Details

sample74.0ms

Algorithm

intervals

Results

52.0ms

311×

body

valid

simplify2.4s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
4.8b	(- (* b b) (* a a))
7.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite386.0ms

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:

83.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
17.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
204.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
88.0ms	(/ 1.0 (- (* b b) (* a a)))
42.0ms	(- (* b b) (* a a))
110.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.0s

Counts

513 → 513

Iterations

Useful iterations: done (1.9s)

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

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize28.0ms

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))
7.4b	(* (* (/ (/ 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:

21.0ms	(/ 1.0 (- b a))
111.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
20.0ms	(/ (/ PI 2.0) (+ b a))
302.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (- b a))
81.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
75.0ms	(/ (/ PI 2.0) (+ b a))
135.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

646 → 646

Iterations

Useful iterations: done (2.2s)

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

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite618.0ms

Algorithm

rewrite-expression-head

Rules

833×	`times-frac`
661×	`*-un-lft-identity`
641×	`add-sqr-sqrt`
613×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
90×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
13×	`fma-neg`
12×	`associate-r` `distribute-lft-out--`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 718

Calls

4 calls:

67.0ms	(- (/ 1.0 a) (/ 1.0 b))
257.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
19.0ms	(/ (/ PI 2.0) (+ b a))
194.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (/ 1.0 a) (/ 1.0 b))
161.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
101.0ms	(/ (/ PI 2.0) (+ b a))
170.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts

730 → 730

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	955	33243
1	2400	30007
done	5000	25138

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a))) (* a b)) (- b a))
0.3b	(/ (* (/ PI 2.0) 1.0) (+ b a))
0.3b	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a)))
0.9b	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a))) (* a b))

rewrite455.0ms

Algorithm

rewrite-expression-head

Rules

251×	`add-exp-log` `add-cbrt-cube`
100×	`prod-exp` `cbrt-unprod`
99×	`cbrt-undiv` `div-exp`
62×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
44×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
40×	`times-frac`
36×	`prod-diff`
12×	`associate-*r/`
10×	`associate-l` `associate-/r*` `div-inv`
9×	`pow1`
7×	`associate-/l/` `associate-/l*`
6×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sub-neg` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `distribute-lft-out`
2×	`flip3-+` `flip-+`
1×	`associate-r` `*-commutative`

Counts

4 → 262

Calls

4 calls:

96.0ms	(/ (/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a))) (* a b)) (- b a))
40.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))
159.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a)))
121.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a))) (* a b))

series574.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a))) (* a b)) (- b a))
85.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))
142.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a)))
210.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (* 1.0 (- b a))) (* a b))

simplify1.2s

Counts

274 → 274

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	427	8778
1	1220	8139
done	5000	6043

prune529.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes100.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	20	23
done	20	23

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

9644×

body

valid