Details

sample25.0ms

Algorithm

intervals

Results

16.0ms

311×

body

valid

simplify38.0ms

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: 14.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.3b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
8.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite50.0ms

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)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
39.0ms	(/ 1.0 (- (* b b) (* a a)))
33.0ms	(- (* b b) (* a a))
85.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify108.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune347.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	158	7	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 8.5b

Counts

166 → 7

localize14.0ms

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)))
8.6b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite103.0ms

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:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
20.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
17.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
37.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
198.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
143.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
315.0ms	(* (* (* (/ 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 (29.0ms)

Iter	Nodes	Cost
0	1344	3063
1	5001	2608

prune609.0ms

Filtered

258 candidates to 164 candidates (63.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	254	4	258
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	258	7	265

Merged error: 0.0b

Counts

265 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (- (/ 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)))

rewrite75.0ms

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:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
24.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
10.0ms	(/ (* PI 1.0) (- b a))
23.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
56.0ms	(/ (* PI 1.0) (- b a))
71.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

simplify95.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (19.0ms)

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

prune415.0ms

Filtered

145 candidates to 98 candidates (67.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	144	8	152

Merged error: 0.0b

Counts

152 → 8

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.7b	(/ 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))

series85.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
20.0ms	(/ PI (* a b))

simplify51.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (11.0ms)

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

prune71.0ms

Filtered

59 candidates to 33 candidates (55.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Merged error: 0.0b

Counts

67 → 7

regimes51.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	7
1	20	7

end0.0ms

sample670.0ms

Algorithm

intervals

Results

512.0ms

9641×

body

valid

Details

sample25.0ms

simplify38.0ms

prune2.0ms

localize15.0ms

rewrite50.0ms

series213.0ms

simplify108.0ms

prune347.0ms

localize14.0ms

rewrite103.0ms

series691.0ms

simplify56.0ms

prune609.0ms

localize11.0ms

rewrite75.0ms

series250.0ms

simplify95.0ms

prune415.0ms

localize8.0ms

rewrite17.0ms

series85.0ms

simplify51.0ms

prune71.0ms

regimes51.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample670.0ms

Profiling