Details

sample63.0ms

Algorithm

intervals

Results

48.0ms

305×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	1476
3	358
2	94
1	32
0	15

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.6s

Algorithm

rewrite-expression-head

Rules

23396×	`times-frac`
18627×	`*-un-lft-identity`
18274×	`associate-/l/`
15651×	`associate-/l*`
11959×	`add-sqr-sqrt`
11793×	`add-cube-cbrt`
9604×	`frac-add` `distribute-neg-frac`
3286×	`distribute-lft-out`
1983×	`associate-/r*`
1672×	`associate-/r/`
1061×	`div-inv`
836×	`flip3-+` `flip-+`
594×	`clear-num` `frac-2neg`
468×	`distribute-rgt-neg-in`
83×	`distribute-lft-out--` `difference-of-squares`
19×	`add-cbrt-cube` `add-exp-log`
9×	`cbrt-undiv` `div-exp`
4×	`pow1` `insert-posit16` `add-log-exp`
3×	`div-sub`
1×	`neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `flip--`

Counts

4 → 10475

Calls

4 calls:

10.5s	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
77.0ms	(/ (/ (/ PI (+ a b)) 2) a)
21.0ms	(/ PI (+ a b))
25.0ms	(/ PI (+ a b))

series968.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ PI (+ a b)) 2) b))) (- b a))
684.0ms	(/ (/ (/ PI (+ a b)) 2) a)
53.0ms	(/ PI (+ a b))
100.0ms	(/ PI (+ a b))

simplify12.5s

Counts

10487 → 10487

Iterations

Iter	Nodes
done	12215
0	12215

prune59.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

14880×	`associate-/l*`
14485×	`*-un-lft-identity`
12876×	`associate-/l/`
11881×	`times-frac`
10315×	`add-sqr-sqrt`
10094×	`frac-times`
10014×	`add-cube-cbrt`
8181×	`frac-add` `distribute-neg-frac`
6998×	`associate-/r*`
2388×	`distribute-lft-out`
2232×	`clear-num`
2231×	`frac-2neg`
1096×	`div-inv`
856×	`associate-/r/`
781×	`distribute-rgt-neg-in`
527×	`flip3-+` `flip-+`
178×	`associate-l`
124×	`distribute-lft-out--` `difference-of-squares`
103×	`associate-*r/`
98×	`associate-*l/`
66×	`associate-r`
61×	`add-exp-log`
40×	`add-cbrt-cube`
33×	`div-exp`
18×	`cbrt-undiv`
14×	`prod-exp` `unswap-sqr`
8×	`un-div-inv` `cbrt-unprod` `add-log-exp`
6×	`pow1` `1-exp`
4×	`insert-posit16`
3×	`div-sub`
2×	`neg-sub0` `associate-+r-` `sum-log` `flip3--` `unsub-neg` `flip--`
1×	`+-commutative` `pow-prod-down` `neg-log` `*-commutative`

Counts

4 → 10911

Calls

4 calls:

54.0ms	(+ (/ 1 a) (- (/ 1 b)))
1.1s	(* (/ (/ (/ PI (+ a b)) 2) 1) (/ (+ (/ 1 a) (- (/ 1 b))) (- b a)))
256.0ms	(/ (+ (/ 1 a) (- (/ 1 b))) (- b a))
21.0ms	(/ PI (+ a b))

series277.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (/ 1 a) (- (/ 1 b)))
135.0ms	(* (/ (/ (/ PI (+ a b)) 2) 1) (/ (+ (/ 1 a) (- (/ 1 b))) (- b a)))
46.0ms	(/ (+ (/ 1 a) (- (/ 1 b))) (- b a))
70.0ms	(/ PI (+ a b))

simplify14.2s

Counts

10923 → 10923

Iterations

Iter	Nodes
done	11547
0	11547

prune54.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (/ (/ (/ 1 (+ a b)) 2) a) (- (/ (/ (/ 1 (+ a b)) 2) b))) (- b a))
0.2b	(/ (/ (/ 1 (+ a b)) 2) b)
0.2b	(/ (/ (/ 1 (+ a b)) 2) a)
0.2b	(* (/ (/ (/ PI 1) 1) 1) (/ (+ (/ (/ (/ 1 (+ a b)) 2) a) (- (/ (/ (/ 1 (+ a b)) 2) b))) (- b a)))

rewrite4.6m

Algorithm

rewrite-expression-head

Rules

2347567×	`times-frac`
1802826×	`associate-/l*`
1799269×	`associate-/l/`
1735875×	`*-un-lft-identity`
1309705×	`add-sqr-sqrt`
1309086×	`add-cube-cbrt`
758716×	`frac-add` `distribute-neg-frac`
747054×	`frac-times`
242582×	`associate-/r*`
212143×	`distribute-lft-out`
127410×	`div-inv`
124996×	`associate-/r/`
75647×	`clear-num`
75646×	`frac-2neg`
62575×	`flip3-+` `flip-+`
9702×	`associate-*r/`
7477×	`distribute-rgt-neg-in`
446×	`associate-r`
255×	`distribute-lft-out--` `difference-of-squares`
145×	`add-exp-log`
133×	`associate-l`
106×	`div-exp`
77×	`associate-*l/`
56×	`add-cbrt-cube`
36×	`1-exp`
30×	`prod-exp` `unswap-sqr`
29×	`cbrt-undiv`
8×	`cbrt-unprod`
6×	`pow1`
4×	`un-div-inv` `insert-posit16` `add-log-exp`
3×	`div-sub`
2×	`rec-exp` `flip3--` `flip--`
1×	`neg-sub0` `associate-+r-` `unsub-neg` `pow-prod-down` `*-commutative`

Counts

4 → 768227

Calls

4 calls:

10.0s	(/ (+ (/ (/ (/ 1 (+ a b)) 2) a) (- (/ (/ (/ 1 (+ a b)) 2) b))) (- b a))
103.0ms	(/ (/ (/ 1 (+ a b)) 2) b)
64.0ms	(/ (/ (/ 1 (+ a b)) 2) a)
55.7s	(* (/ (/ (/ PI 1) 1) 1) (/ (+ (/ (/ (/ 1 (+ a b)) 2) a) (- (/ (/ (/ 1 (+ a b)) 2) b))) (- b a)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (+ (/ (/ (/ 1 (+ a b)) 2) a) (- (/ (/ (/ 1 (+ a b)) 2) b))) (- b a))
46.0ms	(/ (/ (/ 1 (+ a b)) 2) b)
48.0ms	(/ (/ (/ 1 (+ a b)) 2) a)
112.0ms	(* (/ (/ (/ PI 1) 1) 1) (/ (+ (/ (/ (/ 1 (+ a b)) 2) a) (- (/ (/ (/ 1 (+ a b)) 2) b))) (- b a)))

Details

sample63.0ms

simplify1.7s

prune12.0ms

localize33.0ms

rewrite12.6s

series968.0ms

simplify12.5s

prune59.9s

localize59.0ms

rewrite3.4s

series277.0ms

simplify14.2s

prune54.7s

localize32.0ms

rewrite4.6m

series318.0ms

simplify2.7m