Details

sample86.0ms

Algorithm

intervals

Results

66.0ms

312×

body

valid

simplify2.0s

Counts: 1 → 1

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

232×	`times-frac`
159×	`*-un-lft-identity`
149×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
36×	`associate-/l*`
35×	`distribute-lft-out--`
28×	`difference-of-squares`
23×	`div-inv`
22×	`add-cbrt-cube` `add-exp-log`
19×	`distribute-lft-out`
14×	`associate-/r/`
12×	`associate-*r/`
11×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
7×	`flip3--` `flip--`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`
3×	`div-sub`
2×	`prod-exp` `cbrt-unprod`
1×	`flip3-+` `frac-sub` `flip-+`

Counts

4 → 217

Calls

4 calls:

Slowest

71.0ms	(/ (- (/ PI a) (/ PI b)) (* 2 (- b a)))
47.0ms	(/ (/ (- (/ PI a) (/ PI b)) (* 2 (- b a))) (+ a b))
10.0ms	(/ PI a)
7.0ms	(/ PI b)

series286.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(/ (/ (- (/ PI a) (/ PI b)) (* 2 (- b a))) (+ a b))
78.0ms	(/ (- (/ PI a) (/ PI b)) (* 2 (- b a)))
38.0ms	(/ PI b)
37.0ms	(/ PI a)

simplify1.1s

Counts: 229 → 229

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.9b	(/ PI (* a b))
0.2b	(/ (* 1/2 (/ PI (* a b))) (+ a b))
0.0b	(* 1/2 (/ PI (* a b)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `times-frac` `div-exp` `add-cube-cbrt`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`associate-l` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr` `associate-/l/`

Counts

3 → 81

Calls

3 calls:

Slowest

23.0ms	(/ (* 1/2 (/ PI (* a b))) (+ a b))
21.0ms	(* 1/2 (/ PI (* a b)))
6.0ms	(/ PI (* a b))

series170.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

93.0ms	(/ (* 1/2 (/ PI (* a b))) (+ a b))
52.0ms	(* 1/2 (/ PI (* a b)))
25.0ms	(/ PI (* a b))

simplify3.3s

Counts: 90 → 90

prune693.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI a)
0.2b	(/ (/ PI a) b)
0.2b	(/ (* 1/2 (/ (/ PI a) b)) (+ a b))
0.0b	(* 1/2 (/ (/ PI a) b))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
101×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
92×	`add-cube-cbrt`
43×	`associate-r`
34×	`add-cbrt-cube` `add-exp-log`
17×	`associate-/l*`
14×	`cbrt-undiv` `div-exp`
11×	`div-inv`
10×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `unswap-sqr`
2×	`associate-*r/` `associate-/r/` `distribute-lft-out` `associate-/l/`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 196

Calls

4 calls:

Slowest

32.0ms	(/ (* 1/2 (/ (/ PI a) b)) (+ a b))
24.0ms	(* 1/2 (/ (/ PI a) b))
14.0ms	(/ (/ PI a) b)
8.0ms	(/ PI a)

series178.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(/ (* 1/2 (/ (/ PI a) b)) (+ a b))
44.0ms	(* 1/2 (/ (/ PI a) b))
31.0ms	(/ PI a)
23.0ms	(/ (/ PI a) b)

simplify1.2s

Counts: 208 → 208

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ PI (* a b))
0.2b	(* (* 1/2 (/ PI (* a b))) (/ 1 (+ a b)))
0.0b	(* 1/2 (/ PI (* a b)))
0.0b	(/ 1 (+ a b))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
52×	`add-cbrt-cube`
40×	`*-un-lft-identity`
37×	`prod-exp`
30×	`times-frac`
28×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`associate-r`
22×	`div-exp`
21×	`cbrt-unprod`
13×	`cbrt-undiv`
12×	`pow1`
7×	`distribute-lft-out`
6×	`associate-/l*`
5×	`rec-exp` `associate-/r*` `1-exp`
4×	`associate-l` `pow-prod-down` `associate-*r/` `associate-/r/` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `*-commutative` `flip-+`
1×	`frac-times` `associate-*l/` `un-div-inv` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

Slowest

94.0ms	(* (* 1/2 (/ PI (* a b))) (/ 1 (+ a b)))
33.0ms	(* 1/2 (/ PI (* a b)))
14.0ms	(/ 1 (+ a b))
12.0ms	(/ PI (* a b))

series224.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(* (* 1/2 (/ PI (* a b))) (/ 1 (+ a b)))
58.0ms	(/ 1 (+ a b))
44.0ms	(* 1/2 (/ PI (* a b)))
22.0ms	(/ PI (* a b))

simplify725.0ms

Counts: 158 → 158

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

2.0s

9545×

body

valid