Details

sample182.0ms

Algorithm

intervals

Results

150.0ms

431×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1089
2	240
1	74
0	28

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b	(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite1.8m

Algorithm

rewrite-expression-head

Rules

4476×	`associate-*l/`
4446×	`frac-add`
2586×	`associate-/r*`
2184×	`frac-times`
2037×	`associate-/l*`
1829×	`add-sqr-sqrt`
1749×	`*-un-lft-identity`
1592×	`add-cube-cbrt`
1183×	`flip3-+` `flip-+`
679×	`clear-num` `frac-2neg`
563×	`sqrt-prod`
256×	`associate-l`
182×	`associate-*r/`
162×	`unswap-sqr`
155×	`associate-r`
129×	`distribute-lft-out`
119×	`add-exp-log`
76×	`prod-exp`
75×	`add-cbrt-cube`
64×	`times-frac`
44×	`cbrt-unprod`
36×	`pow1`
34×	`div-inv`
22×	`pow-prod-down`
18×	`*-commutative`
15×	`swap-sqr` `div-exp`
12×	`associate-+l+`
9×	`cbrt-undiv`
6×	`distribute-rgt-in` `+-commutative` `rec-exp` `distribute-lft-in` `1-exp`
4×	`insert-posit16` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 2735

Calls

4 calls:

1.8m	(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
2.3s	(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
162.0ms	(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series512.0ms

Counts

4 → 10

Calls

4 calls:

377.0ms	(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
79.0ms	(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
56.0ms	(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify10.4s

Counts

2745 → 2745

Iterations

Iter	Nodes
done	5000
0	3440

prune20.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/21 (pow (fabs x) 7))
0.1b	(* (sqrt (/ 1 PI)) (+ (* 1/5 (pow (fabs x) 5)) (+ (* 2 (fabs x)) (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))))))
0.2b	(* 1/5 (pow (fabs x) 5))
0.2b	(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))

rewrite12.3s

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
85×	`associate-r`
81×	`add-sqr-sqrt`
68×	`associate-l`
58×	`distribute-lft-out`
33×	`add-cube-cbrt`
29×	`unswap-sqr`
27×	`sqrt-div`
25×	`add-exp-log`
19×	`pow1` `add-cbrt-cube`
18×	`frac-times`
16×	`sqrt-prod`
13×	`prod-exp`
12×	`associate-+r+`
11×	`times-frac`
10×	`flip3-+` `flip-+`
9×	`associate-/r` `pow-prod-down` `associate-l/` `cbrt-unprod` `associate-/l*`
8×	`unpow-prod-down` `*-commutative`
6×	`distribute-rgt-in` `+-commutative` `distribute-lft-in`
5×	`swap-sqr`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-exp` `associate-*r/`
1×	`div-inv`

Counts

4 → 207

Calls

4 calls:

24.0ms	(* 1/21 (pow (fabs x) 7))
12.1s	(* (sqrt (/ 1 PI)) (+ (* 1/5 (pow (fabs x) 5)) (+ (* 2 (fabs x)) (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))))))
27.0ms	(* 1/5 (pow (fabs x) 5))
126.0ms	(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* 1/21 (pow (fabs x) 7))
380.0ms	(* (sqrt (/ 1 PI)) (+ (* 1/5 (pow (fabs x) 5)) (+ (* 2 (fabs x)) (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))))))
85.0ms	(* 1/5 (pow (fabs x) 5))
52.0ms	(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))

simplify2.8s

Counts

219 → 219

Iterations

Iter	Nodes
done	5000
2	3895
1	1085
0	348

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (* (cbrt PI) (cbrt PI)))
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
81×	`times-frac`
73×	`cbrt-prod`
71×	`*-un-lft-identity` `add-cube-cbrt`
27×	`associate-/r*`
24×	`swap-sqr` `associate-r` `associate-l`
16×	`unswap-sqr`
15×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
9×	`pow1/3` `pow-flip`
5×	`cbrt-undiv`
4×	`div-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`prod-exp` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `div-inv` `inv-pow`

Counts

4 → 179

Calls

4 calls:

41.0ms	(/ 1 (* (cbrt PI) (cbrt PI)))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ 1 (* (cbrt PI) (cbrt PI)))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify2.4s

Counts

183 → 183

Iterations

Iter	Nodes
done	5010
3	2736
2	1061
1	509
0	191

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))
0.2b	(* 2/3 (* (fabs x) (fabs x)))
0.3b	(/ (* (fabs x) (+ (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (+ (* (* (fabs x) (fabs x)) 1/21) 1/5)) (+ (* 2/3 (* (fabs x) (fabs x))) 2))) (sqrt PI))
1.0b	(sqrt PI)

rewrite23.0s

Algorithm

rewrite-expression-head

Rules

330×	`*-un-lft-identity`
210×	`associate-l`
195×	`add-sqr-sqrt`
150×	`associate-r`
144×	`times-frac`
140×	`distribute-lft-out`
121×	`pow1`
102×	`add-cube-cbrt`
78×	`sqrt-prod`
55×	`unswap-sqr`
49×	`swap-sqr`
36×	`pow-prod-up`
27×	`*-commutative`
26×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
24×	`associate-/l*`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
10×	`associate-*r/`
6×	`associate-/r*` `associate-/l/`
5×	`flip3-+` `flip-+`
4×	`frac-add` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 383

Calls

4 calls:

76.0ms	(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))
32.0ms	(* 2/3 (* (fabs x) (fabs x)))
22.9s	(/ (* (fabs x) (+ (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (+ (* (* (fabs x) (fabs x)) 1/21) 1/5)) (+ (* 2/3 (* (fabs x) (fabs x))) 2))) (sqrt PI))
1.0ms	(sqrt PI)

series394.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))
43.0ms	(* 2/3 (* (fabs x) (fabs x)))
322.0ms	(/ (* (fabs x) (+ (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (+ (* (* (fabs x) (fabs x)) 1/21) 1/5)) (+ (* 2/3 (* (fabs x) (fabs x))) 2))) (sqrt PI))
0.0ms	(sqrt PI)

simplify3.8s

Counts

393 → 393

Iterations

Iter	Nodes
done	5000
2	3822
1	1056
0	335

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes154.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	25

end0.0ms

sample5.0s

Algorithm

intervals

Results

4.7s

13701×

body

valid