Details

sample30.0ms

Algorithm

intervals

Results

17.0ms

304×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
5.2b	(- (* b b) (* a a))
8.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite237.0ms

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:

64.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
16.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
140.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
52.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
157.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts

165 → 165

Iterations

Iter	Nodes
done	5005
2	3712
1	853
0	258

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.7b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite410.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-cbrt-cube` `add-exp-log`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-l/` `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` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

16.0ms	(/ 1.0 (+ b a))
47.0ms	(/ (/ 1.0 (+ b a)) (- b a))
89.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
222.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (+ b a))
73.0ms	(/ (/ 1.0 (+ b a)) (- b a))
82.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
135.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.8s

Counts

370 → 370

Iterations

Iter	Nodes
done	5000
1	1521
0	450

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-cbrt-cube` `add-exp-log`
47×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
36×	`times-frac`
30×	`associate-r`
25×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`distribute-lft-out` `associate-/l/`
6×	`frac-times` `associate-/r/`
5×	`associate-/r*` `flip3--` `div-inv` `flip--` `distribute-lft-out--`
4×	`associate-l` `pow-prod-down` `frac-sub` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

16.0ms	(/ 1.0 (+ b a))
88.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
95.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
48.0ms	(* PI (/ 1.0 (+ b a)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (+ b a))
141.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
152.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
85.0ms	(* PI (/ 1.0 (+ b a)))

simplify2.8s

Counts

160 → 160

Iterations

Iter	Nodes
done	5404
2	3964
1	769
0	234

prune925.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`times-frac`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
12×	`associate-r`
10×	`associate-l` `add-cube-cbrt`
8×	`associate-*r/`
7×	`associate-/l/`
6×	`frac-times` `associate-/r/`
5×	`pow1` `associate-/r*` `flip3--` `div-inv` `flip--` `distribute-lft-out--`
4×	`frac-sub` `difference-of-squares`
3×	`distribute-lft-out` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `flip-+` `associate-/l`
1×	`pow-prod-down` `*-commutative` `unswap-sqr`

Counts

3 → 112

Calls

3 calls:

49.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
20.0ms	(/ (* PI 1.0) (+ b a))
131.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series412.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
81.0ms	(/ (* PI 1.0) (+ b a))
165.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	5004
2	3559
1	715
0	213

prune569.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

9622×

body

valid