Details

sample29.0ms

Algorithm

intervals

Results

18.0ms

300×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
5.5b	(- (* b b) (* a a))
9.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite432.0ms

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:

91.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
32.0ms	(/ 1.0 (- (* b b) (* a a)))
18.0ms	(- (* b b) (* a a))
205.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
52.0ms	(/ 1.0 (- (* b b) (* a a)))
53.0ms	(- (* b b) (* a a))
146.0ms	(* (* (/ 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

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize20.0ms

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))
9.2b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite594.0ms

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:

22.0ms	(/ 1.0 (- b a))
142.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
21.0ms	(/ (/ PI 2.0) (+ b a))
299.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1.0 (- b a))
116.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
60.0ms	(/ (/ PI 2.0) (+ b a))
181.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.1s

Counts

646 → 646

Iterations

Useful iterations: done (2.1s)

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

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log` `add-cbrt-cube`
98×	`times-frac`
85×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
46×	`prod-exp` `cbrt-unprod`
30×	`cbrt-undiv` `div-exp`
14×	`pow1` `distribute-lft-out` `associate-/l*`
12×	`associate-*l/`
7×	`div-inv`
6×	`flip3--` `associate-l` `pow-prod-down` `flip--` `associate-/l/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `frac-2neg` `prod-diff` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 199

Calls

4 calls:

59.0ms	(* (- b a) (* a b))
32.0ms	(/ (/ PI 2.0) (+ b a))
135.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
145.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- b a) (* a b)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (- b a) (* a b))
100.0ms	(/ (/ PI 2.0) (+ b a))
168.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
195.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- b a) (* a b)))

simplify3.6s

Counts

211 → 211

Iterations

Useful iterations: 2 (1.9s)

Iter	Nodes	Cost
0	345	4740
1	970	4535
2	4616	3341
done	5000	3341

prune641.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b a) (* a b))
0.2b	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (* (- b a) (* a b)) (* 1.0 (- b a))))
0.3b	(/ (/ PI 2.0) (+ b a))
13.9b	(/ (* (- b a) (* a b)) (* 1.0 (- b a)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

193×	`add-exp-log` `add-cbrt-cube`
107×	`times-frac`
86×	`*-un-lft-identity`
82×	`cbrt-undiv` `div-exp`
69×	`prod-exp` `cbrt-unprod`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
15×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/r*`
10×	`div-inv`
9×	`pow1` `associate-/r/`
6×	`associate-*r/`
5×	`flip3--` `associate-l` `associate-*l/` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`flip3-+` `associate-r` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 228

Calls

4 calls:

68.0ms	(* (- b a) (* a b))
99.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (* (- b a) (* a b)) (* 1.0 (- b a))))
42.0ms	(/ (/ PI 2.0) (+ b a))
44.0ms	(/ (* (- b a) (* a b)) (* 1.0 (- b a)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- b a) (* a b))
99.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (* (- b a) (* a b)) (* 1.0 (- b a))))
97.0ms	(/ (/ PI 2.0) (+ b a))
23.0ms	(/ (* (- b a) (* a b)) (* 1.0 (- b a)))

simplify3.2s

Counts

240 → 240

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	362	5835
1	985	5550
2	4496	3990
done	5001	3990

prune682.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	16	15
done	16	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

9623×

body

valid