Details

sample22.0ms

Algorithm

intervals

Results

13.0ms

311×

body

valid

simplify37.0ms

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: 14.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.4b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

625×	`frac-times`
368×	`clear-num`
355×	`frac-2neg`
297×	`frac-sub`
219×	`*-commutative`
216×	`difference-of-squares`
212×	`associate-/r*`
102×	`associate-*r/`
71×	`associate-*l/`
37×	`flip3--` `flip--`
13×	`un-div-inv`
8×	`associate-l`
7×	`associate-r` `div-inv`
6×	`associate-/r/`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`distribute-lft-out--`

Counts

4 → 461

Calls

4 calls:

11.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
4.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
22.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms	(/ 1.0 (- (* b b) (* a a)))
33.0ms	(- (* b b) (* a a))
87.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

473 → 473

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2262	6313
1	5002	6009

prune700.0ms

Filtered

473 candidates to 227 candidates (48.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	466	7	473
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	467	7	474

Merged error: 0.0b

Counts

474 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

112×	`clear-num`
99×	`associate-*r/`
90×	`frac-sub`
88×	`frac-times`
87×	`frac-2neg`
59×	`associate-/l/`
46×	`associate-l`
27×	`times-frac`
25×	`un-div-inv`
23×	`associate-r`
21×	`*-commutative`
18×	`div-inv`
16×	`neg-mul-1` `associate-/r/`
11×	`flip3--` `flip--`
9×	`associate-/l*`
8×	`associate-*l/`
7×	`flip3-+` `flip-+`
5×	`distribute-lft-neg-out` `distribute-lft-out--`
3×	`associate-/r*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`distribute-frac-neg`

Counts

4 → 191

Calls

4 calls:

3.0ms	(/ 1.0 (+ b a))
32.0ms	(/ (* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (- 2.0) (- b a)))
12.0ms	(* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
4.0ms	(* (- PI) (/ 1.0 (+ b a)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (+ b a))
93.0ms	(/ (* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (- 2.0) (- b a)))
105.0ms	(* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
52.0ms	(* (- PI) (/ 1.0 (+ b a)))

simplify46.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1197	1931
1	5001	1775

prune579.0ms

Filtered

203 candidates to 174 candidates (85.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	6	203
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	200	10	210

Merged error: 0.0b

Counts

210 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

426×	`frac-times`
282×	`clear-num`
281×	`frac-2neg`
235×	`associate-/l/`
216×	`frac-sub`
123×	`associate-*r/`
89×	`associate-/l*`
70×	`neg-mul-1`
26×	`flip3--` `flip--`
25×	`div-inv`
24×	`associate-l`
22×	`associate-*l/`
20×	`associate-/r/`
14×	`associate-r`
8×	`flip3-+` `*-commutative` `flip-+`
7×	`distribute-lft-out--`
6×	`times-frac`
5×	`associate-/r*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `distribute-frac-neg`
1×	`distribute-lft-neg-out` `neg-sub0` `div-sub` `un-div-inv`

Counts

4 → 371

Calls

4 calls:

3.0ms	(/ 1.0 (+ b a))
27.0ms	(* (/ (- PI) (- b a)) (/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- 2.0)))
3.0ms	(/ (- PI) (- b a))
10.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (+ b a))
96.0ms	(* (/ (- PI) (- b a)) (/ (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- 2.0)))
43.0ms	(/ (- PI) (- b a))
78.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify104.0ms

Algorithm

egg-herbie

Counts

383 → 383

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2878	5020
1	5002	4800

prune1.3s

Filtered

383 candidates to 330 candidates (86.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	377	6	383
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	384	9	393

Merged error: 0b

Counts

393 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ b a))
0.2b	(* (/ (- PI) (- b a)) (/ (* (* 1.0 (/ 1 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- 2.0)))
0.2b	(/ (- PI) (- b a))
0.3b	(* (* 1.0 (/ 1 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

662×	`frac-times`
452×	`clear-num`
379×	`frac-2neg`
365×	`associate-*r/`
355×	`associate-/l/`
324×	`frac-sub`
145×	`un-div-inv`
125×	`associate-/l*`
98×	`neg-mul-1`
38×	`flip3--` `associate-l` `flip--`
37×	`associate-r`
34×	`associate-*l/`
25×	`div-inv`
20×	`associate-/r/`
15×	`*-commutative`
8×	`flip3-+` `times-frac` `flip-+`
7×	`distribute-lft-out--`
5×	`associate-/r*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `distribute-frac-neg`
1×	`distribute-lft-neg-out` `neg-sub0` `div-sub` `inv-pow`

Counts

4 → 530

Calls

4 calls:

4.0ms	(/ 1 (+ b a))
40.0ms	(* (/ (- PI) (- b a)) (/ (* (* 1.0 (/ 1 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- 2.0)))
3.0ms	(/ (- PI) (- b a))
12.0ms	(* (* 1.0 (/ 1 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (+ b a))
95.0ms	(* (/ (- PI) (- b a)) (/ (* (* 1.0 (/ 1 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- 2.0)))
44.0ms	(/ (- PI) (- b a))
77.0ms	(* (* 1.0 (/ 1 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify135.0ms

Algorithm

egg-herbie

Counts

542 → 542

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	3012	7248
1	5001	6947

prune928.0ms

Filtered

542 candidates to 289 candidates (53.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	536	6	542
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	543	8	551

Merged error: 0b

Counts

551 → 8

regimes65.0ms

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	30	12
2	33	12
3	33	12

end0.0ms

sample567.0ms

Algorithm

intervals

Results

415.0ms

9580×

body

valid