Details

sample66.0ms

Algorithm

intervals

Results

52.0ms

301×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
5	4980
4	1403
3	361
2	93
1	31
0	15

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a)) (- b a))
0.2b	(/ (/ PI (* (+ a b) 2)) a)
0.4b	(/ PI (* (+ a b) 2))
0.4b	(/ PI (* (+ a b) 2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/l*`
14×	`associate-/r/`
12×	`associate-*l/`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
8×	`div-inv`
6×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`prod-exp` `cbrt-unprod`
1×	`flip3--` `flip--` `associate-/l/`

Counts

4 → 151

Calls

4 calls:

8.0ms	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a)) (- b a))
16.0ms	(/ (/ PI (* (+ a b) 2)) a)
10.0ms	(/ PI (* (+ a b) 2))
26.0ms	(/ PI (* (+ a b) 2))

series410.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a)) (- b a))
112.0ms	(/ (/ PI (* (+ a b) 2)) a)
64.0ms	(/ PI (* (+ a b) 2))
96.0ms	(/ PI (* (+ a b) 2))

simplify3.7s

Counts

163 → 163

Iterations

Iter	Nodes
3	6763
2	1466
1	505
0	223

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
0.2b	(* a (* (+ a b) 2))
0.3b	(/ PI (* a (* (+ a b) 2)))
0.4b	(/ PI (* (+ a b) 2))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`add-cbrt-cube` `add-exp-log`
21×	`times-frac`
19×	`add-cube-cbrt`
9×	`pow1` `associate-/l*`
7×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/r/`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`clear-num` `frac-2neg` `flip3-+` `associate-l` `pow-prod-down` `flip-+` `div-inv`
1×	`flip3--` `associate-r` `*-commutative` `flip--`

Counts

4 → 117

Calls

4 calls:

17.0ms	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
26.0ms	(* a (* (+ a b) 2))
34.0ms	(/ PI (* a (* (+ a b) 2)))
19.0ms	(/ PI (* (+ a b) 2))

series393.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
47.0ms	(* a (* (+ a b) 2))
115.0ms	(/ PI (* a (* (+ a b) 2)))
103.0ms	(/ PI (* (+ a b) 2))

simplify3.8s

Counts

129 → 129

Iterations

Iter	Nodes
3	7804
2	1405
1	425
0	190

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* a (* (+ a b) 2)) PI)
0.2b	(/ 1 (/ (* a (* (+ a b) 2)) PI))
0.2b	(* a (* (+ a b) 2))
0.4b	(/ PI (* (+ a b) 2))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
39×	`times-frac`
37×	`add-cbrt-cube`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`div-exp`
16×	`prod-exp`
12×	`cbrt-undiv`
11×	`associate-/r*`
10×	`pow1` `cbrt-unprod`
7×	`div-inv` `associate-/l*`
6×	`associate-*l/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `flip3-+` `associate-l` `pow-prod-down` `associate-/r/` `flip-+`
2×	`associate-/l/`
1×	`associate-r` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 140

Calls

4 calls:

25.0ms	(/ (* a (* (+ a b) 2)) PI)
45.0ms	(/ 1 (/ (* a (* (+ a b) 2)) PI))
24.0ms	(* a (* (+ a b) 2))
18.0ms	(/ PI (* (+ a b) 2))

series371.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (* a (* (+ a b) 2)) PI)
84.0ms	(/ 1 (/ (* a (* (+ a b) 2)) PI))
62.0ms	(* a (* (+ a b) 2))
97.0ms	(/ PI (* (+ a b) 2))

simplify12.4s

Counts

152 → 152

Iterations

Iter	Nodes
3	10666
2	1885
1	526
0	206

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ PI (* (+ a b) 2))
19.9b	(cbrt (/ PI (* a (* (+ a b) 2))))
19.9b	(cbrt (/ PI (* a (* (+ a b) 2))))
19.9b	(cbrt (/ PI (* a (* (+ a b) 2))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-*l/` `associate-/r/`
6×	`associate-*r/`
4×	`expm1-log1p-u` `pow1` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod`

Counts

4 → 89

Calls

4 calls:

15.0ms	(/ PI (* (+ a b) 2))
16.0ms	(cbrt (/ PI (* a (* (+ a b) 2))))
17.0ms	(cbrt (/ PI (* a (* (+ a b) 2))))
22.0ms	(cbrt (/ PI (* a (* (+ a b) 2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ PI (* (+ a b) 2))
468.0ms	(cbrt (/ PI (* a (* (+ a b) 2))))
505.0ms	(cbrt (/ PI (* a (* (+ a b) 2))))
504.0ms	(cbrt (/ PI (* a (* (+ a b) 2))))

simplify903.0ms

Counts

101 → 101

Iterations

Iter	Nodes
3	2306
2	720
1	287
0	130

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample2.5s

Algorithm

intervals

Results

2.2s

9595×

body

valid