Details

sample27.0ms

Algorithm

intervals

Results

15.0ms

298×

body

valid

simplify37.0ms

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
done	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.1b	(- (* b b) (* a a))
11.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
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×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

44.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
113.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5002	1342
done	5002	1342

prune382.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
11.1b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-exp-log` `add-cbrt-cube`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

11.0ms	(/ 1.0 (+ b a))
28.0ms	(/ (/ 1.0 (+ b a)) (- b a))
84.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
147.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (+ b a))
52.0ms	(/ (/ 1.0 (+ b a)) (- b a))
64.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
97.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify61.0ms

Counts

370 → 370

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1467	3480
1	5002	3169
done	5002	3169

prune778.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
59×	`*-un-lft-identity`
52×	`times-frac`
33×	`add-cube-cbrt`
30×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
11×	`pow1`
9×	`flip3--` `associate-/r*` `flip--`
8×	`frac-sub`
7×	`distribute-lft-out` `distribute-lft-out--`
6×	`associate-/r/` `div-inv` `difference-of-squares`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

11.0ms	(/ 1.0 (+ b a))
85.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
106.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
35.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (+ b a))
94.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
102.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify39.0ms

Counts

202 → 202

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	963	1767
1	5001	1458
done	5001	1458

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
62×	`times-frac`
59×	`add-exp-log` `add-cbrt-cube`
55×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
20×	`associate-*r/`
19×	`cbrt-undiv` `div-exp`
18×	`distribute-lft-out--`
16×	`associate-/r/` `difference-of-squares`
12×	`associate-r` `div-inv`
9×	`pow1`
8×	`associate-/l*`
7×	`flip3-+` `flip-+`
6×	`associate-/r*` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`sub-neg` `pow-prod-down` `frac-sub`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 160

Calls

4 calls:

24.0ms	(- (/ 1.0 a) (/ 1.0 b))
59.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a))) (- b a))
50.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
71.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a))) (- b a))
101.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
63.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify38.0ms

Counts

172 → 172

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	854	2012
1	5002	1679
done	5002	1679

prune337.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10
done	18	10

end0.0ms

sample622.0ms

Algorithm

intervals

Results

411.0ms

9590×

body

valid