Details

sample24.0ms

Algorithm

intervals

Results

14.0ms

307×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	89	10
2	377	10
3	1779	10
4	5001	10

prune3.0ms

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: 14.8b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.3b	(/ 1.0 (- (* b b) (* a a)))
5.1b	(- (* b b) (* a a))
8.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite7.4s

Algorithm

rewrite-expression-head

Rules

66210×	`add-sqr-sqrt`
63118×	`frac-times`
59991×	`associate-/r*`
34546×	`associate-/l*`
33531×	`*-un-lft-identity`
32562×	`frac-sub`
23106×	`add-cube-cbrt`
21529×	`difference-of-squares`
11572×	`clear-num`
11487×	`frac-2neg`
10332×	`swap-sqr`
8627×	`unswap-sqr`
8613×	`*-commutative`
4310×	`distribute-lft-out--`
3597×	`associate-l`
3398×	`associate-*r/`
1166×	`associate-*l/`
406×	`flip3--` `flip--`
337×	`times-frac`
222×	`associate-r`
170×	`un-div-inv`
36×	`add-exp-log` `add-cbrt-cube`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`diff-log`

Counts

4 → 34666

Calls

4 calls:

71.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
21.0ms	(/ 1.0 (- (* b b) (* a a)))
17.0ms	(- (* b b) (* a a))
887.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
42.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
97.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify9.2s

Algorithm

egg-herbie

Counts

34678 → 34678

Iterations

Useful iterations: 0 (413.0ms)

Iter	Nodes	Cost
0	19332	835878

prune44.4s

Filtered

34678 candidates to 11343 candidates (32.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	34669	9	34678
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34670	9	34679

Merged error: 0b

Counts

34679 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (/ 2.0 PI) (- b a)))
0.4b	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ 2.0 PI) (- b a))

rewrite735.0ms

Algorithm

rewrite-expression-head

Rules

3455×	`add-sqr-sqrt`
3265×	`*-un-lft-identity`
2554×	`times-frac`
2159×	`add-cube-cbrt`
2149×	`associate-/l*`
2123×	`associate-/r*`
2106×	`frac-sub`
2028×	`frac-times`
1850×	`associate-*r/`
1593×	`associate-l`
1091×	`associate-/l/`
1080×	`associate-r`
812×	`clear-num`
644×	`frac-2neg`
459×	`unswap-sqr`
336×	`un-div-inv`
253×	`distribute-lft-out`
189×	`distribute-lft-out--`
162×	`difference-of-squares`
137×	`div-inv`
108×	`*-commutative`
106×	`add-exp-log`
85×	`associate-/r/`
74×	`add-cbrt-cube`
50×	`prod-exp`
46×	`flip3--` `flip--`
42×	`associate-*l/`
34×	`div-exp`
30×	`cbrt-unprod`
28×	`flip3-+` `flip-+`
22×	`cbrt-undiv`
11×	`pow1`
8×	`1-exp`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `add-log-exp`

Counts

4 → 3796

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
217.0ms	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (/ 2.0 PI) (- b a)))
70.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
11.0ms	(* (/ 2.0 PI) (- b a))

series305.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (+ b a))
101.0ms	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (/ 2.0 PI) (- b a)))
83.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
80.0ms	(* (/ 2.0 PI) (- b a))

simplify664.0ms

Algorithm

egg-herbie

Counts

3808 → 3808

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5001	58949

prune8.6s

Filtered

3808 candidates to 2473 candidates (64.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	3805	3	3808
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	3809	8	3817

Merged error: 0b

Counts

3817 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(* (/ 1 (* (/ 2.0 PI) 1)) (/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
0.4b	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite8.0s

Algorithm

rewrite-expression-head

Rules

58228×	`frac-times`
56017×	`associate-/r*`
38513×	`add-sqr-sqrt`
38101×	`*-un-lft-identity`
32900×	`associate-/l*`
30459×	`associate-/l/`
30294×	`frac-sub`
29569×	`add-cube-cbrt`
13517×	`associate-l`
12261×	`times-frac`
10593×	`clear-num`
10592×	`frac-2neg`
4074×	`unswap-sqr`
3790×	`associate-*r/`
3635×	`associate-r`
2992×	`distribute-lft-out`
1108×	`div-inv`
1017×	`*-commutative`
380×	`associate-*l/`
376×	`flip3--` `flip--`
327×	`distribute-lft-out--`
312×	`add-exp-log`
283×	`difference-of-squares`
148×	`prod-exp`
134×	`div-exp`
103×	`associate-/r/`
100×	`add-cbrt-cube`
45×	`flip3-+` `flip-+`
44×	`1-exp`
38×	`cbrt-undiv`
36×	`cbrt-unprod`
20×	`rec-exp`
8×	`pow1`
4×	`add-log-exp`
3×	`un-div-inv`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down`

Counts

4 → 33595

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
125.0ms	(/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
1.1s	(* (/ 1 (* (/ 2.0 PI) 1)) (/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
60.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (+ b a))
79.0ms	(/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
103.0ms	(* (/ 1 (* (/ 2.0 PI) 1)) (/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
84.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify10.3s

Algorithm

egg-herbie

Counts

33607 → 33607

Iterations

Useful iterations: 0 (714.0ms)

Iter	Nodes	Cost
0	30646	818042

prune1.4m

Filtered

33607 candidates to 19678 candidates (58.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	33604	3	33607
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	33608	7	33615

Merged error: 0b

Counts

33615 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- b a) (- (/ 1 a) (/ 1 b)))
0.4b	(* (/ 1 (/ 1 (sqrt PI))) (* (/ 1.0 (+ b a)) 1.0))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

684×	`add-sqr-sqrt`
599×	`times-frac`
594×	`*-un-lft-identity`
437×	`associate-/r*`
367×	`add-cube-cbrt`
318×	`associate-*l/`
280×	`frac-times`
182×	`associate-/l*`
147×	`sqrt-prod`
144×	`add-exp-log`
100×	`associate-l`
97×	`associate-/r/`
81×	`frac-sub`
74×	`difference-of-squares`
65×	`prod-exp`
62×	`distribute-lft-out--`
60×	`frac-2neg` `clear-num`
57×	`unswap-sqr`
56×	`div-exp`
42×	`add-cbrt-cube`
41×	`div-inv`
32×	`distribute-lft-out`
31×	`associate-r`
21×	`rec-exp` `1-exp`
15×	`cbrt-unprod`
13×	`cbrt-undiv`
11×	`pow1`
10×	`associate-*r/`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `associate-/l/`
1×	`flip3-+` `div-sub` `flip-+`

Counts

4 → 762

Calls

4 calls:

30.0ms	(/ (- b a) (- (/ 1 a) (/ 1 b)))
69.0ms	(* (/ 1 (/ 1 (sqrt PI))) (* (/ 1.0 (+ b a)) 1.0))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series154.0ms

Counts

4 → 8

Calls

4 calls:

35.0ms	(/ (- b a) (- (/ 1 a) (/ 1 b)))
118.0ms	(* (/ 1 (/ 1 (sqrt PI))) (* (/ 1.0 (+ b a)) 1.0))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify177.0ms

Algorithm

egg-herbie

Counts

770 → 770

Iterations

Useful iterations: 1 (88.0ms)

Iter	Nodes	Cost
0	3953	7848
1	5001	7171

prune1.3s

Filtered

770 candidates to 351 candidates (45.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	770	0	770
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	770	7	777

Merged error: 0b

Counts

777 → 7

regimes67.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	26	12
2	26	12

end0.0ms

sample616.0ms

Algorithm

intervals

Results

452.0ms

9648×

body

valid