Details

sample30.0ms

Algorithm

intervals

Results

19.0ms

306×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	1476
3	358
2	94
1	32
0	15

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI (+ a b)) 2) b)
0.2b	(/ (/ (/ PI (+ a b)) 2) a)
0.2b	(/ PI (+ a b))
0.2b	(/ PI (+ a b))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

1092×	`times-frac`
644×	`*-un-lft-identity`
484×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`associate-/l*`
80×	`distribute-lft-out`
52×	`associate-/r/`
36×	`div-inv`
26×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
14×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 574

Calls

4 calls:

34.0ms	(/ (/ (/ PI (+ a b)) 2) b)
38.0ms	(/ (/ (/ PI (+ a b)) 2) a)
11.0ms	(/ PI (+ a b))
13.0ms	(/ PI (+ a b))

series371.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (/ (/ PI (+ a b)) 2) b)
114.0ms	(/ (/ (/ PI (+ a b)) 2) a)
80.0ms	(/ PI (+ a b))
68.0ms	(/ PI (+ a b))

simplify2.9s

Counts

586 → 586

Iterations

Iter	Nodes
done	5000
2	4922
1	1841
0	812

prune3.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI (+ a b)) 2) b)
0.2b	(/ a (/ (/ 1 (+ a b)) 2))
0.2b	(/ PI (+ a b))
0.6b	(/ (/ PI 1) (/ a (/ (/ 1 (+ a b)) 2)))

rewrite753.0ms

Algorithm

rewrite-expression-head

Rules

11243×	`times-frac`
5275×	`*-un-lft-identity`
4367×	`add-sqr-sqrt` `add-cube-cbrt`
454×	`distribute-lft-out`
398×	`div-inv`
318×	`associate-/r/`
244×	`associate-/r*`
151×	`flip3-+` `flip-+`
102×	`add-exp-log`
81×	`div-exp`
77×	`associate-/l*`
56×	`add-cbrt-cube`
37×	`cbrt-undiv`
10×	`1-exp`
4×	`pow1` `rec-exp` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 3100

Calls

4 calls:

58.0ms	(/ (/ (/ PI (+ a b)) 2) b)
43.0ms	(/ a (/ (/ 1 (+ a b)) 2))
20.0ms	(/ PI (+ a b))
139.0ms	(/ (/ PI 1) (/ a (/ (/ 1 (+ a b)) 2)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (/ PI (+ a b)) 2) b)
63.0ms	(/ a (/ (/ 1 (+ a b)) 2))
76.0ms	(/ PI (+ a b))
117.0ms	(/ (/ PI 1) (/ a (/ (/ 1 (+ a b)) 2)))

simplify6.1s

Counts

3112 → 3112

Iterations

Iter	Nodes
done	5000
0	4546

prune19.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (/ (/ PI 1) (* (+ a b) (/ a (/ 1 2)))) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
0.2b	(/ (/ (/ PI (+ a b)) 2) b)
0.2b	(/ PI (+ a b))
0.6b	(/ (/ PI 1) (* (+ a b) (/ a (/ 1 2))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

602×	`times-frac`
386×	`*-un-lft-identity`
282×	`add-sqr-sqrt`
270×	`add-cube-cbrt`
89×	`add-exp-log`
79×	`associate-/l*`
56×	`div-exp`
52×	`distribute-lft-out`
49×	`add-cbrt-cube`
33×	`associate-/r/`
26×	`cbrt-undiv`
22×	`div-inv`
16×	`flip3-+` `flip-+`
15×	`prod-exp`
13×	`associate-/r*`
9×	`1-exp`
6×	`distribute-rgt-neg-in` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
5×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
3×	`rec-exp` `div-sub`
2×	`frac-times` `associate-*l/`
1×	`neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `frac-add` `associate-*r/` `flip--` `distribute-neg-frac`

Counts

4 → 413

Calls

4 calls:

1.6s	(/ (+ (/ (/ PI 1) (* (+ a b) (/ a (/ 1 2)))) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
68.0ms	(/ (/ (/ PI (+ a b)) 2) b)
21.0ms	(/ PI (+ a b))
57.0ms	(/ (/ PI 1) (* (+ a b) (/ a (/ 1 2))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ (/ (/ PI 1) (* (+ a b) (/ a (/ 1 2)))) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
100.0ms	(/ (/ (/ PI (+ a b)) 2) b)
51.0ms	(/ PI (+ a b))
108.0ms	(/ (/ PI 1) (* (+ a b) (/ a (/ 1 2))))

simplify1.6s

Counts

425 → 425

Iterations

Iter	Nodes
done	5001
1	1745
0	733

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI (+ a b)) 2) b)
0.2b	(* (+ (/ (/ PI 1) (* (+ a b) (/ a (/ 1 2)))) (- (/ (/ (/ PI (+ a b)) 2) b))) (/ 1 (- b a)))
0.2b	(/ PI (+ a b))
0.6b	(/ (/ PI 1) (* (+ a b) (/ a (/ 1 2))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

594×	`times-frac`
359×	`*-un-lft-identity`
281×	`add-sqr-sqrt`
268×	`add-cube-cbrt`
96×	`add-exp-log`
74×	`associate-/l*`
57×	`div-exp`
52×	`add-cbrt-cube`
42×	`distribute-lft-out`
33×	`associate-/r/`
26×	`cbrt-undiv`
22×	`div-inv`
21×	`associate-r`
19×	`prod-exp`
17×	`flip3-+` `flip-+`
10×	`1-exp`
8×	`associate-/r*` `cbrt-unprod`
6×	`pow1`
5×	`frac-times` `associate-l` `associate-*l/`
4×	`rec-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`frac-add` `associate-*r/` `distribute-neg-frac` `associate-/l/`
1×	`distribute-rgt-neg-in` `flip3--` `pow-prod-down` `un-div-inv` `*-commutative` `flip--`

Counts

4 → 410

Calls

4 calls:

44.0ms	(/ (/ (/ PI (+ a b)) 2) b)
2.2s	(* (+ (/ (/ PI 1) (* (+ a b) (/ a (/ 1 2)))) (- (/ (/ (/ PI (+ a b)) 2) b))) (/ 1 (- b a)))
14.0ms	(/ PI (+ a b))
45.0ms	(/ (/ PI 1) (* (+ a b) (/ a (/ 1 2))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (/ (/ PI (+ a b)) 2) b)
177.0ms	(* (+ (/ (/ PI 1) (* (+ a b) (/ a (/ 1 2)))) (- (/ (/ (/ PI (+ a b)) 2) b))) (/ 1 (- b a)))
50.0ms	(/ PI (+ a b))
100.0ms	(/ (/ PI 1) (* (+ a b) (/ a (/ 1 2))))

simplify1.6s

Counts

422 → 422

Iterations

Iter	Nodes
done	5000
1	1877
0	758

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	34
3	34
2	31
1	29
0	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

9533×

body

valid