Details

sample45.0ms

Algorithm

intervals

Results

29.0ms

452×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	28	67
1	69	67
2	221	48
3	781	37
4	2529	37
done	5000	37

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (pow (fabs x) 6) (/ 1.0 21.0))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
0.1b	(* (pow (fabs x) 4) (/ 1.0 5.0))
0.2b	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b	(sqrt PI)

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

296×	`times-frac`
179×	`add-sqr-sqrt`
157×	`add-cube-cbrt` `*-un-lft-identity`
41×	`unpow-prod-down`
40×	`associate-/r*`
36×	`cube-prod`
32×	`add-exp-log`
29×	`associate-l`
19×	`add-cbrt-cube`
16×	`associate-r`
15×	`sqr-pow`
13×	`sqrt-prod`
12×	`cube-mult` `unpow3`
11×	`div-exp`
9×	`associate-*r/` `unswap-sqr`
8×	`prod-exp`
7×	`pow1` `div-inv`
5×	`cbrt-undiv`
4×	`frac-times` `flip3-+` `frac-add` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/l*`
2×	`*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/`

Counts

4 → 288

Calls

4 calls:

202.0ms	(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (pow (fabs x) 6) (/ 1.0 21.0))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
10.0ms	(* (pow (fabs x) 4) (/ 1.0 5.0))
11.0ms	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms	(sqrt PI)

series426.0ms

Counts

4 → 10

Calls

4 calls:

331.0ms	(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (pow (fabs x) 6) (/ 1.0 21.0))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
51.0ms	(* (pow (fabs x) 4) (/ 1.0 5.0))
44.0ms	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms	(sqrt PI)

simplify501.0ms

Counts

298 → 298

Iterations

Useful iterations: done (490.0ms)

Iter	Nodes	Cost
0	531	6858
1	1436	6159
done	5000	6080

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (fabs x) 4) (/ 1.0 5.0))
0.2b	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
159×	`add-sqr-sqrt`
144×	`add-cube-cbrt` `*-un-lft-identity`
41×	`unpow-prod-down`
40×	`associate-/r*`
36×	`cube-prod`
27×	`add-exp-log`
15×	`sqr-pow`
14×	`add-cbrt-cube`
13×	`associate-r`
12×	`cube-mult` `unpow3`
10×	`div-exp`
7×	`associate-l`
6×	`pow1` `prod-exp` `sqrt-prod` `div-inv` `unswap-sqr`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `cbrt-unprod`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r/` `-commutative`

Counts

4 → 249

Calls

4 calls:

10.0ms	(* (pow (fabs x) 4) (/ 1.0 5.0))
11.0ms	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series94.0ms

Counts

4 → 8

Calls

4 calls:

50.0ms	(* (pow (fabs x) 4) (/ 1.0 5.0))
44.0ms	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify1.5s

Counts

257 → 257

Iterations

Useful iterations: 2 (657.0ms)

Iter	Nodes	Cost
0	417	4096
1	946	3479
2	3525	3291
done	5001	3291

prune957.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.047619047619047616 (pow (fabs x) 7))
0.1b	(* 0.2 (pow (fabs x) 5))
0.1b	(* 0.6666666666666666 (pow (fabs x) 3))
0.1b	(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
29×	`associate-r`
25×	`associate-l`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`add-exp-log`
16×	`sqrt-prod`
14×	`unswap-sqr`
12×	`unpow-prod-down` `add-cbrt-cube`
11×	`times-frac`
10×	`prod-exp`
6×	`pow1` `sqr-pow`
4×	`cube-prod` `*-commutative` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `sqrt-div` `pow-exp`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `pow-prod-down` `associate-*l/` `div-inv`

Counts

4 → 122

Calls

4 calls:

5.0ms	(* 0.047619047619047616 (pow (fabs x) 7))
5.0ms	(* 0.2 (pow (fabs x) 5))
7.0ms	(* 0.6666666666666666 (pow (fabs x) 3))
91.0ms	(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 0.047619047619047616 (pow (fabs x) 7))
61.0ms	(* 0.2 (pow (fabs x) 5))
43.0ms	(* 0.6666666666666666 (pow (fabs x) 3))
283.0ms	(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify747.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	228	2601
1	598	2449
2	1883	2298
done	5001	2298

prune521.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.2 (pow (fabs x) 5))
0.1b	(* 0.6666666666666666 (pow (fabs x) 3))
0.3b	(/ (* (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) 1) (sqrt PI))
1.0b	(sqrt PI)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`add-exp-log`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube`
9×	`sqrt-prod`
8×	`unpow-prod-down` `prod-exp`
7×	`unswap-sqr`
6×	`times-frac` `associate-l` `associate-/r*`
5×	`pow1`
4×	`cube-prod` `add-log-exp` `sqr-pow`
3×	`div-exp` `cbrt-unprod`
2×	`cbrt-undiv` `pow-to-exp` `associate-l/` `pow-exp` `-commutative` `associate-/l/`
1×	`cube-mult` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `unpow3` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

6.0ms	(* 0.2 (pow (fabs x) 5))
9.0ms	(* 0.6666666666666666 (pow (fabs x) 3))
25.0ms	(/ (* (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) 1) (sqrt PI))
1.0ms	(sqrt PI)

series389.0ms

Counts

4 → 10

Calls

4 calls:

61.0ms	(* 0.2 (pow (fabs x) 5))
43.0ms	(* 0.6666666666666666 (pow (fabs x) 3))
284.0ms	(/ (* (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) 1) (sqrt PI))
0.0ms	(sqrt PI)

simplify645.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	179	1901
1	431	1721
2	1358	1525
done	5000	1525

prune371.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	42
1	37	42
done	37	42

end0.0ms

sample1.1s

Algorithm

intervals

Results

915.0ms

13952×

body

valid