Details

sample63.0ms

Algorithm

intervals

Results

35.0ms

302×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	89	21
3	378	21
4	1789	21
done	5000	21

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize41.0ms

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)))
3.4b	(- (* b b) (* a a))
9.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite352.0ms

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:

81.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
29.0ms	(/ 1.0 (- (* b b) (* a a)))
14.0ms	(- (* b b) (* a a))
216.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
72.0ms	(/ 1.0 (- (* b b) (* a a)))
66.0ms	(- (* b b) (* a a))
152.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify696.0ms

Counts

165 → 165

Iterations

Useful iterations: done (688.0ms)

Iter	Nodes	Cost
0	258	3239
1	873	3170
done	5000	2752

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
9.7b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite499.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

20.0ms	(/ 1.0 (- b a))
139.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
33.0ms	(/ (/ PI 2.0) (+ b a))
273.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1.0 (- b a))
110.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
99.0ms	(/ (/ PI 2.0) (+ b a))
163.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify959.0ms

Counts

300 → 300

Iterations

Useful iterations: done (943.0ms)

Iter	Nodes	Cost
0	406	5324
1	1338	5143
done	5001	4635

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.2b	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (- b a)))

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
61×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
57×	`times-frac`
35×	`add-cube-cbrt`
33×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`associate-/r*`
8×	`frac-sub`
6×	`associate-/r/` `div-inv`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 195

Calls

4 calls:

20.0ms	(/ 1.0 (- b a))
156.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
194.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
76.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 1.0 (- b a))
179.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
124.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
106.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify785.0ms

Counts

207 → 207

Iterations

Useful iterations: done (774.0ms)

Iter	Nodes	Cost
0	305	3755
1	1014	3632
done	5000	3086

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

226×	`times-frac`
193×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
79×	`associate-l`
52×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
15×	`div-inv`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 292

Calls

4 calls:

20.0ms	(/ 1.0 (- b a))
248.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
32.0ms	(/ (/ PI 2.0) (+ b a))
179.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (- b a))
164.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
97.0ms	(/ (/ PI 2.0) (+ b a))
110.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify946.0ms

Counts

304 → 304

Iterations

Useful iterations: done (930.0ms)

Iter	Nodes	Cost
0	412	5786
1	1329	5628
done	5001	5120

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes189.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	14	13
done	14	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.9s

9585×

body

valid