Details

sample48.0ms

Algorithm

intervals

Results

26.0ms

302×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1772
3	378
2	89
1	30
0	15

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.0b	(* (+ a b) (- b a))
0.3b	(* (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) PI)
7.8b	(/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) PI) (/ (* (+ a b) (- b a)) 1.0))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
90×	`times-frac`
71×	`*-un-lft-identity`
47×	`add-cbrt-cube` `add-exp-log`
44×	`associate-l`
35×	`add-cube-cbrt`
21×	`distribute-lft-out--`
19×	`cbrt-undiv` `div-exp`
17×	`difference-of-squares`
12×	`prod-exp` `cbrt-unprod` `div-inv`
8×	`pow1` `associate-r`
7×	`associate-/r*`
6×	`add-log-exp`
4×	`frac-times` `flip3--` `associate-*l/` `flip--`
3×	`sub-neg` `flip3-+` `flip-+` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-r/` `-commutative`
1×	`clear-num` `frac-2neg` `diff-log` `associate-/r/` `frac-sub` `distribute-lft-out` `associate-/l*` `associate-/l/`

Counts

4 → 159

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
29.0ms	(* (+ a b) (- b a))
123.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) PI)
54.0ms	(/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) PI) (/ (* (+ a b) (- b a)) 1.0))

series352.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
47.0ms	(* (+ a b) (- b a))
99.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) PI)
167.0ms	(/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) PI) (/ (* (+ a b) (- b a)) 1.0))

simplify470.0ms

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
1	918
0	311

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

1169×	`times-frac`
938×	`add-sqr-sqrt`
795×	`*-un-lft-identity`
347×	`add-cube-cbrt`
251×	`distribute-lft-out--`
217×	`difference-of-squares`
206×	`associate-r`
83×	`div-inv`
43×	`associate-/l*`
32×	`add-cbrt-cube` `add-exp-log`
18×	`associate-l`
13×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
8×	`associate-/r/`
7×	`distribute-lft-out`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `flip3-+` `div-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `frac-sub` `associate-/l/`

Counts

4 → 572

Calls

4 calls:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
263.0ms	(* (/ PI (+ a b)) (/ (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) (- b a)))
95.0ms	(/ (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) (- b a))
9.0ms	(/ PI (+ a b))

series337.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
143.0ms	(* (/ PI (+ a b)) (/ (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) (- b a)))
87.0ms	(/ (/ (- (/ 1.0 a) (/ 1.0 b)) 2.0) (- b a))
67.0ms	(/ PI (+ a b))

simplify1.1s

Counts

584 → 584

Iterations

Iter	Nodes
done	5000
1	2482
0	743

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ PI (+ a b)) (/ 0.5 (* a b)))
0.2b	(/ PI (+ a b))
0.6b	(/ 0.5 (* a b))

rewrite65.0ms

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×	`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 → 105

Calls

3 calls:

36.0ms	(* (/ PI (+ a b)) (/ 0.5 (* a b)))
13.0ms	(/ PI (+ a b))
6.0ms	(/ 0.5 (* a b))

series169.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(* (/ PI (+ a b)) (/ 0.5 (* a b)))
54.0ms	(/ PI (+ a b))
37.0ms	(/ 0.5 (* a b))

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2184
1	431
0	151

prune551.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* 0.5 PI) (+ a b)) (* b a))
0.2b	(/ (* 0.5 PI) (+ a b))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-cbrt-cube` `add-exp-log`
22×	`times-frac`
16×	`*-un-lft-identity`
12×	`cbrt-undiv` `div-exp`
11×	`associate-/l*`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-exp` `associate-/r/` `cbrt-unprod`
5×	`associate-/r*`
4×	`div-inv` `distribute-lft-out`
3×	`flip3-+` `flip-+`
2×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 69

Calls

2 calls:

22.0ms	(/ (/ (* 0.5 PI) (+ a b)) (* b a))
13.0ms	(/ (* 0.5 PI) (+ a b))

series206.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(/ (/ (* 0.5 PI) (+ a b)) (* b a))
102.0ms	(/ (* 0.5 PI) (+ a b))

simplify2.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	2219
1	358
0	126

prune419.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	23
2	23
1	21
0	14

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.5s

9578×

body

valid