Details

sample29.0ms

Algorithm

intervals

Results

19.0ms

307×

body

valid

simplify39.0ms

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

prune2.0ms

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: 16.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
5.6b	(- (* b b) (* a a))
9.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
23.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5001	1342

prune388.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	11	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 9.6b

Counts

166 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
9.7b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log` `add-cbrt-cube`
103×	`add-sqr-sqrt`
90×	`times-frac`
88×	`*-un-lft-identity`
78×	`associate-r`
51×	`prod-exp` `cbrt-unprod`
48×	`add-cube-cbrt`
47×	`frac-times`
33×	`associate-*l/`
30×	`cbrt-undiv` `div-exp`
29×	`sqrt-prod`
20×	`pow1`
19×	`associate-*r/`
16×	`distribute-lft-out--`
15×	`associate-l`
14×	`difference-of-squares`
10×	`flip3--` `pow-prod-down` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`sub-neg` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`flip3-+` `diff-log` `flip-+`

Counts

4 → 246

Calls

4 calls:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
19.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
17.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
33.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
209.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
150.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
289.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify56.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1344	3063
1	5001	2608

prune539.0ms

Filtered

258 candidates to 164 candidates (63.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	251	7	258
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	257	12	269

Merged error: 0.0b

Counts

269 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
0.3b	(/ (* PI 1.0) (- b a))
0.3b	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
45×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
31×	`times-frac`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
13×	`add-cube-cbrt` `distribute-lft-out--`
12×	`associate-l`
11×	`associate-r` `difference-of-squares`
7×	`flip3--` `flip--` `div-inv` `associate-/l/`
6×	`pow1` `frac-times` `associate-l/` `associate-/r` `associate-/r/` `add-log-exp`
5×	`frac-sub`
4×	`associate-*r/`
2×	`frac-2neg` `clear-num` `associate-/l*`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
27.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
6.0ms	(/ (* PI 1.0) (- b a))
31.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
220.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
51.0ms	(/ (* PI 1.0) (- b a))
73.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

simplify91.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	695	1331
1	4083	1048
2	5002	1048

prune290.0ms

Filtered

145 candidates to 98 candidates (67.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	148	9	157

Merged error: 0b

Counts

157 → 9

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.9b	(/ PI (* a b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
3×	`associate-*r/`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `div-inv` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

10.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
4.0ms	(/ PI (* a b))

series86.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
19.0ms	(/ PI (* a b))

simplify50.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	390	416
1	2377	290
2	5003	290

prune77.0ms

Filtered

59 candidates to 33 candidates (55.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	59	9	68

Merged error: 0b

Counts

68 → 9

regimes63.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	6
1	15	6

end0.0ms

sample673.0ms

Algorithm

intervals

Results

515.0ms

9617×

body

valid

Details

sample29.0ms

simplify39.0ms

prune2.0ms

localize12.0ms

rewrite51.0ms

series216.0ms

simplify106.0ms

prune388.0ms

localize18.0ms

rewrite96.0ms

series679.0ms

simplify56.0ms

prune539.0ms

localize21.0ms

rewrite82.0ms

series378.0ms

simplify91.0ms

prune290.0ms

localize8.0ms

rewrite17.0ms

series86.0ms

simplify50.0ms

prune77.0ms

regimes63.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample673.0ms

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