Details

sample70.0ms

Algorithm

intervals

Results

33.0ms

306×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1543
3	363
2	88
1	30
0	15

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.1b	(/ 1.0 (- (* b b) (* a a)))
4.4b	(- (* b b) (* a a))
8.3b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite362.0ms

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` `insert-posit16` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log`

Counts

4 → 157

Calls

4 calls:

87.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
34.0ms	(/ 1.0 (- (* b b) (* a a)))
21.0ms	(- (* b b) (* a a))
193.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
89.0ms	(/ 1.0 (- (* b b) (* a a)))
69.0ms	(- (* b b) (* a a))
179.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify5.7s

Counts

169 → 169

Iterations

Iter	Nodes
done	5002
2	3803
1	860
0	262

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a)))
0.2b	(/ PI (+ a b))
8.3b	(* (* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite555.0ms

Algorithm

rewrite-expression-head

Rules

146×	`times-frac`
121×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
70×	`add-cube-cbrt`
59×	`associate-l`
56×	`add-cbrt-cube` `add-exp-log`
33×	`associate-r`
19×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`distribute-lft-out` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`associate-/r/` `div-inv`
8×	`associate-l/` `associate-r/`
6×	`flip3--` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`associate-/r*` `flip3-+` `pow-prod-down` `flip-+` `insert-posit16`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log`

Counts

4 → 224

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
166.0ms	(* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a)))
15.0ms	(/ PI (+ a b))
305.0ms	(* (* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (/ 1.0 a) (/ 1.0 b))
109.0ms	(* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a)))
58.0ms	(/ PI (+ a b))
147.0ms	(* (* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.7s

Counts

236 → 236

Iterations

Iter	Nodes
done	5000
1	1206
0	372

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (/ (/ PI (+ a b)) 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(/ PI (+ a b))
0.3b	(* (* (/ (/ PI (+ a b)) 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite492.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cbrt-cube` `add-exp-log`
37×	`times-frac`
20×	`add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod`
12×	`cbrt-undiv` `div-exp` `associate-r` `distribute-lft-out--`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `div-inv` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/` `insert-posit16` `distribute-lft-out` `associate-/l*`
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 → 141

Calls

4 calls:

44.0ms	(- (/ 1.0 a) (/ 1.0 b))
186.0ms	(/ (* (* (/ (/ PI (+ a b)) 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
20.0ms	(/ PI (+ a b))
227.0ms	(* (* (/ (/ PI (+ a b)) 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ 1.0 a) (/ 1.0 b))
163.0ms	(/ (* (* (/ (/ PI (+ a b)) 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
98.0ms	(/ PI (+ a b))
177.0ms	(* (* (/ (/ PI (+ a b)) 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify5.1s

Counts

153 → 153

Iterations

Iter	Nodes
done	5006
2	3303
1	736
0	253

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

429×	`times-frac`
380×	`add-sqr-sqrt`
320×	`*-un-lft-identity`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
102×	`add-cube-cbrt`
83×	`associate-/r*`
40×	`add-cbrt-cube` `add-exp-log`
39×	`div-inv`
20×	`cbrt-undiv` `div-exp`
12×	`associate-/r/`
9×	`associate-/l*`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `frac-sub` `insert-posit16` `distribute-lft-out`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 317

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
181.0ms	(/ (* (/ (/ PI (+ a b)) 2.0) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
131.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
29.0ms	(/ PI (+ a b))

series345.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ 1.0 a) (/ 1.0 b))
153.0ms	(/ (* (/ (/ PI (+ a b)) 2.0) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
64.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
68.0ms	(/ PI (+ a b))

simplify3.1s

Counts

329 → 329

Iterations

Iter	Nodes
done	5001
1	1379
0	457

prune3.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes395.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s

9533×

body

valid