Details

sample88.0ms

Algorithm

intervals

Results

73.0ms

306×

body

valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2014
5	2014
4	1476
3	358
2	94
1	32
0	15

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 a) (/ 1 b))
0.1b	(/ (/ PI (+ a b)) (* 2 (- b a)))
0.3b	(/ PI (+ a b))
10.1b	(* (/ (/ PI (+ a b)) (* 2 (- b a))) (- (/ 1 a) (/ 1 b)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
101×	`*-un-lft-identity`
93×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
36×	`add-cbrt-cube` `add-exp-log`
24×	`associate-l`
21×	`associate-/l*`
19×	`associate-r`
18×	`difference-of-squares`
14×	`div-inv` `distribute-lft-out--`
13×	`cbrt-undiv` `div-exp` `distribute-lft-out`
12×	`associate-/r/`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-*r/`
6×	`pow1` `add-log-exp`
5×	`associate-/r*` `flip3--` `flip--`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`frac-times` `sub-neg` `frac-sub`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`diff-log` `pow-prod-down` `associate-l/` `-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 198

Calls

4 calls:

12.0ms	(- (/ 1 a) (/ 1 b))
25.0ms	(/ (/ PI (+ a b)) (* 2 (- b a)))
18.0ms	(/ PI (+ a b))
106.0ms	(* (/ (/ PI (+ a b)) (* 2 (- b a))) (- (/ 1 a) (/ 1 b)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (/ 1 a) (/ 1 b))
85.0ms	(/ (/ PI (+ a b)) (* 2 (- b a)))
75.0ms	(/ PI (+ a b))
141.0ms	(* (/ (/ PI (+ a b)) (* 2 (- b a))) (- (/ 1 a) (/ 1 b)))

simplify1.1s

Counts

210 → 210

Iterations

Iter	Nodes
done	2002
2	2002
1	889
0	288

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 a) (/ 1 b))
0.1b	(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (* 2 (- b a)))
0.3b	(/ PI (+ a b))
0.5b	(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
62×	`times-frac`
32×	`add-cbrt-cube` `add-exp-log`
26×	`add-cube-cbrt`
19×	`associate-r`
18×	`associate-l` `difference-of-squares`
14×	`distribute-lft-out--`
11×	`div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-*r/`
7×	`distribute-lft-out` `associate-/l/`
6×	`frac-times` `pow1` `flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`associate-/r*` `frac-sub`
4×	`insert-posit16` `associate-/l*`
3×	`sub-neg`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-*l/` `flip-+` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 163

Calls

4 calls:

12.0ms	(- (/ 1 a) (/ 1 b))
30.0ms	(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (* 2 (- b a)))
8.0ms	(/ PI (+ a b))
86.0ms	(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (/ 1 a) (/ 1 b))
130.0ms	(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (* 2 (- b a)))
74.0ms	(/ PI (+ a b))
94.0ms	(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))

simplify1.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	2002
2	2002
1	790
0	247

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (/ PI (+ b a)) (- b a)) (* a b)) (* 2 (- b a)))
0.3b	(/ PI (+ b a))
0.3b	(* (/ PI (+ b a)) (- b a))
1.2b	(/ (* (/ PI (+ b a)) (- b a)) (* a b))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 166

Calls

4 calls:

34.0ms	(/ (/ (* (/ PI (+ b a)) (- b a)) (* a b)) (* 2 (- b a)))
16.0ms	(/ PI (+ b a))
41.0ms	(* (/ PI (+ b a)) (- b a))
33.0ms	(/ (* (/ PI (+ b a)) (- b a)) (* a b))

series439.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (* (/ PI (+ b a)) (- b a)) (* a b)) (* 2 (- b a)))
53.0ms	(/ PI (+ b a))
115.0ms	(* (/ PI (+ b a)) (- b a))
169.0ms	(/ (* (/ PI (+ b a)) (- b a)) (* a b))

simplify1.1s

Counts

178 → 178

Iterations

Iter	Nodes
done	2002
2	2002
1	695
0	238

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* PI (/ (- b a) (+ a b)))
0.0b	(/ (- b a) (+ a b))
0.1b	(/ (/ (* PI (/ (- b a) (+ a b))) (* a b)) (* 2 (- b a)))
1.2b	(/ (* PI (/ (- b a) (+ a b))) (* a b))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-cbrt-cube` `add-exp-log`
68×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
49×	`times-frac`
40×	`cbrt-undiv` `div-exp`
30×	`prod-exp` `cbrt-unprod`
28×	`add-cube-cbrt`
26×	`associate-r`
11×	`distribute-lft-out` `associate-/l*`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `associate-/r*` `associate-/r/` `div-inv`
4×	`associate-*r/` `insert-posit16` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`flip3-+` `flip3--` `flip-+` `flip--` `unswap-sqr`
1×	`div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 173

Calls

4 calls:

39.0ms	(* PI (/ (- b a) (+ a b)))
17.0ms	(/ (- b a) (+ a b))
48.0ms	(/ (/ (* PI (/ (- b a) (+ a b))) (* a b)) (* 2 (- b a)))
28.0ms	(/ (* PI (/ (- b a) (+ a b))) (* a b))

series523.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* PI (/ (- b a) (+ a b)))
105.0ms	(/ (- b a) (+ a b))
107.0ms	(/ (/ (* PI (/ (- b a) (+ a b))) (* a b)) (* 2 (- b a)))
190.0ms	(/ (* PI (/ (- b a) (+ a b))) (* a b))

simplify1.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	2001
2	2001
1	690
0	239

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes155.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample2.5s

Algorithm

intervals

Results

2.2s

9656×

body

valid