Details

sample62.0ms

Algorithm

intervals

Results

38.0ms

314×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	90	21
3	384	21
4	1663	21
done	5000	21

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.7b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

50.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
16.0ms	(/ 1.0 (- (* b b) (* a a)))
17.0ms	(- (* b b) (* a a))
226.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms	(/ 1.0 (- (* b b) (* a a)))
38.0ms	(- (* b b) (* a a))
105.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts

513 → 513

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	886	27857
1	2290	25797
done	5000	22403

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
9.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
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*`
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×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

19.0ms	(/ 1.0 (- b a))
111.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
20.0ms	(/ (/ PI 2.0) (+ b a))
290.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- b a))
91.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
58.0ms	(/ (/ PI 2.0) (+ b a))
129.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

646 → 646

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	1031	29916
1	2733	27749
done	5001	24229

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite519.0ms

Algorithm

rewrite-expression-head

Rules

451×	`times-frac`
358×	`*-un-lft-identity`
317×	`add-sqr-sqrt`
290×	`add-cube-cbrt`
169×	`prod-diff`
58×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
42×	`div-inv`
27×	`distribute-lft-out`
20×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`fma-neg` `prod-exp` `cbrt-unprod`
11×	`associate-r`
9×	`associate-/r*`
8×	`associate-/r/` `distribute-lft-out--`
7×	`difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `associate-/l/`
3×	`unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 430

Calls

4 calls:

50.0ms	(- (/ 1.0 a) (/ 1.0 b))
212.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
183.0ms	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
27.0ms	(/ (/ PI 2.0) (+ b a))

series372.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (/ 1.0 a) (/ 1.0 b))
130.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
93.0ms	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
107.0ms	(/ (/ PI 2.0) (+ b a))

simplify2.8s

Counts

442 → 442

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	615	12603
1	1591	11429
2	4872	8855
done	5000	8855

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
0.3b	(/ (/ PI 2.0) (+ b a))
0.5b	(/ 1.0 (* a b))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
152×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
58×	`associate-l`
49×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
20×	`cbrt-undiv` `div-exp`
16×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod` `div-inv`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

3 → 211

Calls

3 calls:

93.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
38.0ms	(/ (/ PI 2.0) (+ b a))
16.0ms	(/ 1.0 (* a b))

series255.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
94.0ms	(/ (/ PI 2.0) (+ b a))
41.0ms	(/ 1.0 (* a b))

simplify1.8s

Counts

220 → 220

Iterations

Useful iterations: 2 (658.0ms)

Iter	Nodes	Cost
0	292	3284
1	829	3148
2	3086	2820
done	5001	2820

prune725.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes98.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

9575×

body

valid