Details

sample24.0ms

Algorithm

intervals

Results

13.0ms

299×

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: 14.1b

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)))
4.3b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite103.0ms

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

series226.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
94.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify156.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune841.0ms

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: 8.9b

Counts

514 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
9.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
46.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
14.0ms	(/ (/ PI 2.0) (+ b a))
57.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (- b a))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
53.0ms	(/ (/ PI 2.0) (+ b a))
97.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify185.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	2933	16072
1	5002	14991

prune1.1s

Filtered

646 candidates to 303 candidates (46.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	641	5	646
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	646	9	655

Merged error: 0.0b

Counts

655 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

1630×	`times-frac`
1285×	`*-un-lft-identity`
1240×	`add-sqr-sqrt`
1209×	`add-cube-cbrt`
1014×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
171×	`div-inv`
79×	`associate-l`
52×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 1314

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
82.0ms	(* (/ (/ 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)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (- b a))
92.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
51.0ms	(/ (/ PI 2.0) (+ b a))
58.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify354.0ms

Algorithm

egg-herbie

Counts

1326 → 1326

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	40379

prune4.2s

Filtered

1326 candidates to 1025 candidates (77.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1322	4	1326
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	1326	9	1335

Merged error: 0b

Counts

1335 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

2485×	`times-frac`
1791×	`*-un-lft-identity`
1590×	`add-sqr-sqrt`
1567×	`add-cube-cbrt`
1014×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
202×	`div-inv`
197×	`associate-l`
161×	`add-exp-log`
105×	`distribute-lft-out`
77×	`add-cbrt-cube`
74×	`div-exp`
70×	`associate-/r*`
52×	`prod-exp`
32×	`cbrt-undiv`
22×	`cbrt-unprod`
16×	`frac-times` `associate-*r/`
13×	`associate-r`
12×	`pow1` `rec-exp` `1-exp` `associate-/r/`
8×	`distribute-lft-out--`
7×	`flip3--` `flip--` `associate-/l*` `difference-of-squares`
6×	`sub-neg` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 1675

Calls

4 calls:

83.0ms	(* (/ 1 (/ (+ b a) (/ PI 2.0))) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
8.0ms	(/ (+ b a) (/ PI 2.0))
41.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
16.0ms	(/ 1 (/ (+ b a) (/ PI 2.0)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (/ 1 (/ (+ b a) (/ PI 2.0))) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
72.0ms	(/ (+ b a) (/ PI 2.0))
53.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
60.0ms	(/ 1 (/ (+ b a) (/ PI 2.0)))

simplify426.0ms

Algorithm

egg-herbie

Counts

1687 → 1687

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5002	46399

prune5.3s

Filtered

1687 candidates to 1261 candidates (74.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1687	0	1687
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	1687	9	1696

Merged error: 0b

Counts

1696 → 9

regimes63.0ms

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

sample583.0ms

Algorithm

intervals

Results

431.0ms

9562×

body

valid