Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

314×

body

valid

simplify1.6s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
3.9b	(- (* b b) (* a a))
9.3b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite269.0ms

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:

46.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
14.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
154.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
32.0ms	(- (* b b) (* a a))
91.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

513 → 513

Iterations

Useful iterations: done (1.3s)

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

prune903.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.1b

localize12.0ms

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))
9.3b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite392.0ms

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))
83.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
18.0ms	(/ (/ PI 2.0) (+ b a))
184.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
70.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
275.0ms	(/ (/ PI 2.0) (+ b a))
105.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.5s

Counts

813 → 813

Iterations

Useful iterations: done (1.4s)

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

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite462.0ms

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:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
177.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
19.0ms	(/ (/ PI 2.0) (+ b a))
161.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
100.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
55.0ms	(/ (/ PI 2.0) (+ b a))
111.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

730 → 730

Iterations

Useful iterations: done (1.2s)

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

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize12.0ms

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

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

757×	`times-frac`
609×	`add-sqr-sqrt`
569×	`*-un-lft-identity`
331×	`add-cube-cbrt`
169×	`prod-diff`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
83×	`associate-/r*`
71×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
13×	`fma-neg`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `frac-sub` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 556

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
77.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
19.0ms	(/ (/ PI 2.0) (+ b a))
57.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
103.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
54.0ms	(/ (/ PI 2.0) (+ b a))
58.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

simplify844.0ms

Counts

568 → 568

Iterations

Useful iterations: done (823.0ms)

Iter	Nodes	Cost
0	795	16145
1	1978	14698
done	5000	12394

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes89.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	17	21
done	17	21

end0.0ms

sample637.0ms

Algorithm

intervals

Results

403.0ms

9629×

body

valid