Details

sample59.0ms

Algorithm

intervals

Results

35.0ms

306×

body

valid

simplify2.0s

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: 15.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.2b	(/ 1.0 (- (* b b) (* a a)))
4.1b	(- (* b b) (* a a))
9.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite257.0ms

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:

69.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
15.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
156.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
64.0ms	(/ 1.0 (- (* b b) (* a a)))
50.0ms	(- (* b b) (* a a))
156.0ms	(* (* (/ 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

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize32.0ms

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))
9.6b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-cbrt-cube` `associate-l` `add-exp-log`
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-l/` `associate-r/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`associate-/r*` `pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `diff-log` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

21.0ms	(- (/ 1.0 a) (/ 1.0 b))
83.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
24.0ms	(/ (/ PI 2.0) (+ a b))
169.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
102.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
61.0ms	(/ (/ PI 2.0) (+ a b))
126.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

285 → 285

Iterations

Iter	Nodes
done	5001
1	1341
0	406

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(/ (/ PI 2.0) (+ a b))
0.3b	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite307.0ms

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:

28.0ms	(- (/ 1.0 a) (/ 1.0 b))
113.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
15.0ms	(/ (/ PI 2.0) (+ a b))
136.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 a) (/ 1.0 b))
140.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
63.0ms	(/ (/ PI 2.0) (+ a b))
142.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.1s

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: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

268×	`add-sqr-sqrt`
249×	`times-frac`
221×	`*-un-lft-identity`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
69×	`add-cube-cbrt`
66×	`associate-r`
47×	`add-cbrt-cube` `add-exp-log`
28×	`div-inv`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`associate-/l*`
10×	`associate-l`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-*l/` `frac-sub` `flip-+` `unswap-sqr`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 251

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
198.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
103.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
22.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

series347.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (/ 1.0 a) (/ 1.0 b))
151.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
63.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
87.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

simplify1.3s

Counts

263 → 263

Iterations

Iter	Nodes
done	5001
1	1174
0	351

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes207.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

9607×

body

valid