Details

sample61.0ms

Algorithm

intervals

Results

37.0ms

311×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	89	21
3	377	21
4	1644	21
done	5000	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
4.8b	(- (* b b) (* a a))
7.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite343.0ms

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:

76.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
29.0ms	(/ 1.0 (- (* b b) (* a a)))
18.0ms	(- (* b b) (* a a))
206.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
76.0ms	(/ 1.0 (- (* b b) (* a a)))
45.0ms	(- (* b b) (* a a))
133.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.4s

Counts

165 → 165

Iterations

Useful iterations: 2 (742.0ms)

Iter	Nodes	Cost
0	258	3239
1	776	3164
2	3267	2690
done	5000	2690

prune598.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite627.0ms

Algorithm

rewrite-expression-head

Rules

286×	`add-sqr-sqrt`
265×	`times-frac`
232×	`*-un-lft-identity`
85×	`distribute-lft-out--`
80×	`add-cube-cbrt`
79×	`associate-l`
73×	`difference-of-squares`
59×	`add-exp-log` `add-cbrt-cube`
28×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
19×	`associate-r`
18×	`cbrt-undiv` `div-exp`
12×	`associate-/l*`
11×	`pow1`
6×	`frac-times` `associate-*r/` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `unswap-sqr`
3×	`associate-/l/` `distribute-lft-out`
2×	`*-commutative` `frac-sub`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `clear-num` `flip-+`

Counts

4 → 276

Calls

4 calls:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
225.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
84.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
226.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 a) (/ 1.0 b))
125.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
61.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
115.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))

simplify2.2s

Counts

288 → 288

Iterations

Useful iterations: 2 (941.0ms)

Iter	Nodes	Cost
0	388	6213
1	1181	6052
2	3647	5342
done	5000	5342

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
0.2b	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.3b	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

rewrite542.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
143×	`times-frac`
132×	`*-un-lft-identity`
56×	`add-exp-log` `add-cbrt-cube`
48×	`distribute-lft-out--`
46×	`add-cube-cbrt`
41×	`difference-of-squares`
20×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
17×	`div-inv`
13×	`associate-l` `associate-/l*`
9×	`pow1` `associate-/r*`
6×	`associate-*l/` `associate-/l/` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num` `frac-sub` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r` `*-commutative` `flip-+`

Counts

4 → 194

Calls

4 calls:

56.0ms	(- (/ 1.0 a) (/ 1.0 b))
165.0ms	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
102.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
201.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

series401.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (/ 1.0 a) (/ 1.0 b))
160.0ms	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
92.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
100.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

simplify1.9s

Counts

206 → 206

Iterations

Useful iterations: 2 (769.0ms)

Iter	Nodes	Cost
0	325	4481
1	879	4338
2	2844	3698
done	5000	3698

prune709.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b a))
0.5b	(cbrt (- b a))
0.5b	(cbrt (- b a))
0.5b	(* (cbrt (- b a)) (cbrt (- b a)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

8.0ms	(cbrt (- b a))
8.0ms	(cbrt (- b a))
5.0ms	(cbrt (- b a))
67.0ms	(* (cbrt (- b a)) (cbrt (- b a)))

series868.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt (- b a))
259.0ms	(cbrt (- b a))
228.0ms	(cbrt (- b a))
186.0ms	(* (cbrt (- b a)) (cbrt (- b a)))

simplify3.1s

Counts

113 → 113

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	131	1384
1	262	1281
2	618	1223
3	1341	1122
4	3516	1080
done	5000	1032

prune630.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 0b

regimes196.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s

9644×

body

valid