Details

sample37.0ms

Algorithm

intervals

Results

20.0ms

320×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	89	21
3	378	21
4	1789	21
done	5000	21

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (- (* b b) (* a a)))
0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
3.4b	(- (* b b) (* a a))
9.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite262.0ms

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:

15.0ms	(/ 1.0 (- (* b b) (* a a)))
70.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
9.0ms	(- (* b b) (* a a))
162.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1.0 (- (* b b) (* a a)))
63.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
48.0ms	(- (* b b) (* a a))
121.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify563.0ms

Counts

165 → 165

Iterations

Useful iterations: done (554.0ms)

Iter	Nodes	Cost
0	258	3239
1	873	3170
done	5000	2752

prune909.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.0b

localize45.0ms

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)))
9.1b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite541.0ms

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:

13.0ms	(/ 1.0 (+ b a))
57.0ms	(/ (/ 1.0 (+ b a)) (- b a))
136.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
298.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1.0 (+ b a))
88.0ms	(/ (/ 1.0 (+ b a)) (- b a))
105.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
154.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify836.0ms

Counts

370 → 370

Iterations

Useful iterations: done (815.0ms)

Iter	Nodes	Cost
0	450	7073
1	1574	6680
done	5001	6136

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* PI (/ 1.0 (+ b a)))
0.3b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
47×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
36×	`times-frac`
30×	`associate-r`
25×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`associate-/l/` `distribute-lft-out`
6×	`frac-times` `associate-/r/`
5×	`flip3--` `associate-/r*` `flip--` `div-inv` `distribute-lft-out--`
4×	`associate-l` `pow-prod-down` `frac-sub` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `clear-num` `-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

13.0ms	(/ 1.0 (+ b a))
115.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
53.0ms	(* PI (/ 1.0 (+ b a)))
163.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1.0 (+ b a))
126.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
75.0ms	(* PI (/ 1.0 (+ b a)))
146.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify560.0ms

Counts

160 → 160

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	234	2770
1	778	2678
done	5000	2160

prune817.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
89×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
52×	`add-exp-log` `add-cbrt-cube`
36×	`add-cube-cbrt`
35×	`associate-/r*`
22×	`cbrt-undiv` `div-exp`
20×	`distribute-lft-out--`
18×	`associate-r`
16×	`difference-of-squares`
14×	`associate-/r/` `div-inv`
12×	`prod-exp` `cbrt-unprod`
7×	`distribute-lft-out`
6×	`pow1`
5×	`associate-/l*`
4×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `frac-sub` `associate-/l/`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 183

Calls

4 calls:

12.0ms	(/ 1.0 (+ b a))
81.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
74.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
38.0ms	(* PI (/ 1.0 (+ b a)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (+ b a))
154.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
97.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
76.0ms	(* PI (/ 1.0 (+ b a)))

simplify572.0ms

Counts

195 → 195

Iterations

Useful iterations: done (556.0ms)

Iter	Nodes	Cost
0	301	3602
1	938	3476
done	5001	2978

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes141.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	23	25
done	23	25

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.4s

9650×

body

valid