Details

sample81.0ms

Algorithm

intervals

Results

65.0ms

305×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
15×	`associate-/l*`
12×	`associate-*l/` `associate-/r/`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`flip3-+` `flip-+`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

4 → 118

Calls

4 calls:

14.0ms	(/ (/ PI (* (+ a b) 2)) a)
0.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
15.0ms	(/ PI (* (+ a b) 2))
17.0ms	(/ PI (* (+ a b) 2))

series384.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (/ PI (* (+ a b) 2)) a)
139.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
68.0ms	(/ PI (* (+ a b) 2))
74.0ms	(/ PI (* (+ a b) 2))

simplify3.1s

Counts

130 → 130

Iterations

Iter	Nodes
3	6179
2	1264
1	412
0	173

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
37×	`add-exp-log`
29×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
12×	`associate-l/` `prod-exp` `associate-/r/` `associate-/l`
11×	`div-exp`
9×	`cbrt-undiv` `associate-r`
7×	`div-inv`
6×	`pow1` `flip3-+` `cbrt-unprod` `flip-+`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

27.0ms	(/ (/ PI (* (+ a b) 2)) a)
0.0ms	(fma (* PI (/ 1 (* (+ a b) 2))) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
16.0ms	(/ PI (* (+ a b) 2))
70.0ms	(* PI (/ 1 (* (+ a b) 2)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ PI (* (+ a b) 2)) a)
169.0ms	(fma (* PI (/ 1 (* (+ a b) 2))) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
62.0ms	(/ PI (* (+ a b) 2))
67.0ms	(* PI (/ 1 (* (+ a b) 2)))

simplify20.6s

Counts

141 → 141

Iterations

Iter	Nodes
3	11757
2	1985
1	559
0	228

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
35×	`add-exp-log`
24×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube`
16×	`div-exp`
11×	`associate-/r*`
9×	`cbrt-undiv`
7×	`div-inv` `associate-/l*`
5×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/r/` `cbrt-unprod`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`fma-udef` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

0.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ 1 (/ (* (+ a b) 2) PI)) a))
11.0ms	(/ (* (+ a b) 2) PI)
9.0ms	(/ PI (* (+ a b) 2))
25.0ms	(/ 1 (/ (* (+ a b) 2) PI))

series386.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ 1 (/ (* (+ a b) 2) PI)) a))
89.0ms	(/ (* (+ a b) 2) PI)
85.0ms	(/ PI (* (+ a b) 2))
85.0ms	(/ 1 (/ (* (+ a b) 2) PI))

simplify12.1s

Counts

130 → 130

Iterations

Iter	Nodes
3	9366
2	1869
1	475
0	186

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

79×	`times-frac`
56×	`add-exp-log`
46×	`add-sqr-sqrt`
41×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube`
31×	`associate-r`
24×	`div-exp`
16×	`associate-*l/` `associate-/r/`
15×	`prod-exp`
12×	`cbrt-undiv` `associate-/l*`
10×	`div-inv`
8×	`flip3-+` `flip-+`
7×	`cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `associate-/r*` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`pow-prod-down` `associate-r/` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 157

Calls

4 calls:

21.0ms	(/ (/ 1 (* (+ a b) 2)) a)
0.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (* PI (/ (/ 1 (* (+ a b) 2)) a)))
9.0ms	(/ PI (* (+ a b) 2))
61.0ms	(* PI (/ (/ 1 (* (+ a b) 2)) a))

series382.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (/ 1 (* (+ a b) 2)) a)
151.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (* PI (/ (/ 1 (* (+ a b) 2)) a)))
63.0ms	(/ PI (* (+ a b) 2))
83.0ms	(* PI (/ (/ 1 (* (+ a b) 2)) a))

simplify716.0ms

Counts

169 → 169

Iterations

Iter	Nodes
2	2106
1	657
0	251

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes182.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.5s

9559×

body

valid