Details

sample26.0ms

Algorithm

intervals

Results

16.0ms

304×

body

valid

simplify471.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	86	21
3	352	21
4	1426	21
done	5001	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.8b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite110.0ms

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:

22.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
71.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
47.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
91.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Counts

165 → 165

Iterations

Useful iterations: 2 (309.0ms)

Iter	Nodes	Cost
0	258	3239
1	810	3164
2	4287	2682
done	5000	2682

prune417.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.6b

localize13.0ms

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))
9.8b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite195.0ms

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:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
56.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
96.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
54.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify413.0ms

Counts

285 → 285

Iterations

Useful iterations: 1 (99.0ms)

Iter	Nodes	Cost
0	405	5259
1	1282	5078
done	5000	5078

prune685.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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

rewrite209.0ms

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:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
91.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
76.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(/ (/ PI 2.0) (+ b a))

series239.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
101.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
51.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(/ (/ PI 2.0) (+ b a))

simplify400.0ms

Counts

289 → 289

Iterations

Useful iterations: done (391.0ms)

Iter	Nodes	Cost
0	409	5721
1	1234	5569
done	5001	5545

prune885.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
169×	`*-un-lft-identity`
128×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
58×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
20×	`cbrt-undiv` `div-exp`
15×	`div-inv`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`associate-r`
9×	`associate-/r*`
8×	`associate-/r/` `distribute-lft-out--`
7×	`difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`flip3--` `associate-*r/` `flip--` `associate-/l/`
3×	`unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 240

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
23.0ms	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
10.0ms	(/ (/ PI 2.0) (+ b a))

series232.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
54.0ms	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
53.0ms	(/ (/ PI 2.0) (+ b a))

simplify1.6s

Counts

252 → 252

Iterations

Useful iterations: 2 (365.0ms)

Iter	Nodes	Cost
0	357	4933
1	1074	4789
2	4830	4215
done	5000	4215

prune586.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.2b 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	11	13
1	14	13
done	14	13

end0.0ms

sample595.0ms

Algorithm

intervals

Results

433.0ms

9589×

body

valid