Details

sample127.0ms

Algorithm

intervals

Results

94.0ms

443×

body

valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 3 (174.0ms)

Iter	Nodes	Cost
0	28	67
1	69	67
2	228	48
3	875	37
4	4155	37
done	5002	37

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite17.7s

Algorithm

rewrite-expression-head

Rules

131×	`add-exp-log` `add-cbrt-cube`
88×	`prod-exp` `cbrt-unprod`
62×	`pow1`
48×	`associate-l`
44×	`pow-prod-down`
42×	`add-sqr-sqrt`
38×	`times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-*l/`
13×	`cbrt-undiv` `div-exp` `sqrt-prod`
12×	`frac-add`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 175

Calls

4 calls:

1.9s	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
14.7s	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.1s	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series645.0ms

Counts

4 → 10

Calls

4 calls:

470.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
98.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
77.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify949.0ms

Counts

185 → 185

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	378	9516
1	1390	6792
done	5001	5199

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ (sqrt 1.0) (* (cbrt 21.0) (cbrt 21.0))) (* (* (/ (sqrt 1.0) (cbrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b	(* (cbrt 21.0) (cbrt 21.0))
1.0b	(sqrt PI)

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
54×	`associate-*l/` `add-cbrt-cube`
51×	`add-sqr-sqrt`
41×	`associate-l`
36×	`frac-add`
34×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
33×	`prod-exp` `cbrt-unprod`
29×	`times-frac`
22×	`frac-times` `associate-*r/`
18×	`pow-prod-down`
16×	`cbrt-prod`
14×	`flip3-+` `flip-+`
13×	`sqrt-prod`
10×	`associate-r`
7×	`unswap-sqr`
6×	`cbrt-undiv` `pow1/3` `swap-sqr` `div-exp`
4×	`add-log-exp`
3×	`*-commutative`
2×	`pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2`

Counts

4 → 173

Calls

4 calls:

962.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ (sqrt 1.0) (* (cbrt 21.0) (cbrt 21.0))) (* (* (/ (sqrt 1.0) (cbrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
1.0s	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
12.0ms	(* (cbrt 21.0) (cbrt 21.0))
2.0ms	(sqrt PI)

series818.0ms

Counts

4 → 8

Calls

4 calls:

747.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ (sqrt 1.0) (* (cbrt 21.0) (cbrt 21.0))) (* (* (/ (sqrt 1.0) (cbrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
71.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms	(* (cbrt 21.0) (cbrt 21.0))
0.0ms	(sqrt PI)

simplify746.0ms

Counts

181 → 181

Iterations

Useful iterations: done (733.0ms)

Iter	Nodes	Cost
0	392	10651
1	1429	8400
done	5001	7343

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ (sqrt 1.0) (pow 21.0 2/3)) (* (* (/ (sqrt 1.0) (cbrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b	(pow 21.0 2/3)
1.0b	(sqrt PI)

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
54×	`associate-*l/` `add-cbrt-cube`
37×	`add-sqr-sqrt`
36×	`frac-add`
35×	`associate-l`
32×	`prod-exp` `cbrt-unprod`
29×	`times-frac`
28×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
22×	`frac-times` `associate-*r/`
16×	`pow-prod-down`
14×	`flip3-+` `flip-+`
13×	`sqrt-prod`
6×	`cbrt-undiv` `div-exp`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `sqr-pow`

Counts

4 → 150

Calls

4 calls:

814.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ (sqrt 1.0) (pow 21.0 2/3)) (* (* (/ (sqrt 1.0) (cbrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
1.1s	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
3.0ms	(pow 21.0 2/3)
1.0ms	(sqrt PI)

series1.2s

Counts

4 → 8

Calls

4 calls:

1.1s	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ (sqrt 1.0) (pow 21.0 2/3)) (* (* (/ (sqrt 1.0) (cbrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
110.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms	(pow 21.0 2/3)
0.0ms	(sqrt PI)

simplify936.0ms

Counts

158 → 158

Iterations

Useful iterations: done (923.0ms)

Iter	Nodes	Cost
0	388	10261
1	1437	8045
done	5001	7066

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (cbrt 1.0) (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (pow (fabs x) (+ 3 1)) (/ 1.0 5.0)) (/ (* 1.0 (pow (fabs x) (* 2 3))) 21.0))))) (sqrt (sqrt PI)))
0.3b	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (cbrt 1.0) (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (pow (fabs x) (+ 3 1)) (/ 1.0 5.0)) (/ (* 1.0 (pow (fabs x) (* 2 3))) 21.0))))) (sqrt (sqrt PI))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `sqrt-prod`
35×	`add-cbrt-cube`
30×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
17×	`associate-*r/`
16×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r` `associate-l`
9×	`associate-/r*`
8×	`pow1` `frac-add` `associate-/l/`
6×	`flip3-+` `flip-+`
4×	`add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l*`

Counts

4 → 127

Calls

4 calls:

110.0ms	(/ (* (cbrt 1.0) (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (pow (fabs x) (+ 3 1)) (/ 1.0 5.0)) (/ (* 1.0 (pow (fabs x) (* 2 3))) 21.0))))) (sqrt (sqrt PI)))
144.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (cbrt 1.0) (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (pow (fabs x) (+ 3 1)) (/ 1.0 5.0)) (/ (* 1.0 (pow (fabs x) (* 2 3))) 21.0))))) (sqrt (sqrt PI))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series1.3s

Counts

4 → 8

Calls

4 calls:

776.0ms	(/ (* (cbrt 1.0) (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (pow (fabs x) (+ 3 1)) (/ 1.0 5.0)) (/ (* 1.0 (pow (fabs x) (* 2 3))) 21.0))))) (sqrt (sqrt PI)))
563.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (cbrt 1.0) (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (pow (fabs x) (+ 3 1)) (/ 1.0 5.0)) (/ (* 1.0 (pow (fabs x) (* 2 3))) 21.0))))) (sqrt (sqrt PI))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify3.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (719.0ms)

Iter	Nodes	Cost
0	223	7031
1	758	6278
2	4872	5042
done	5000	5042

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes107.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	37	65
1	52	63
done	52	63

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.3s

13943×

body

valid