Details

sample97.0ms

Algorithm

intervals

Results

79.0ms

305×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite694.0ms

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:

545.0ms	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
42.0ms	(/ (/ (/ PI (+ a b)) 2) a)
15.0ms	(/ PI (+ a b))
17.0ms	(/ PI (+ a b))

series429.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
110.0ms	(/ (/ (/ PI (+ a b)) 2) a)
72.0ms	(/ PI (+ a b))
74.0ms	(/ PI (+ a b))

simplify2.2s

Counts

851 → 851

Iterations

Iter	Nodes
done	5000
1	2276
0	1147

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

288×	`add-sqr-sqrt`
268×	`times-frac`
242×	`*-un-lft-identity`
85×	`distribute-lft-out--`
82×	`add-cube-cbrt`
73×	`difference-of-squares`
66×	`associate-r`
28×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
18×	`associate-l`
15×	`associate-/l*`
9×	`associate-/r*`
8×	`associate-/r/`
7×	`distribute-lft-out`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`flip3--` `prod-exp` `cbrt-unprod` `insert-posit16` `flip--` `unswap-sqr`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 262

Calls

4 calls:

18.0ms	(- (/ 1/2 a) (/ 1/2 b))
56.0ms	(* (/ PI (+ b a)) (/ (- (/ 1/2 a) (/ 1/2 b)) (- b a)))
37.0ms	(/ (- (/ 1/2 a) (/ 1/2 b)) (- b a))
12.0ms	(/ PI (+ b a))

series283.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (/ 1/2 a) (/ 1/2 b))
122.0ms	(* (/ PI (+ b a)) (/ (- (/ 1/2 a) (/ 1/2 b)) (- b a)))
66.0ms	(/ (- (/ 1/2 a) (/ 1/2 b)) (- b a))
52.0ms	(/ PI (+ b a))

simplify2.7s

Counts

274 → 274

Iterations

Iter	Nodes
done	5002
2	3390
1	1048
0	339

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ PI (+ b a)) (/ 1/2 (* a b)))
0.3b	(/ PI (+ b a))
0.6b	(/ 1/2 (* a b))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
31×	`times-frac` `add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `distribute-lft-out`
6×	`associate-/l*`
5×	`pow1` `associate-/r*`
4×	`associate-/r/` `div-inv`
3×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 108

Calls

3 calls:

61.0ms	(* (/ PI (+ b a)) (/ 1/2 (* a b)))
15.0ms	(/ PI (+ b a))
12.0ms	(/ 1/2 (* a b))

series193.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(* (/ PI (+ b a)) (/ 1/2 (* a b)))
48.0ms	(/ PI (+ b a))
39.0ms	(/ 1/2 (* a b))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1669
1	428
0	155

prune329.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* PI (/ 1/2 (* a b))) (+ b a))
0.3b	(* PI (/ 1/2 (* a b)))
0.6b	(/ 1/2 (* a b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `times-frac` `div-exp` `add-cube-cbrt`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`associate-l` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr` `associate-/l/`

Counts

3 → 81

Calls

3 calls:

20.0ms	(/ (* PI (/ 1/2 (* a b))) (+ b a))
16.0ms	(* PI (/ 1/2 (* a b)))
8.0ms	(/ 1/2 (* a b))

series158.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (* PI (/ 1/2 (* a b))) (+ b a))
38.0ms	(* PI (/ 1/2 (* a b)))
27.0ms	(/ 1/2 (* a b))

simplify1.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1303
1	348
0	128

prune287.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

2.3s

9637×

body

valid