Details

sample58.0ms

Algorithm

intervals

Results

37.0ms

310×

body

valid

simplify2.8s

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: 13.1b

localize32.0ms

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)))
5.1b	(- (* b b) (* a a))
7.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite394.0ms

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:

59.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
27.0ms	(/ 1.0 (- (* b b) (* a a)))
23.0ms	(- (* b b) (* a a))
234.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
68.0ms	(/ 1.0 (- (* b b) (* a a)))
45.0ms	(- (* b b) (* a a))
115.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts

513 → 513

Iterations

Useful iterations: done (1.8s)

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

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize28.0ms

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))
7.2b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite450.0ms

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:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
81.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
18.0ms	(/ (/ PI 2.0) (+ b a))
246.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
100.0ms	(* (/ (/ 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

813 → 813

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	1024	37421
1	2727	34154
done	5001	29197

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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)))

rewrite749.0ms

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:

60.0ms	(- (/ 1.0 a) (/ 1.0 b))
285.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
26.0ms	(/ (/ PI 2.0) (+ b a))
275.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ 1.0 a) (/ 1.0 b))
127.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
93.0ms	(/ (/ PI 2.0) (+ b a))
146.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.0s

Counts

730 → 730

Iterations

Useful iterations: done (2.0s)

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

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- b a) (* a b))
0.2b	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- 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)))

rewrite351.0ms

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:

62.0ms	(* (- b a) (* a b))
131.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- b a) (* a b)))
32.0ms	(/ (/ PI 2.0) (+ b a))
103.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (- b a) (* a b))
249.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- b a) (* a b)))
95.0ms	(/ (/ PI 2.0) (+ b a))
129.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))

simplify3.0s

Counts

211 → 211

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	345	4740
1	970	4535
2	4694	3341
done	5000	3341

prune708.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

9560×

body

valid