Details

sample96.0ms

Algorithm

intervals

Results

66.0ms

456×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (2.2s)

Iter	Nodes	Cost
0	28	67
1	70	66
2	250	47
3	1028	35
4	4001	34
done	5000	34

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

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 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)

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log` `add-cbrt-cube`
48×	`associate-l`
44×	`prod-exp` `cbrt-unprod`
42×	`add-sqr-sqrt`
38×	`times-frac`
36×	`pow1`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`pow-prod-down`
15×	`associate-*l/`
13×	`sqrt-prod`
12×	`frac-add`
9×	`cbrt-undiv` `div-exp`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 163

Calls

4 calls:

1.7s	(* (/ 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)))))
968.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
110.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
3.0ms	(sqrt PI)

series629.0ms

Counts

4 → 10

Calls

4 calls:

471.0ms	(* (/ 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)))))
96.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
61.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify941.0ms

Counts

173 → 173

Iterations

Useful iterations: done (928.0ms)

Iter	Nodes	Cost
0	350	8160
1	1136	5868
done	5001	4750

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
0.1b	(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))))
0.2b	(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b	(sqrt PI)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
48×	`associate-l`
45×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
35×	`add-exp-log`
22×	`associate-r`
19×	`add-cbrt-cube`
17×	`unswap-sqr`
14×	`prod-exp`
13×	`sqrt-prod`
10×	`unpow-prod-down`
7×	`pow1` `div-exp`
6×	`cbrt-unprod` `sqr-pow`
5×	`cube-prod`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l/` `-commutative` `div-inv`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down`

Counts

4 → 162

Calls

4 calls:

26.0ms	(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
64.0ms	(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))))
27.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
2.0ms	(sqrt PI)

series654.0ms

Counts

4 → 10

Calls

4 calls:

85.0ms	(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
503.0ms	(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))))
66.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms	(sqrt PI)

simplify2.5s

Counts

172 → 172

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	309	4312
1	881	3725
2	3583	3374
done	5001	3367

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
0.1b	(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (* (pow (fabs x) 6) (/ 1.0 (sqrt 21.0))))))))
0.2b	(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b	(sqrt PI)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
48×	`associate-l`
45×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
35×	`add-exp-log`
23×	`associate-r`
19×	`add-cbrt-cube`
17×	`unswap-sqr`
14×	`prod-exp`
13×	`sqrt-prod`
10×	`unpow-prod-down`
7×	`pow1` `div-exp`
6×	`cbrt-unprod` `sqr-pow`
5×	`cube-prod`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l/` `-commutative` `div-inv`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
1×	`unpow-prod-up` `distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down`

Counts

4 → 163

Calls

4 calls:

46.0ms	(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
41.0ms	(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (* (pow (fabs x) 6) (/ 1.0 (sqrt 21.0))))))))
46.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
3.0ms	(sqrt PI)

series868.0ms

Counts

4 → 10

Calls

4 calls:

87.0ms	(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
707.0ms	(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (* (pow (fabs x) 6) (/ 1.0 (sqrt 21.0))))))))
74.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms	(sqrt PI)

simplify2.6s

Counts

173 → 173

Iterations

Useful iterations: 2 (965.0ms)

Iter	Nodes	Cost
0	320	4599
1	918	4144
2	3670	3622
done	5000	3622

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 3.0 (pow (fabs x) 3))
0.3b	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
0.6b	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b	(sqrt PI)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

438×	`times-frac`
235×	`add-sqr-sqrt`
234×	`add-cube-cbrt` `*-un-lft-identity`
74×	`associate-/r*`
48×	`unpow-prod-down` `cube-prod`
39×	`sqrt-prod`
24×	`add-exp-log`
16×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
13×	`div-exp`
11×	`div-inv`
9×	`associate-/l*`
7×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-to-exp` `pow-exp` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 372

Calls

4 calls:

9.0ms	(/ 3.0 (pow (fabs x) 3))
34.0ms	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
37.0ms	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
3.0ms	(sqrt PI)

series594.0ms

Counts

4 → 10

Calls

4 calls:

61.0ms	(/ 3.0 (pow (fabs x) 3))
454.0ms	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
80.0ms	(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms	(sqrt PI)

simplify3.0s

Counts

382 → 382

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	544	10863
1	1073	9979
2	3793	9589
done	5000	9589

prune2.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes274.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: done (11.0ms)

Iter	Nodes	Cost
0	34	51
1	47	47
done	47	45

end0.0ms

sample3.3s

Algorithm

intervals

Results

3.0s

13874×

body

valid