Details

sample26.0ms

Algorithm

intervals

Results

16.0ms

297×

body

valid

simplify40.0ms

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: 14.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.8b	(- (* b b) (* a a))
8.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite98.0ms

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:

16.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
35.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
42.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify162.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune796.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	504	9	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	505	9	514

Merged error: 7.6b

Counts

514 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

940×	`times-frac`
738×	`*-un-lft-identity`
713×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 801

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
42.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
55.0ms	(/ (/ PI 2.0) (+ b a))
99.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify220.0ms

Algorithm

egg-herbie

Counts

813 → 813

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2928	20392
1	5001	18352

prune1.5s

Filtered

813 candidates to 378 candidates (46.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	809	4	813
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	813	9	822

Merged error: 0.0b

Counts

822 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.2b	(/ (/ PI 2.0) (+ b a))
0.6b	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

1868×	`times-frac`
1466×	`*-un-lft-identity`
1425×	`add-sqr-sqrt`
1390×	`add-cube-cbrt`
1183×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
199×	`div-inv`
79×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
13×	`fma-neg` `associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-l/` `associate-/r` `log1p-expm1-u`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 1481

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
64.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
8.0ms	(/ (/ PI 2.0) (+ b a))
38.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
55.0ms	(/ (/ PI 2.0) (+ b a))
53.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify398.0ms

Algorithm

egg-herbie

Counts

1493 → 1493

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5002	44700

prune4.7s

Filtered

1493 candidates to 1159 candidates (77.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1488	5	1493
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	1494	8	1502

Merged error: 0b

Counts

1502 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
0.2b	(/ (/ PI 2.0) (+ b a))
0.5b	(/ 1.0 (* a b))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
152×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
58×	`associate-l`
49×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
20×	`cbrt-undiv` `div-exp`
16×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod` `div-inv`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

3 → 211

Calls

3 calls:

21.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
8.0ms	(/ (/ PI 2.0) (+ b a))
4.0ms	(/ 1.0 (* a b))

series149.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
55.0ms	(/ (/ PI 2.0) (+ b a))
22.0ms	(/ 1.0 (* a b))

simplify88.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	855	1627
1	4116	1460
2	5001	1460

prune368.0ms

Filtered

220 candidates to 149 candidates (67.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	220	8	228

Merged error: 0b

Counts

228 → 8

regimes55.0ms

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	14	6
1	14	6

end0.0ms

sample582.0ms

Algorithm

intervals

Results

423.0ms

9633×

body

valid