Details

sample33.0ms

Algorithm

intervals

Results

17.0ms

313×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	405
1	30	405
2	89	405
3	378	405
4	1772	405
done	5000	405

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
3.5b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite239.0ms

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:

70.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
10.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
143.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
70.0ms	(/ 1.0 (- (* b b) (* a a)))
43.0ms	(- (* b b) (* a a))
154.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.4s

Counts

165 → 165

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	258	61224
1	873	55912
done	5001	55028

prune999.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
7.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-cbrt-cube` `add-exp-log`
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-l/` `associate-r/` `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` `flip3-+` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

12.0ms	(/ 1.0 (- b a))
130.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
21.0ms	(/ (/ PI 2.0) (+ b a))
187.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1.0 (- b a))
101.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
78.0ms	(/ (/ PI 2.0) (+ b a))
143.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.7s

Counts

300 → 300

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	406	109324
1	1338	101585
done	5000	99860

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (- b a)))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
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-l/` `associate-r/` `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` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 195

Calls

4 calls:

18.0ms	(/ 1.0 (- b a))
88.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
140.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
57.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1.0 (- b a))
156.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
115.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
91.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify1.4s

Counts

207 → 207

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	305	70279
1	1014	64080
done	5000	62556

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

207×	`times-frac`
199×	`*-un-lft-identity`
194×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
54×	`associate-r`
53×	`distribute-lft-out--`
47×	`add-cbrt-cube` `add-exp-log`
43×	`difference-of-squares`
25×	`distribute-lft-out`
24×	`div-inv`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`associate-/l*`
11×	`associate-l`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
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 → 229

Calls

4 calls:

41.0ms	(- (/ 1.0 a) (/ 1.0 b))
134.0ms	(* (/ (* (/ PI 2.0) 1.0) (- b a)) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))
348.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
26.0ms	(/ (* (/ PI 2.0) 1.0) (- b a))

series402.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (/ 1.0 a) (/ 1.0 b))
158.0ms	(* (/ (* (/ PI 2.0) 1.0) (- b a)) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))
117.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
81.0ms	(/ (* (/ PI 2.0) 1.0) (- b a))

simplify1.5s

Counts

241 → 241

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	323	94751
1	1046	87650
done	5001	86160

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	405
1	18	405
done	18	405

end0.0ms

sample1.1s

Algorithm

intervals

Results

851.0ms

9545×

body

valid