Details

sample33.0ms

Algorithm

intervals

Results

20.0ms

302×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
5.7b	(- (* b b) (* a a))
8.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite420.0ms

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:

55.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
28.0ms	(/ 1.0 (- (* b b) (* a a)))
18.0ms	(- (* b b) (* a a))
262.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
81.0ms	(/ 1.0 (- (* b b) (* a a)))
56.0ms	(- (* b b) (* a a))
150.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.1s

Counts

513 → 513

Iterations

Useful iterations: done (2.1s)

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: 8.8b

localize18.0ms

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)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.9b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite631.0ms

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:

67.0ms	(- (/ 1.0 a) (/ 1.0 b))
136.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
19.0ms	(/ (/ PI 2.0) (+ b a))
268.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (/ 1.0 a) (/ 1.0 b))
84.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
80.0ms	(/ (/ PI 2.0) (+ b a))
129.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.8s

Counts

813 → 813

Iterations

Useful iterations: done (2.7s)

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

prune3.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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

rewrite595.0ms

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:

41.0ms	(- (/ 1.0 a) (/ 1.0 b))
213.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
23.0ms	(/ (/ PI 2.0) (+ b a))
232.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 a) (/ 1.0 b))
157.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
84.0ms	(/ (/ PI 2.0) (+ b a))
161.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.1s

Counts

730 → 730

Iterations

Useful iterations: done (2.0s)

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

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize23.0ms

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))) (/ 1 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite887.0ms

Algorithm

rewrite-expression-head

Rules

843×	`times-frac`
670×	`*-un-lft-identity`
650×	`add-sqr-sqrt`
620×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`add-exp-log`
90×	`div-inv`
68×	`add-cbrt-cube`
55×	`prod-exp`
33×	`associate-r`
31×	`cbrt-unprod`
28×	`div-exp`
22×	`associate-*l/`
18×	`pow1`
17×	`cbrt-undiv`
16×	`frac-times`
14×	`distribute-lft-out`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`difference-of-squares`
10×	`associate-*r/`
9×	`pow-prod-down`
8×	`flip3--` `flip--`
7×	`frac-sub`
6×	`add-log-exp`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg`
2×	`associate-l` `*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `un-div-inv` `flip-+` `associate-/l/`

Counts

4 → 757

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
495.0ms	(* (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (/ 1 (- b a)))
38.0ms	(/ (/ PI 2.0) (+ b a))
219.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ 1.0 a) (/ 1.0 b))
121.0ms	(* (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (/ 1 (- b a)))
84.0ms	(/ (/ PI 2.0) (+ b a))
212.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.7s

Counts

769 → 769

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	1017	34662
1	3181	31357
done	5000	27438

prune2.6s

Pruning

9 alts after pruning (8 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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

9582×

body

valid