Details

sample63.0ms

Algorithm

intervals

Results

38.0ms

314×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize19.0ms

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)))
3.7b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite294.0ms

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:

49.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
27.0ms	(/ 1.0 (- (* b b) (* a a)))
17.0ms	(- (* b b) (* a a))
194.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
72.0ms	(/ 1.0 (- (* b b) (* a a)))
47.0ms	(- (* b b) (* a a))
156.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.9s

Counts

165 → 165

Iterations

Useful iterations: 2 (745.0ms)

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

prune692.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite567.0ms

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:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
114.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
206.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
187.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (/ 1.0 a) (/ 1.0 b))
55.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
97.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
135.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))

simplify2.3s

Counts

288 → 288

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	388	6213
1	1181	6052
2	3640	5342
done	5001	5342

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
131×	`times-frac`
120×	`*-un-lft-identity`
48×	`distribute-lft-out--`
47×	`add-exp-log` `add-cbrt-cube`
41×	`difference-of-squares`
38×	`add-cube-cbrt`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
13×	`associate-/l*`
12×	`cbrt-undiv` `div-exp`
9×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`associate-*r/` `associate-/r/` `associate-/l/`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`frac-2neg` `associate-*l/` `clear-num` `frac-sub`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r` `*-commutative` `flip-+`

Counts

4 → 170

Calls

4 calls:

28.0ms	(- (/ 1.0 a) (/ 1.0 b))
139.0ms	(/ (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (* 2.0 (+ b a)))
81.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
144.0ms	(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

series355.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (/ 1.0 a) (/ 1.0 b))
150.0ms	(/ (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (* 2.0 (+ b a)))
52.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
94.0ms	(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

simplify1.6s

Counts

182 → 182

Iterations

Useful iterations: 2 (653.0ms)

Iter	Nodes	Cost
0	286	3918
1	802	3790
2	3116	3228
done	5001	3228

prune683.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (/ 1 (* 2.0 (+ b a))))
0.2b	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.3b	(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))
0.4b	(/ 1 (* 2.0 (+ b a)))

rewrite903.0ms

Algorithm

rewrite-expression-head

Rules

144×	`add-exp-log`
138×	`add-sqr-sqrt`
126×	`times-frac`
114×	`*-un-lft-identity`
83×	`prod-exp`
74×	`add-cbrt-cube`
43×	`distribute-lft-out--`
40×	`add-cube-cbrt`
37×	`cbrt-unprod` `difference-of-squares`
29×	`div-exp`
21×	`pow1`
15×	`cbrt-undiv` `div-inv` `associate-/l*`
10×	`rec-exp` `1-exp` `associate-r` `pow-prod-down`
8×	`associate-*r/`
6×	`associate-/r*` `associate-/r/`
4×	`associate-l` `associate-*l/` `add-log-exp`
3×	`associate-/l/`
2×	`flip3--` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip--` `flip-+`
1×	`frac-times` `div-sub` `un-div-inv` `frac-sub` `inv-pow`

Counts

4 → 211

Calls

4 calls:

566.0ms	(* (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (/ 1 (* 2.0 (+ b a))))
118.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
166.0ms	(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))
31.0ms	(/ 1 (* 2.0 (+ b a)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (/ 1 (* 2.0 (+ b a))))
66.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
98.0ms	(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))
70.0ms	(/ 1 (* 2.0 (+ b a)))

simplify3.2s

Counts

223 → 223

Iterations

Useful iterations: 2 (741.0ms)

Iter	Nodes	Cost
0	331	4984
1	873	4632
2	2916	3846
done	5000	3846

prune697.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes126.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	23
1	24	23
done	24	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.5s

9575×

body

valid