Details

sample57.0ms

Algorithm

intervals

Results

32.0ms

316×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize46.0ms

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)))

rewrite222.0ms

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))))
11.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
154.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
72.0ms	(/ 1.0 (- (* b b) (* a a)))
56.0ms	(- (* b b) (* a a))
137.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.9s

Counts

165 → 165

Iterations

Iter	Nodes
done	5005
2	3712
1	853
0	258

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

151×	`times-frac`
126×	`*-un-lft-identity`
125×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
59×	`associate-l`
58×	`add-cbrt-cube` `add-exp-log`
33×	`associate-r`
20×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`distribute-lft-out`
12×	`associate-/r/` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*` `div-inv`
8×	`associate-l/` `associate-r/`
6×	`flip3--` `flip--` `associate-/l*` `unswap-sqr`
4×	`flip3-+` `pow-prod-down` `frac-sub` `flip-+` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `*-commutative`

Counts

4 → 235

Calls

4 calls:

18.0ms	(/ 1.0 (- b a))
91.0ms	(* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a)))
9.0ms	(/ PI (+ a b))
187.0ms	(* (* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1.0 (- b a))
84.0ms	(* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a)))
53.0ms	(/ PI (+ a b))
134.0ms	(* (* (/ (/ PI (+ a b)) 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.7s

Counts

247 → 247

Iterations

Iter	Nodes
done	5000
1	1208
0	369

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-cbrt-cube` `add-exp-log`
42×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`times-frac`
19×	`prod-exp` `cbrt-unprod`
18×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp` `associate-r`
10×	`associate-*l/` `distribute-lft-out--`
9×	`pow1`
8×	`associate-*r/` `difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `div-inv` `flip--` `add-log-exp`
5×	`associate-/r*` `frac-sub`
4×	`associate-/r/` `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 → 133

Calls

4 calls:

41.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (* (* (/ PI (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
9.0ms	(/ PI (+ a b))
113.0ms	(* (* (/ PI (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
132.0ms	(/ (* (* (/ PI (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
70.0ms	(/ PI (+ a b))
170.0ms	(* (* (/ PI (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

145 → 145

Iterations

Iter	Nodes
done	5047
2	3738
1	721
0	236

prune722.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b)) (* a b)) (* 2.0 (- b a)))
0.2b	(* (* PI 1.0) (* 1.0 (- b a)))
0.3b	(/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b))
0.9b	(/ (/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b)) (* a b))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

243×	`add-cbrt-cube` `add-exp-log`
97×	`cbrt-undiv` `div-exp`
95×	`prod-exp` `cbrt-unprod`
64×	`times-frac`
28×	`*-un-lft-identity`
25×	`associate-/l*`
16×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
12×	`associate-/r/`
10×	`associate-*r/`
9×	`div-inv`
8×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
6×	`associate-/r*` `distribute-lft-out`
5×	`flip3-+` `flip-+`
4×	`sub-neg` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 215

Calls

4 calls:

91.0ms	(/ (/ (/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b)) (* a b)) (* 2.0 (- b a)))
47.0ms	(* (* PI 1.0) (* 1.0 (- b a)))
87.0ms	(/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b))
48.0ms	(/ (/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b)) (* a b))

series539.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b)) (* a b)) (* 2.0 (- b a)))
76.0ms	(* (* PI 1.0) (* 1.0 (- b a)))
156.0ms	(/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b))
204.0ms	(/ (/ (* (* PI 1.0) (* 1.0 (- b a))) (+ a b)) (* a b))

simplify3.2s

Counts

227 → 227

Iterations

Iter	Nodes
done	5004
2	4667
1	1006
0	325

prune856.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

9576×

body

valid