Details

sample100.0ms

Algorithm

intervals

Results

81.0ms

310×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	1476
3	358
2	94
1	32
0	15

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI (+ a b)) 2) a)
0.2b	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
0.3b	(/ PI (+ a b))
0.3b	(/ PI (+ a b))

rewrite619.0ms

Algorithm

rewrite-expression-head

Rules

3392×	`times-frac`
2732×	`*-un-lft-identity`
1168×	`add-sqr-sqrt`
1002×	`add-cube-cbrt`
734×	`distribute-lft-out`
468×	`distribute-rgt-neg-in`
146×	`associate-/l*`
102×	`associate-/r/`
83×	`distribute-lft-out--` `difference-of-squares`
80×	`div-inv`
51×	`flip3-+` `flip-+`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`
3×	`div-sub`
1×	`neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `frac-add` `flip--` `distribute-neg-frac`

Counts

4 → 839

Calls

4 calls:

19.0ms	(/ (/ (/ PI (+ a b)) 2) a)
512.0ms	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
10.0ms	(/ PI (+ a b))
7.0ms	(/ PI (+ a b))

series369.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (/ (/ PI (+ a b)) 2) a)
131.0ms	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
62.0ms	(/ PI (+ a b))
60.0ms	(/ PI (+ a b))

simplify2.2s

Counts

851 → 851

Iterations

Iter	Nodes
done	5000
1	2244
0	1147

prune3.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1/2 a) (/ 1/2 b))
0.2b	(/ (/ (/ PI (+ a b)) 1) (/ (- b a) (- (/ 1/2 a) (/ 1/2 b))))
0.2b	(/ (- b a) (- (/ 1/2 a) (/ 1/2 b)))
0.3b	(/ PI (+ a b))

rewrite804.0ms

Algorithm

rewrite-expression-head

Rules

16638×	`times-frac`
9712×	`*-un-lft-identity`
9688×	`add-sqr-sqrt`
4622×	`add-cube-cbrt`
2231×	`distribute-lft-out--`
1929×	`difference-of-squares`
938×	`div-inv`
616×	`distribute-lft-out`
591×	`associate-/r/`
205×	`flip3-+` `flip-+`
83×	`associate-/r*`
66×	`associate-/l*`
62×	`flip3--` `flip--`
61×	`frac-sub`
41×	`add-exp-log`
29×	`add-cbrt-cube` `div-exp`
17×	`cbrt-undiv`
6×	`add-log-exp`
4×	`pow1` `1-exp` `insert-posit16`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 4193

Calls

4 calls:

21.0ms	(- (/ 1/2 a) (/ 1/2 b))
54.0ms	(/ (/ (/ PI (+ a b)) 1) (/ (- b a) (- (/ 1/2 a) (/ 1/2 b))))
22.0ms	(/ (- b a) (- (/ 1/2 a) (/ 1/2 b)))
13.0ms	(/ PI (+ a b))

series264.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1/2 a) (/ 1/2 b))
111.0ms	(/ (/ (/ PI (+ a b)) 1) (/ (- b a) (- (/ 1/2 a) (/ 1/2 b))))
75.0ms	(/ (- b a) (- (/ 1/2 a) (/ 1/2 b)))
44.0ms	(/ PI (+ a b))

simplify4.9s

Counts

4205 → 4205

Iterations

Iter	Nodes
done	5031
0	5031

prune22.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ 1 (/ (+ a b) PI)) 2) b))) (- b a))
0.3b	(/ (+ a b) PI)
0.3b	(/ PI (+ a b))
0.3b	(/ 1 (/ (+ a b) PI))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

630×	`*-un-lft-identity`
582×	`times-frac`
182×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
128×	`distribute-lft-out`
84×	`distribute-rgt-neg-in`
28×	`associate-/r` `associate-/l`
26×	`div-inv`
21×	`add-exp-log`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`add-cbrt-cube`
10×	`div-exp`
6×	`cbrt-undiv`
5×	`pow1` `associate-/r/` `associate-/l/`
4×	`clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
3×	`flip3-+` `div-sub` `flip-+`
2×	`rec-exp` `1-exp`
1×	`neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `frac-add` `pow-flip` `flip--` `distribute-neg-frac` `inv-pow`

Counts

4 → 291

Calls

4 calls:

1.4s	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ 1 (/ (+ a b) PI)) 2) b))) (- b a))
25.0ms	(/ (+ a b) PI)
7.0ms	(/ PI (+ a b))
10.0ms	(/ 1 (/ (+ a b) PI))

series337.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ 1 (/ (+ a b) PI)) 2) b))) (- b a))
73.0ms	(/ (+ a b) PI)
56.0ms	(/ PI (+ a b))
66.0ms	(/ 1 (/ (+ a b) PI))

simplify1.8s

Counts

303 → 303

Iterations

Iter	Nodes
done	5001
2	2148
1	779
0	336

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (/ (sqrt 1/2) 1))
1.0b	(/ (/ (/ (sqrt PI) 1) 1) (/ 1 (/ (sqrt 1/2) 1)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite541.0ms

Algorithm

rewrite-expression-head

Rules

22268×	`times-frac`
8949×	`add-sqr-sqrt`
8947×	`*-un-lft-identity` `add-cube-cbrt`
3903×	`sqrt-prod`
578×	`div-inv`
266×	`div-exp`
251×	`add-exp-log`
98×	`1-exp`
93×	`associate-/r*`
73×	`associate-/r/` `associate-/l*`
45×	`add-cbrt-cube`
30×	`cbrt-undiv`
24×	`rec-exp`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 5347

Calls

4 calls:

8.0ms	(/ 1 (/ (sqrt 1/2) 1))
39.0ms	(/ (/ (/ (sqrt PI) 1) 1) (/ 1 (/ (sqrt 1/2) 1)))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ 1 (/ (sqrt 1/2) 1))
0.0ms	(/ (/ (/ (sqrt PI) 1) 1) (/ 1 (/ (sqrt 1/2) 1)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify7.2s

Counts

5351 → 5351

Iterations

Iter	Nodes
done	6313
0	6313

prune42.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
3	28
2	25
1	23
0	17

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

9599×

body

valid