Details

sample24.0ms

Algorithm

intervals

Results

14.0ms

305×

body

valid

simplify41.0ms

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 (100.0%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.0b	(/ 1.0 (- (* b b) (* a a)))
3.6b	(- (* b b) (* a a))
9.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite7.6s

Algorithm

rewrite-expression-head

Rules

66210×	`add-sqr-sqrt`
63118×	`frac-times`
59991×	`associate-/r*`
34546×	`associate-/l*`
33531×	`*-un-lft-identity`
32562×	`frac-sub`
23106×	`add-cube-cbrt`
21529×	`difference-of-squares`
11572×	`clear-num`
11487×	`frac-2neg`
10332×	`swap-sqr`
8627×	`unswap-sqr`
8613×	`*-commutative`
4310×	`distribute-lft-out--`
3597×	`associate-l`
3398×	`associate-*r/`
1166×	`associate-*l/`
406×	`flip3--` `flip--`
337×	`times-frac`
222×	`associate-r`
170×	`un-div-inv`
36×	`add-exp-log` `add-cbrt-cube`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`diff-log`

Counts

4 → 34666

Calls

4 calls:

71.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
21.0ms	(/ 1.0 (- (* b b) (* a a)))
16.0ms	(- (* b b) (* a a))
1.0s	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series232.0ms

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)))
34.0ms	(- (* b b) (* a a))
97.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify8.4s

Algorithm

egg-herbie

Counts

34678 → 34678

Iterations

Useful iterations: 0 (385.0ms)

Iter	Nodes	Cost
0	19332	835891

prune46.4s

Filtered

34678 candidates to 11346 candidates (67.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	34670	8	34678
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34670	9	34679

Merged error: 0b

Counts

34679 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

33636×	`frac-times`
24492×	`associate-/r*`
23028×	`associate-/l*`
19208×	`*-un-lft-identity`
18225×	`frac-sub`
15865×	`add-sqr-sqrt`
15421×	`add-cube-cbrt`
9407×	`associate-/l/`
7769×	`clear-num`
7600×	`frac-2neg`
1856×	`associate-*r/`
1743×	`associate-*l/`
1714×	`distribute-lft-out`
618×	`times-frac`
384×	`associate-l`
338×	`un-div-inv`
228×	`associate-r`
226×	`flip3--` `flip--`
103×	`distribute-lft-out--`
95×	`difference-of-squares` `unswap-sqr`
59×	`add-exp-log` `add-cbrt-cube`
33×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp` `associate-/r/`
15×	`*-commutative`
11×	`pow1`
8×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`diff-log`

Counts

4 → 19561

Calls

4 calls:

19.0ms	(- (/ 1.0 a) (/ 1.0 b))
873.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
267.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
22.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
106.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
110.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
65.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify3.9s

Algorithm

egg-herbie

Counts

19573 → 19573

Iterations

Useful iterations: 0 (221.0ms)

Iter	Nodes	Cost
0	13184	285543

prune45.4s

Filtered

19573 candidates to 11565 candidates (40.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	19566	7	19573
Fresh	7	0	7
Picked	1	0	1
Done	0	1	1
Total	19574	8	19582

Merged error: 0b

Counts

19582 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (/ (* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b))) (/ (+ b a) 1.0)) (- b a))
0.2b	(/ (* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b))) (/ (+ b a) 1.0))
0.4b	(* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

11246×	`times-frac`
8603×	`*-un-lft-identity`
8272×	`add-sqr-sqrt`
5247×	`add-cube-cbrt`
3050×	`associate-/l*`
2582×	`associate-/l/`
2511×	`frac-sub`
2488×	`associate-/r*`
2241×	`frac-times`
1495×	`associate-l`
1380×	`associate-r`
1109×	`distribute-lft-out--`
993×	`difference-of-squares`
820×	`frac-2neg` `clear-num`
685×	`distribute-lft-out`
581×	`div-inv`
249×	`associate-*r/`
230×	`unswap-sqr`
115×	`*-commutative`
86×	`associate-/r/`
59×	`add-exp-log` `add-cbrt-cube`
32×	`flip3--` `flip--`
30×	`cbrt-undiv` `div-exp`
27×	`associate-*l/`
10×	`prod-exp` `cbrt-unprod`
7×	`flip3-+` `flip-+`
6×	`pow1` `add-log-exp`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`diff-log` `pow-prod-down`

