Details

sample57.0ms

Algorithm

intervals

Results

42.0ms

311×

body

valid

simplify2.7s

Counts: 1 → 1

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize26.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (- (/ PI a) (/ PI b)) (/ (- (* b b) (* a a)) 1/2))
4.3b	(- (* b b) (* a a))
0.3b	(/ PI a)
0.3b	(/ PI b)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

536×	`times-frac`
379×	`add-sqr-sqrt`
311×	`*-un-lft-identity`
175×	`add-cube-cbrt`
108×	`difference-of-squares`
85×	`distribute-lft-out--`
50×	`div-inv`
22×	`associate-/r*`
18×	`associate-/l*`
13×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `associate-/r/` `frac-sub`

Counts

4 → 320

Calls

4 calls:

Slowest

39.0ms	(/ (- (/ PI a) (/ PI b)) (/ (- (* b b) (* a a)) 1/2))
12.0ms	(- (* b b) (* a a))
11.0ms	(/ PI b)
7.0ms	(/ PI a)

series249.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(/ (- (/ PI a) (/ PI b)) (/ (- (* b b) (* a a)) 1/2))
56.0ms	(- (* b b) (* a a))
34.0ms	(/ PI b)
25.0ms	(/ PI a)

simplify845.0ms

Counts: 332 → 332

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (/ PI a) (/ PI b)) (/ (- b a) 1/2))
0.3b	(/ PI a)
0.3b	(/ PI b)
0.2b	(* (/ 1 (+ a b)) (/ (- (/ PI a) (/ PI b)) (/ (- b a) 1/2)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

1266×	`times-frac`
1019×	`add-sqr-sqrt`
842×	`*-un-lft-identity`
371×	`add-cube-cbrt`
270×	`distribute-lft-out--`
233×	`associate-r`
231×	`difference-of-squares`
108×	`div-inv`
52×	`add-exp-log`
34×	`add-cbrt-cube`
25×	`associate-/r*`
23×	`div-exp`
18×	`associate-l` `associate-/l*`
14×	`cbrt-undiv`
12×	`prod-exp`
9×	`unswap-sqr`
6×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `distribute-lft-out` `associate-/l/`
1×	`frac-times` `flip3-+` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `frac-sub` `flip-+` `flip--`

Counts

4 → 634

Calls

4 calls:

Slowest

92.0ms	(* (/ 1 (+ a b)) (/ (- (/ PI a) (/ PI b)) (/ (- b a) 1/2)))
68.0ms	(/ (- (/ PI a) (/ PI b)) (/ (- b a) 1/2))
7.0ms	(/ PI b)
7.0ms	(/ PI a)

series306.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(* (/ 1 (+ a b)) (/ (- (/ PI a) (/ PI b)) (/ (- b a) 1/2)))
103.0ms	(/ (- (/ PI a) (/ PI b)) (/ (- b a) 1/2))
51.0ms	(/ PI b)
43.0ms	(/ PI a)

simplify1.6s

Counts: 646 → 646

prune7.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (/ PI a) (/ 1 (/ b PI))) (/ (- b a) 1/2))
0.3b	(/ 1 (/ b PI))
0.3b	(/ PI a)
0.2b	(* (/ 1 (+ a b)) (/ (- (/ PI a) (/ 1 (/ b PI))) (/ (- b a) 1/2)))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

1955×	`times-frac`
1914×	`add-sqr-sqrt`
1035×	`*-un-lft-identity`
489×	`difference-of-squares`
399×	`add-cube-cbrt`
309×	`associate-r`
216×	`distribute-lft-out--`
81×	`div-inv`
61×	`add-exp-log`
37×	`add-cbrt-cube`
35×	`associate-/r*`
29×	`div-exp`
22×	`associate-/l*`
18×	`associate-l`
16×	`cbrt-undiv`
12×	`prod-exp`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
5×	`rec-exp` `1-exp` `associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `distribute-lft-out` `associate-/l/`
1×	`frac-times` `flip3-+` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `frac-sub` `flip-+` `pow-flip` `flip--` `inv-pow`

Counts

4 → 839

Calls

4 calls:

Slowest

109.0ms	(* (/ 1 (+ a b)) (/ (- (/ PI a) (/ 1 (/ b PI))) (/ (- b a) 1/2)))
90.0ms	(/ (- (/ PI a) (/ 1 (/ b PI))) (/ (- b a) 1/2))
13.0ms	(/ 1 (/ b PI))
7.0ms	(/ PI a)

series285.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(* (/ 1 (+ a b)) (/ (- (/ PI a) (/ 1 (/ b PI))) (/ (- b a) 1/2)))
114.0ms	(/ (- (/ PI a) (/ 1 (/ b PI))) (/ (- b a) 1/2))
28.0ms	(/ PI a)
26.0ms	(/ 1 (/ b PI))

simplify2.6s

Counts: 851 → 851

prune10.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

Slowest

1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify866.0ms

Counts: 60 → 60

prune935.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

2.0s

9606×

body

valid