Details

sample68.0ms

Algorithm

intervals

Results

55.0ms

300×

body

valid

simplify2.1s

Counts: 1 → 1

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize58.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (- (/ PI a) (/ PI b)) (* (- (* b b) (* a a)) 2))
3.2b	(- (* b b) (* a a))
0.3b	(/ PI b)
0.3b	(/ PI a)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `times-frac`
42×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`associate-/l*`
13×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`associate-/r*` `div-inv`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp` `insert-posit16`
3×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
2×	`associate-*l/` `associate-/r/`
1×	`sub-neg` `diff-log` `div-sub` `prod-exp` `frac-sub` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

Slowest

76.0ms	(/ (- (/ PI a) (/ PI b)) (* (- (* b b) (* a a)) 2))
14.0ms	(- (* b b) (* a a))
7.0ms	(/ PI a)
7.0ms	(/ PI b)

series214.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(/ (- (/ PI a) (/ PI b)) (* (- (* b b) (* a a)) 2))
49.0ms	(- (* b b) (* a a))
34.0ms	(/ PI b)
25.0ms	(/ PI a)

simplify617.0ms

Counts: 128 → 128

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize38.0ms

Local error

Found 4 expressions with local error:

8.8b	(* (/ (/ 1 (+ a b)) (- b a)) (/ (- (/ PI a) (/ PI b)) 2))
0.3b	(/ PI b)
0.3b	(/ PI a)
0.1b	(/ (/ 1 (+ a b)) (- b a))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

410×	`times-frac`
334×	`*-un-lft-identity`
306×	`add-sqr-sqrt`
168×	`add-cube-cbrt`
96×	`associate-l`
52×	`add-exp-log` `distribute-lft-out--`
49×	`difference-of-squares`
40×	`associate-r`
34×	`add-cbrt-cube`
33×	`distribute-lft-out`
26×	`associate-/r/`
25×	`div-exp`
24×	`associate-/l*`
22×	`div-inv`
14×	`cbrt-undiv`
11×	`associate-/r*` `flip3-+` `flip-+`
10×	`prod-exp`
8×	`unswap-sqr`
6×	`pow1` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 362

Calls

4 calls:

Slowest

82.0ms	(* (/ (/ 1 (+ a b)) (- b a)) (/ (- (/ PI a) (/ PI b)) 2))
32.0ms	(/ (/ 1 (+ a b)) (- b a))
5.0ms	(/ PI a)
4.0ms	(/ PI b)

series284.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(* (/ (/ 1 (+ a b)) (- b a)) (/ (- (/ PI a) (/ PI b)) 2))
88.0ms	(/ (/ 1 (+ a b)) (- b a))
44.0ms	(/ PI a)
35.0ms	(/ PI b)

simplify706.0ms

Counts: 374 → 374

prune4.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
50×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`times-frac`
34×	`add-cbrt-cube`
31×	`add-cube-cbrt`
18×	`div-exp` `associate-l`
17×	`prod-exp`
12×	`associate-r`
11×	`cbrt-undiv`
9×	`cbrt-unprod`
7×	`associate-/r` `associate-/l` `associate-/l/`
6×	`frac-times` `pow1` `associate-*r/` `div-inv`
5×	`flip3--` `flip--` `distribute-lft-out--`
4×	`associate-*l/` `associate-/r/` `frac-sub` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `distribute-lft-out` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 155

Calls

4 calls:

Slowest

44.0ms	(* (/ 1 (+ a b)) (- (/ PI a) (/ PI b)))
29.0ms	(/ (* (/ 1 (+ a b)) (- (/ PI a) (/ PI b))) (* (- b a) 2))
4.0ms	(/ PI a)
4.0ms	(/ PI b)

series314.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(/ (* (/ 1 (+ a b)) (- (/ PI a) (/ PI b))) (* (- b a) 2))
105.0ms	(* (/ 1 (+ a b)) (- (/ PI a) (/ PI b)))
45.0ms	(/ PI a)
35.0ms	(/ PI b)

simplify1.4s

Counts: 167 → 167

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

1050×	`times-frac`
550×	`*-un-lft-identity`
514×	`add-sqr-sqrt`
262×	`add-cube-cbrt`
105×	`distribute-lft-out--`
101×	`associate-/r/`
85×	`div-inv`
84×	`difference-of-squares`
60×	`distribute-lft-out`
52×	`add-exp-log`
37×	`associate-/r*`
34×	`add-cbrt-cube`
30×	`div-exp`
25×	`associate-/l*`
21×	`flip3--` `flip--`
20×	`flip3-+` `frac-sub` `flip-+`
17×	`cbrt-undiv`
5×	`prod-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
3×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l/`
2×	`associate-*l/`

Counts

4 → 511

Calls

4 calls:

Slowest

43.0ms	(/ (/ 1 (+ a b)) (/ (* (- b a) 2) (- (/ PI a) (/ PI b))))
33.0ms	(/ (* (- b a) 2) (- (/ PI a) (/ PI b)))
7.0ms	(/ PI a)
4.0ms	(/ PI b)

series304.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(/ (/ 1 (+ a b)) (/ (* (- b a) 2) (- (/ PI a) (/ PI b))))
83.0ms	(/ (* (- b a) 2) (- (/ PI a) (/ PI b)))
43.0ms	(/ PI b)
35.0ms	(/ PI a)

simplify1.3s

Counts: 523 → 523

prune6.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.7s

9589×

body

valid