Details

sample47.0ms

Algorithm

intervals

Results

27.0ms

308×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.2b	(/ 1.0 (- (* b b) (* a a)))
2.8b	(- (* b b) (* a a))
10.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite302.0ms

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:

61.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
28.0ms	(/ 1.0 (- (* b b) (* a a)))
18.0ms	(- (* b b) (* a a))
182.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
74.0ms	(/ 1.0 (- (* b b) (* a a)))
41.0ms	(- (* b b) (* a a))
140.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify601.0ms

Counts

165 → 165

Iterations

Useful iterations: done (591.0ms)

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

prune627.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.6b

localize15.0ms

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.8b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
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`
16×	`div-inv`
14×	`frac-times`
13×	`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×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

50.0ms	(- (/ 1.0 a) (/ 1.0 b))
132.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
21.0ms	(/ (/ PI 2.0) (+ b a))
190.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (/ 1.0 a) (/ 1.0 b))
116.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
88.0ms	(/ (/ PI 2.0) (+ b a))
127.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify671.0ms

Counts

285 → 285

Iterations

Useful iterations: done (650.0ms)

Iter	Nodes	Cost
0	405	5259
1	1335	5084
done	5001	4552

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
185×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
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` `div-inv`
13×	`associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

53.0ms	(- (/ 1.0 a) (/ 1.0 b))
233.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
24.0ms	(/ (/ PI 2.0) (+ b a))
137.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
561.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
81.0ms	(/ (/ PI 2.0) (+ b a))
62.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify649.0ms

Counts

289 → 289

Iterations

Useful iterations: done (629.0ms)

Iter	Nodes	Cost
0	409	5721
1	1299	5569
done	5000	5045

prune825.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite113.0ms

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×	`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 → 205

Calls

3 calls:

70.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
18.0ms	(/ (/ PI 2.0) (+ b a))
13.0ms	(/ 1.0 (* a b))

series213.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
81.0ms	(/ (/ PI 2.0) (+ b a))
30.0ms	(/ 1.0 (* a b))

simplify2.1s

Counts

214 → 214

Iterations

Useful iterations: 2 (737.0ms)

Iter	Nodes	Cost
0	286	3228
1	884	3095
2	4709	2765
done	5001	2765

prune511.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes83.0ms

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	11	13
1	14	13
done	14	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

9597×

body

valid