Details

sample30.0ms

Algorithm

intervals

Results

18.0ms

307×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1543
3	363
2	88
1	30
0	15

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize32.0ms

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)))
4.5b	(- (* b b) (* a a))
6.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log`

Counts

4 → 153

Calls

4 calls:

37.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
10.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
158.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
75.0ms	(/ 1.0 (- (* b b) (* a a)))
41.0ms	(- (* b b) (* a a))
98.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.6s

Counts

165 → 165

Iterations

Iter	Nodes
done	5005
2	3712
1	853
0	258

prune922.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
6.2b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite353.0ms

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-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

9.0ms	(/ 1.0 (+ b a))
91.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
36.0ms	(/ (/ 1.0 (+ b a)) (- b a))
182.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1.0 (+ b a))
97.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
82.0ms	(/ (/ 1.0 (+ b a)) (- b a))
140.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.7s

Counts

370 → 370

Iterations

Iter	Nodes
done	5000
1	1534
0	450

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

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

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-cbrt-cube` `add-exp-log`
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×	`distribute-lft-out` `associate-/l/`
6×	`frac-times` `associate-/r/`
5×	`associate-/r*` `flip3--` `div-inv` `flip--` `distribute-lft-out--`
4×	`associate-l` `pow-prod-down` `frac-sub` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

18.0ms	(/ 1.0 (+ b a))
63.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
151.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
22.0ms	(* PI (/ 1.0 (+ b a)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (+ b a))
137.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
154.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
73.0ms	(* PI (/ 1.0 (+ b a)))

simplify2.6s

Counts

160 → 160

Iterations

Iter	Nodes
done	5404
2	3964
1	769
0	234

prune855.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize44.0ms

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)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
89×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
52×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg` `associate-l` `frac-sub` `associate-/l/`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 183

Calls

4 calls:

9.0ms	(/ 1.0 (+ b a))
74.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
56.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
41.0ms	(* PI (/ 1.0 (+ b a)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1.0 (+ b a))
145.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
95.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
73.0ms	(* PI (/ 1.0 (+ b a)))

simplify2.2s

Counts

195 → 195

Iterations

Iter	Nodes
done	5029
2	3845
1	905
0	301

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes237.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

9527×

body

valid