms

(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) 1) (+ (+ alpha beta) (* 2.0 1.0)))

306.0ms

(/ (/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) 1) (+ (+ alpha beta) (* 2.0 1.0))))

30.0ms

(/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))

series298.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms

(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) 1) (+ (+ alpha beta) (* 2.0 1.0)))

172.0ms

(/ (/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) 1) (+ (+ alpha beta) (* 2.0 1.0))))

85.0ms

(/ (- (+ (+ (fma alpha beta beta) alpha) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))

simplify2.9s

Algorithm

egg-herbie

Counts

9577 → 9577

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5001	280215

prune7.8s

Filtered

9577 candidates to 1805 candidates (81.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	9575	2	9577
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	9577	7	9584

Merged error: 2.1b

Counts

9584 → 7

regimes80.0ms

Accuracy

-31% (3.4b remaining)

Error of 4.6b against oracle of 1.2b and baseline of 3.8b

bsearch37.0ms

Steps

Iters	Range		Point
5	3.7657386264108734e+112	1.4894876854092099e+113	1.4657012306921548e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	66	30
2	68	30
3	68	30

end0.0ms

sample524.0ms

Algorithm

intervals

Results

288.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true