Details

sample45.0ms

Algorithm

intervals

Results

29.0ms

437×

body

valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (78.0ms)

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: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log` `add-cbrt-cube`
53×	`pow1`
45×	`prod-exp` `cbrt-unprod`
27×	`associate-l`
24×	`pow-prod-down`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`cbrt-undiv` `div-exp`
6×	`pow-plus` `pow-prod-up`
5×	`associate-r`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `associate-*l/` `pow-sqr` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

7.0ms	(* (* (fabs x) (fabs x)) (fabs x))
503.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
29.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series133.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(* (* (fabs x) (fabs x)) (fabs x))
57.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
47.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify834.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	216	2448
1	598	1707
2	2039	1163
done	5000	1163

prune428.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log` `add-cbrt-cube`
53×	`pow1`
45×	`prod-exp` `cbrt-unprod`
27×	`associate-l`
24×	`pow-prod-down`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`cbrt-undiv` `div-exp`
6×	`pow-plus` `pow-prod-up`
5×	`associate-r`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `associate-*l/` `pow-sqr` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
318.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series131.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
61.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
44.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify863.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (295.0ms)

Iter	Nodes	Cost
0	218	2444
1	609	1527
2	2058	1025
done	5001	1025

prune454.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 21.0) (* (pow (fabs x) 6) (fabs x)))
0.1b	(* (+ (+ (* (/ 1.0 21.0) (* (pow (fabs x) 6) (fabs x))) (* 2.0 (fabs x))) (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (* (/ 2.0 3.0) (pow (fabs x) 3)))) (/ 1.0 (sqrt PI)))
0.2b	(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b	(sqrt PI)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
46×	`add-exp-log`
42×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
35×	`associate-r`
30×	`associate-l`
26×	`add-cbrt-cube`
22×	`prod-exp`
16×	`frac-add`
14×	`associate-*l/`
13×	`sqrt-prod`
12×	`flip3-+` `flip-+`
11×	`unswap-sqr`
10×	`cbrt-unprod`
9×	`pow1`
8×	`frac-times` `div-exp`
5×	`unpow-prod-down` `cube-prod`
4×	`cbrt-undiv` `pow-to-exp` `pow-exp` `add-log-exp`
3×	`*-commutative` `div-inv` `sqr-pow`
2×	`pow-prod-down`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `associate-*r/` `distribute-lft-out`

Counts

4 → 158

Calls

4 calls:

13.0ms	(* (/ 1.0 21.0) (* (pow (fabs x) 6) (fabs x)))
207.0ms	(* (+ (+ (* (/ 1.0 21.0) (* (pow (fabs x) 6) (fabs x))) (* 2.0 (fabs x))) (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (* (/ 2.0 3.0) (pow (fabs x) 3)))) (/ 1.0 (sqrt PI)))
12.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0ms	(sqrt PI)

series437.0ms

Counts

4 → 10

Calls

4 calls:

73.0ms	(* (/ 1.0 21.0) (* (pow (fabs x) 6) (fabs x)))
320.0ms	(* (+ (+ (* (/ 1.0 21.0) (* (pow (fabs x) 6) (fabs x))) (* 2.0 (fabs x))) (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (* (/ 2.0 3.0) (pow (fabs x) 3)))) (/ 1.0 (sqrt PI)))
44.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms	(sqrt PI)

simplify1.7s

Counts

168 → 168

Iterations

Useful iterations: 2 (633.0ms)

Iter	Nodes	Cost
0	352	5636
1	1042	4863
2	4607	4478
done	5000	4478

prune740.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (fabs x) 7) (/ 1.0 21.0))
0.2b	(* (/ 2.0 3.0) (pow (fabs x) 3))
0.3b	(/ (* 1.0 (+ (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (* (/ 2.0 3.0) (pow (fabs x) 3))) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) (/ 1.0 21.0))))) (sqrt PI))
1.0b	(sqrt PI)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

13.0ms	(* (pow (fabs x) 7) (/ 1.0 21.0))
12.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
48.0ms	(/ (* 1.0 (+ (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (* (/ 2.0 3.0) (pow (fabs x) 3))) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) (/ 1.0 21.0))))) (sqrt PI))
1.0ms	(sqrt PI)

series447.0ms

Counts

4 → 10

Calls

4 calls:

75.0ms	(* (pow (fabs x) 7) (/ 1.0 21.0))
49.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
322.0ms	(/ (* 1.0 (+ (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (* (/ 2.0 3.0) (pow (fabs x) 3))) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) (/ 1.0 21.0))))) (sqrt PI))
0.0ms	(sqrt PI)

simplify1.2s

Counts

151 → 151

Iterations

Useful iterations: 2 (462.0ms)

Iter	Nodes	Cost
0	284	3084
1	797	2890
2	3306	2606
done	5000	2606

prune600.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	40
1	38	40
done	38	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

926.0ms

13989×

body

valid