Details

sample60.0ms

Algorithm

intervals

Results

45.0ms

300×

body

valid

simplify1.9s

Counts: 1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

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

74.0ms	(/ (/ (- (/ PI a) (/ PI b)) (* 2 (- b a))) (+ a b))
68.0ms	(/ (- (/ PI a) (/ PI b)) (* 2 (- b a)))
7.0ms	(/ PI a)
7.0ms	(/ PI b)

series304.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(/ (/ (- (/ PI a) (/ PI b)) (* 2 (- b a))) (+ a b))
92.0ms	(/ (- (/ PI a) (/ PI b)) (* 2 (- b a)))
45.0ms	(/ PI a)
45.0ms	(/ PI b)

simplify1.1s

Counts: 229 → 229

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.7b	(/ PI (* a b))
0.2b	(/ (* 1/2 (/ PI (* a b))) (+ a b))
0.0b	(* 1/2 (/ PI (* a b)))

rewrite57.0ms

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

29.0ms	(/ (* 1/2 (/ PI (* a b))) (+ a b))
21.0ms	(* 1/2 (/ PI (* a b)))
6.0ms	(/ PI (* a b))

series145.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

85.0ms	(/ (* 1/2 (/ PI (* a b))) (+ a b))
38.0ms	(* 1/2 (/ PI (* a b)))
22.0ms	(/ PI (* a b))

simplify3.2s

Counts: 90 → 90

prune732.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`times-frac`
34×	`add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
21×	`associate-r`
12×	`associate-l`
10×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/l*` `difference-of-squares` `associate-/l/`
6×	`frac-times` `pow1` `associate-*l/` `div-inv`
5×	`flip3--` `flip--`
4×	`prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-*r/` `distribute-lft-out` `unswap-sqr`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 147

Calls

4 calls:

Slowest

68.0ms	(/ (* (- (/ PI a) (/ PI b)) (/ 1/2 (- b a))) (+ a b))
66.0ms	(* (- (/ PI a) (/ PI b)) (/ 1/2 (- b a)))
7.0ms	(/ PI b)
7.0ms	(/ PI a)

series337.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(/ (* (- (/ PI a) (/ PI b)) (/ 1/2 (- b a))) (+ a b))
103.0ms	(* (- (/ PI a) (/ PI b)) (/ 1/2 (- b a)))
46.0ms	(/ PI a)
42.0ms	(/ PI b)

simplify865.0ms

Counts: 159 → 159

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite711.0ms

Algorithm

rewrite-expression-head

Rules

2712×	`times-frac`
2221×	`add-sqr-sqrt`
2190×	`*-un-lft-identity`
659×	`difference-of-squares`
570×	`add-cube-cbrt`
555×	`distribute-lft-out--`
410×	`associate-r`
221×	`div-inv`
203×	`distribute-lft-out`
120×	`associate-/l*`
32×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r/`
13×	`cbrt-undiv` `div-exp` `associate-l`
12×	`flip3--` `flip--`
9×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`insert-posit16` `associate-/l/`
3×	`div-sub`
2×	`clear-num` `frac-2neg` `flip3-+` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1150

Calls

4 calls:

Slowest

425.0ms	(/ (/ (- (/ 1 a) (/ 1 b)) (- b a)) (+ a b))
112.0ms	(* (/ PI 2) (/ (/ (- (/ 1 a) (/ 1 b)) (- b a)) (+ a b)))
68.0ms	(/ (- (/ 1 a) (/ 1 b)) (- b a))
21.0ms	(- (/ 1 a) (/ 1 b))

series267.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(* (/ PI 2) (/ (/ (- (/ 1 a) (/ 1 b)) (- b a)) (+ a b)))
91.0ms	(/ (/ (- (/ 1 a) (/ 1 b)) (- b a)) (+ a b))
36.0ms	(/ (- (/ 1 a) (/ 1 b)) (- b a))
14.0ms	(- (/ 1 a) (/ 1 b))

simplify2.1s

Counts: 1162 → 1162

prune13.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes133.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

2.1s

9597×

body

valid