Details

sample57.0ms

Algorithm

intervals

Results

36.0ms

308×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	90	21
3	385	21
4	1860	21
done	5001	21

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.2b	(/ 1.0 (- (* b b) (* a a)))
2.8b	(- (* b b) (* a a))
10.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite333.0ms

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:

61.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
14.0ms	(/ 1.0 (- (* b b) (* a a)))
16.0ms	(- (* b b) (* a a))
195.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
90.0ms	(/ 1.0 (- (* b b) (* a a)))
44.0ms	(- (* b b) (* a a))
105.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts

513 → 513

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	886	27857
1	2914	25859
done	5002	23272

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.6b

localize29.0ms

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 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.8b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

940×	`times-frac`
738×	`*-un-lft-identity`
713×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 801

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
86.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
17.0ms	(/ (/ PI 2.0) (+ b a))
221.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
84.0ms	(/ (/ PI 2.0) (+ b a))
153.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

813 → 813

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	1024	37421
1	3368	34352
done	5001	30536

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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

rewrite642.0ms

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:

51.0ms	(- (/ 1.0 a) (/ 1.0 b))
230.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
18.0ms	(/ (/ PI 2.0) (+ b a))
253.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ 1.0 a) (/ 1.0 b))
176.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
85.0ms	(/ (/ PI 2.0) (+ b a))
188.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

730 → 730

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	955	33243
1	2949	30085
done	5000	26463

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

129×	`times-frac`
125×	`add-exp-log` `add-cbrt-cube`
106×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
49×	`cbrt-undiv` `div-exp`
45×	`prod-exp` `cbrt-unprod`
19×	`associate-/l*`
14×	`div-inv` `distribute-lft-out`
10×	`associate-/r*`
9×	`pow1`
8×	`associate-*l/`
7×	`associate-/l/`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `pow-prod-down` `clear-num`
2×	`sub-neg` `prod-diff`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 235

Calls

4 calls:

110.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b)) (- b a))
18.0ms	(/ (/ PI 2.0) (+ b a))
103.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
108.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b))

series678.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b)) (- b a))
93.0ms	(/ (/ PI 2.0) (+ b a))
178.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
218.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b))

simplify751.0ms

Counts

247 → 247

Iterations

Useful iterations: done (738.0ms)

Iter	Nodes	Cost
0	395	6600
1	1184	6337
done	5000	4977

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 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

simplify9.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	25
1	25	23
2	26	23
done	26	23

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

9597×

body

valid