Details

sample33.0ms

Algorithm

intervals

Results

19.0ms

316×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
6.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log`

Counts

4 → 153

Calls

4 calls:

40.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
14.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
128.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
71.0ms	(/ 1.0 (- (* b b) (* a a)))
60.0ms	(- (* b b) (* a a))
140.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
1	873
0	258

prune892.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ a b))
6.5b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-cbrt-cube` `add-exp-log`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-l/` `associate-r/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

13.0ms	(/ 1.0 (- b a))
82.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
13.0ms	(/ (/ PI 2.0) (+ a b))
179.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1.0 (- b a))
103.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
71.0ms	(/ (/ PI 2.0) (+ a b))
130.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.4s

Counts

300 → 300

Iterations

Iter	Nodes
done	5000
1	1344
0	407

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

21.0ms	(- (/ 1.0 a) (/ 1.0 b))
122.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
28.0ms	(/ (/ PI 2.0) (+ a b))
116.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (/ 1.0 a) (/ 1.0 b))
158.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
79.0ms	(/ (/ PI 2.0) (+ a b))
159.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
1	969
0	337

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

514×	`times-frac`
420×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
142×	`add-cube-cbrt`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
83×	`associate-/r*`
44×	`div-inv`
43×	`add-cbrt-cube` `add-exp-log`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `frac-sub` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 366

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
54.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
115.0ms	(/ (* (/ (/ PI 2.0) (+ a b)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
13.0ms	(/ (/ PI 2.0) (+ a b))

series356.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
139.0ms	(/ (* (/ (/ PI 2.0) (+ a b)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
83.0ms	(/ (/ PI 2.0) (+ a b))

simplify1.8s

Counts

378 → 378

Iterations

Iter	Nodes
done	5001
1	1656
0	541

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes123.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

984.0ms

9576×

body

valid