Counts

4 → 6507

Calls

4 calls:

19.0ms	(- (/ 1.0 a) (/ 1.0 b))
321.0ms	(/ (/ (* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b))) (/ (+ b a) 1.0)) (- b a))
135.0ms	(/ (* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b))) (/ (+ b a) 1.0))
56.0ms	(* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
104.0ms	(/ (/ (* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b))) (/ (+ b a) 1.0)) (- b a))
109.0ms	(/ (* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b))) (/ (+ b a) 1.0))
78.0ms	(* (/ PI 2.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Algorithm

egg-herbie

Counts

6519 → 6519

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	6370	108462

prune16.0s

Filtered

6519 candidates to 4213 candidates (35.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	6515	4	6519
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	6521	6	6527

Merged error: 0b

Counts

6527 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.6s

Algorithm

rewrite-expression-head

Rules

39518×	`times-frac`
35499×	`add-sqr-sqrt`
31611×	`*-un-lft-identity`
20431×	`add-cube-cbrt`
19916×	`associate-/l/`
16768×	`associate-/l*`
16443×	`associate-/r*`
15162×	`frac-times`
9558×	`frac-sub`
9140×	`associate-l`
7414×	`sqrt-prod`
5123×	`associate-r`
4221×	`difference-of-squares`
3545×	`distribute-lft-out--`
2795×	`clear-num`
2793×	`frac-2neg`
2526×	`associate-*l/`
2512×	`div-inv`
1622×	`distribute-lft-out`
1572×	`unswap-sqr`
446×	`add-exp-log`
429×	`*-commutative`
266×	`associate-*r/`
253×	`div-exp`
248×	`add-cbrt-cube`
206×	`associate-/r/`
133×	`cbrt-undiv`
126×	`prod-exp`
119×	`flip3--` `flip--`
66×	`cbrt-unprod`
18×	`rec-exp` `1-exp`
12×	`un-div-inv`
8×	`flip3-+` `flip-+`
6×	`pow1` `add-log-exp`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down`

Counts

4 → 24492

Calls

4 calls:

36.0ms	(- (/ 1 a) (/ 1 b))
4.0s	(/ (* (/ (* (/ PI 2.0) 1.0) (/ 1 (sqrt 1.0))) (/ (- (/ 1 a) (/ 1 b)) (/ (+ b a) (sqrt 1.0)))) (- b a))
55.0ms	(/ (- (/ 1 a) (/ 1 b)) (/ (+ b a) (sqrt 1.0)))
3.2s	(* (/ (* (/ PI 2.0) 1.0) (/ 1 (sqrt 1.0))) (/ (- (/ 1 a) (/ 1 b)) (/ (+ b a) (sqrt 1.0))))

series818.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (/ 1 a) (/ 1 b))
292.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (/ 1 (sqrt 1.0))) (/ (- (/ 1 a) (/ 1 b)) (/ (+ b a) (sqrt 1.0)))) (- b a))
141.0ms	(/ (- (/ 1 a) (/ 1 b)) (/ (+ b a) (sqrt 1.0)))
372.0ms	(* (/ (* (/ PI 2.0) 1.0) (/ 1 (sqrt 1.0))) (/ (- (/ 1 a) (/ 1 b)) (/ (+ b a) (sqrt 1.0))))

simplify5.7s

Algorithm

egg-herbie

Counts

24504 → 24504

Iterations

Useful iterations: 0 (367.0ms)

Iter	Nodes	Cost
0	20430	518816

prune1.1m

Filtered

24504 candidates to 14195 candidates (42.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	24504	0	24504
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	24504	6	24510

Merged error: 0b

Counts

24510 → 6

regimes78.0ms

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	25	15
1	25	15

end0.0ms

sample593.0ms

Algorithm

intervals

Results

435.0ms

9561×

body

valid