Details

sample57.0ms

Algorithm

intervals

Results

35.0ms

308×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	405
1	30	405
2	88	405
3	363	405
4	1543	405
done	5001	405

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.1b	(/ 1.0 (- (* b b) (* a a)))
6.5b	(- (* b b) (* a a))
10.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite192.0ms

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:

43.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
11.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
123.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
55.0ms	(/ 1.0 (- (* b b) (* a a)))
55.0ms	(- (* b b) (* a a))
146.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.8s

Counts

165 → 165

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	258	61224
1	853	55952
2	3712	55028
done	5005	54468

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.5b

localize47.0ms

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)))
10.6b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite356.0ms

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:

10.0ms	(/ 1.0 (+ b a))
30.0ms	(/ (/ 1.0 (+ b a)) (- b a))
92.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
195.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1.0 (+ b a))
93.0ms	(/ (/ 1.0 (+ b a)) (- b a))
105.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
136.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

370 → 370

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	450	147066
1	1521	132100
done	5000	129689

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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)))

rewrite274.0ms

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:

8.0ms	(/ 1.0 (+ b a))
92.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
30.0ms	(* PI (/ 1.0 (+ b a)))
138.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1.0 (+ b a))
179.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
71.0ms	(* PI (/ 1.0 (+ b a)))
163.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.3s

Counts

160 → 160

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	234	50076
1	756	45253
2	3960	43851
done	5003	43531

prune817.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

275×	`add-sqr-sqrt`
259×	`times-frac`
235×	`*-un-lft-identity`
84×	`associate-r`
83×	`add-cube-cbrt`
80×	`distribute-lft-out--`
69×	`difference-of-squares`
45×	`add-cbrt-cube` `add-exp-log`
27×	`div-inv`
15×	`cbrt-undiv` `div-exp` `associate-/l*`
14×	`prod-exp` `cbrt-unprod`
10×	`associate-l`
9×	`associate-/r*`
8×	`pow1` `associate-/r/`
7×	`distribute-lft-out`
4×	`add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `associate-r/` `-commutative` `flip-+`
1×	`frac-times` `div-sub` `associate-*l/` `frac-sub`

Counts

4 → 268

Calls

4 calls:

9.0ms	(/ 1.0 (+ b a))
151.0ms	(* (/ (* PI (/ 1.0 (+ b a))) 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
72.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
26.0ms	(* PI (/ 1.0 (+ b a)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (+ b a))
127.0ms	(* (/ (* PI (/ 1.0 (+ b a))) 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
62.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
77.0ms	(* PI (/ 1.0 (+ b a)))

simplify4.4s

Counts

280 → 280

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	368	107504
1	1121	100000
2	4195	98508
done	5001	97068

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes176.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	12	285
1	16	285
done	16	285

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.4s

9584×

body

valid