Details

sample28.0ms

Algorithm

intervals

Results

17.0ms

307×

body

valid

simplify40.0ms

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: 13.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
4.6b	(- (* b b) (* a a))
8.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite80.0ms

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:

8.0ms	(* (/ 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)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify103.0ms

Algorithm

egg-herbie

Counts

473 → 473

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2262	6313
1	5002	6009

prune715.0ms

Filtered

473 candidates to 227 candidates (48.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	465	8	473
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	466	8	474

Merged error: 0.0b

Counts

474 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* PI (/ 1.0 (+ b a)))
0.3b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

117×	`clear-num`
99×	`associate-*r/` `frac-sub`
92×	`frac-2neg`
88×	`frac-times`
59×	`associate-/l/`
25×	`un-div-inv`
20×	`associate-l`
19×	`associate-r`
18×	`*-commutative`
16×	`times-frac` `div-inv`
12×	`flip3--` `associate-/r/` `flip--`
8×	`associate-l/` `associate-/l`
5×	`flip3-+` `flip-+` `distribute-lft-out--`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`

Counts

4 → 182

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
17.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
7.0ms	(* PI (/ 1.0 (+ b a)))
11.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
54.0ms	(* PI (/ 1.0 (+ b a)))
101.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify123.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1052	1651
1	4989	1514
2	5001	1514

prune500.0ms

Filtered

194 candidates to 161 candidates (83.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	195	7	202

Merged error: 0.0b

Counts

202 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.2b	(/ (* PI 1.0) (+ b a))
0.3b	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

117×	`frac-sub`
110×	`frac-times`
104×	`frac-2neg` `clear-num`
71×	`associate-/l/`
56×	`associate-/l*`
36×	`*-commutative`
24×	`associate-*r/`
16×	`div-inv`
14×	`flip3--` `flip--`
12×	`times-frac` `associate-l` `associate-/r/`
10×	`associate-*l/`
5×	`flip3-+` `flip-+` `distribute-lft-out--`
4×	`associate-r`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`

Counts

4 → 197

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
18.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
4.0ms	(/ (* PI 1.0) (+ b a))
11.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
98.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
54.0ms	(/ (* PI 1.0) (+ b a))
103.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify45.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1218	1849
1	5001	1711

prune566.0ms

Filtered

209 candidates to 180 candidates (86.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	209	7	216

Merged error: 0.0b

Counts

216 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* PI 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))) (* 2.0 (- b a)))
0.2b	(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
0.3b	(* (* PI 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

49×	`associate-/l/`
36×	`frac-sub`
32×	`associate-*r/`
30×	`clear-num`
28×	`frac-2neg`
16×	`*-commutative`
14×	`times-frac` `div-inv`
12×	`associate-r` `associate-/r/`
10×	`associate-/l*`
8×	`associate-l`
5×	`flip3--` `flip3-+` `flip--` `flip-+`
4×	`distribute-lft-out--`
2×	`associate-/r*` `un-div-inv`
1×	`sub-neg` `div-sub`

Counts

4 → 98

Calls

4 calls:

5.0ms	(- (/ 1.0 a) (/ 1.0 b))
19.0ms	(/ (* (* PI 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))) (* 2.0 (- b a)))
8.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
10.0ms	(* (* PI 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (* PI 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))) (* 2.0 (- b a)))
207.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
105.0ms	(* (* PI 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	579	722
1	2809	680
2	5001	680

prune279.0ms

Filtered

110 candidates to 96 candidates (87.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	110	7	117

Merged error: 0.0b

Counts

117 → 7

regimes51.0ms

Accuracy

0% (0.2b 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	19	10
1	19	10

end0.0ms

sample586.0ms

Algorithm

intervals

Results

427.0ms

9632×

body

valid