Details

sample82.0ms

Algorithm

intervals

Results

65.0ms

296×

body

valid

simplify373.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

373.0ms

(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize37.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
3.8b	(- (* b b) (* a a))
0.4b	(/ PI (- (* b b) (* a a)))
0.2b	(/ 2 (- (/ 1 a) (/ 1 b)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

4182×	`times-frac`
2580×	`add-sqr-sqrt`
2092×	`*-un-lft-identity`
1116×	`add-cube-cbrt`
749×	`difference-of-squares`
427×	`distribute-lft-out--`
331×	`div-inv`
193×	`associate-/r/`
87×	`associate-/r*` `flip3--` `flip--`
24×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log` `frac-sub`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg`
1×	`sub-neg` `diff-log` `associate-/l/`

Counts

4 → 1398

Calls

4 calls:

Slowest

48.0ms	(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
30.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))
27.0ms	(/ PI (- (* b b) (* a a)))
15.0ms	(- (* b b) (* a a))

series318.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
56.0ms	(/ PI (- (* b b) (* a a)))
56.0ms	(- (* b b) (* a a))
53.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))

simplify7.6m

Counts

2582 → 1410

Calls

2582 calls:

Slowest

917.0ms	(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
885.0ms	(/ (/ (* (cbrt PI) (cbrt PI)) 1) (/ (* (cbrt 2) (cbrt 2)) 1))
823.0ms	(/ (/ (* (cbrt PI) (cbrt PI)) (sqrt (- (* b b) (* a a)))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt (- (/ 1 a) (/ 1 b))) (cbrt (- (/ 1 a) (/ 1 b))))))
793.0ms	(/ (/ (* (cbrt PI) (cbrt PI)) 1) (/ (* (cbrt 2) (cbrt 2)) 1))
762.0ms	(/ (/ (* (cbrt PI) (cbrt PI)) 1) (/ 1 (+ (/ 1 (sqrt a)) (/ 1 (sqrt b)))))

prune10.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

133452×	`times-frac`
72705×	`add-sqr-sqrt`
70669×	`*-un-lft-identity`
34603×	`add-cube-cbrt`
15250×	`difference-of-squares`
12716×	`distribute-lft-out--`
8143×	`div-inv`
6551×	`associate-/r/`
4050×	`distribute-lft-out`
1704×	`flip3--` `flip--`
1394×	`associate-/r*`
1350×	`flip3-+` `flip-+`
422×	`frac-sub`
97×	`add-exp-log`
88×	`associate-/l*`
72×	`div-exp`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
5×	`rec-exp` `1-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 27275

Calls

4 calls:

Slowest

102.0ms	(/ (/ 1 (+ b a)) (/ (/ 2 (- (/ 1 a) (/ 1 b))) (/ PI (- b a))))
39.0ms	(/ (/ 2 (- (/ 1 a) (/ 1 b))) (/ PI (- b a)))
16.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))
8.0ms	(/ PI (- b a))

series226.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

77.0ms	(/ (/ 1 (+ b a)) (/ (/ 2 (- (/ 1 a) (/ 1 b))) (/ PI (- b a))))
53.0ms	(/ (/ 2 (- (/ 1 a) (/ 1 b))) (/ PI (- b a)))
52.0ms	(/ PI (- b a))
44.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))