Details

sample58.0ms

Algorithm

intervals

Results

36.0ms

296×

body

valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1526
3	363
2	88
1	30
0	15

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize52.0ms

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)))
2.6b	(- (* b b) (* a a))
7.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite359.0ms

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:

86.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
26.0ms	(/ 1.0 (- (* b b) (* a a)))
15.0ms	(- (* b b) (* a a))
221.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
93.0ms	(/ 1.0 (- (* b b) (* a a)))
62.0ms	(- (* b b) (* a a))
182.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify4.0s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
2	3696
1	853
0	258

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize54.0ms

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 (- b a)))
0.3b	(/ (/ PI 2.0) (+ a b))
7.0b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite600.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

56.0ms	(- (/ 1.0 a) (/ 1.0 b))
160.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
37.0ms	(/ (/ PI 2.0) (+ a b))
313.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (/ 1.0 a) (/ 1.0 b))
135.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
84.0ms	(/ (/ PI 2.0) (+ a b))
183.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts

285 → 285

Iterations

Iter	Nodes
done	5000
1	1303
0	406

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
0.3b	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (- b a)))

rewrite547.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
53×	`*-un-lft-identity`
52×	`times-frac`
33×	`associate-r`
27×	`frac-times` `add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
13×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `unswap-sqr`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `distribute-lft-out`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 180

Calls

4 calls:

29.0ms	(- (/ 1.0 a) (/ 1.0 b))
180.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
242.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
80.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (/ 1.0 a) (/ 1.0 b))
190.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
139.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
101.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify4.5s

Counts

192 → 192

Iterations

Iter	Nodes
done	5002
2	4422
1	1006
0	305

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

70.0ms	(/ (* 0.5 (/ PI (* a b))) (+ a b))
16.0ms	(/ PI (* a b))

series167.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(/ (* 0.5 (/ PI (* a b))) (+ a b))
37.0ms	(/ PI (* a b))

simplify2.1s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
2	1224
1	294
0	107

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes266.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

2.1s

9606×

body

valid