Details

sample27.0ms

Algorithm

intervals

Results

16.0ms

307×

body

valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	90	10
2	384	10
3	1828	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

localize15.0ms

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)))
5.5b	(- (* b b) (* a a))
8.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
36.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
34.0ms	(- (* b b) (* a a))
109.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify159.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune767.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	506	7	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	507	7	514

Merged error: 7.8b

Counts

514 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.0b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

1061×	`times-frac`
851×	`*-un-lft-identity`
814×	`add-sqr-sqrt`
695×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`associate-r`
97×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`associate-/l*`
14×	`frac-times` `associate-l`
13×	`fma-neg`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
2×	`*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 875

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
14.0ms	(/ (/ 1.0 (+ b a)) (- b a))
39.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
46.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
53.0ms	(/ (/ 1.0 (+ b a)) (- b a))
66.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
102.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify238.0ms

Algorithm

egg-herbie

Counts

887 → 887

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	3156	21276
1	5003	19725

prune1.5s

Filtered

887 candidates to 414 candidates (46.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	884	3	887
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	886	8	894

Merged error: 0.0b

Counts

894 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

745×	`times-frac`
600×	`add-sqr-sqrt`
593×	`*-un-lft-identity`
571×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
85×	`div-inv`
50×	`add-exp-log` `add-cbrt-cube`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`fma-neg`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `distribute-lft-out`
2×	`associate-l/` `-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 665

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
50.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
39.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(* PI (/ 1.0 (+ b a)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
105.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
119.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(* PI (/ 1.0 (+ b a)))

simplify190.0ms

Algorithm

egg-herbie

Counts

677 → 677

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2418	17086
1	5001	15039

prune1.3s

Filtered

677 candidates to 284 candidates (41.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	672	5	677
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	674	11	685

Merged error: 0b

Counts

685 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

740×	`times-frac`
592×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
566×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
86×	`div-inv`
50×	`add-exp-log` `add-cbrt-cube`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
13×	`fma-neg`
12×	`associate-r`
10×	`associate-l` `distribute-lft-out--`
8×	`associate-*r/` `difference-of-squares`
7×	`associate-/l/`
6×	`pow1` `frac-times` `flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`associate-/r*` `frac-sub`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-lft-out`
2×	`frac-2neg` `flip3-+` `associate-l/` `clear-num` `flip-+` `associate-/l`
1×	`diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 662

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
49.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
38.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
7.0ms	(/ (* PI 1.0) (+ b a))

series301.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
112.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(/ (* PI 1.0) (+ b a))

simplify185.0ms

Algorithm

egg-herbie

Counts

674 → 674

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2400	17101
1	5002	14141

prune1.0s

Filtered

674 candidates to 283 candidates (42.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	673	1	674
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	675	10	685

Merged error: 0b

Counts

685 → 10

regimes76.0ms

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	18	10
1	18	10

end0.0ms

sample686.0ms

Algorithm

intervals

Results

527.0ms

9660×

body

valid