Details

sample120.0ms

Algorithm

intervals

Results

85.0ms

452×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	28	67
1	87	67
2	794	45
done	5000	40

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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)

rewrite1.1s

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:

39.0ms	(* (* (fabs x) (fabs x)) (fabs x))
945.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
111.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series202.0ms

Counts

4 → 10

Calls

4 calls:

47.0ms	(* (* (fabs x) (fabs x)) (fabs x))
83.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
71.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify2.2s

Counts

137 → 137

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	216	2448
1	1240	1584
done	5001	1241

prune687.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0)))
0.3b	(/ (+ (* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0))) (/ (sqrt PI) 1.0))
0.7b	(/ 1.0 (/ 5.0 (* (fabs x) (fabs x))))
1.0b	(sqrt PI)

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
108×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
100×	`add-cube-cbrt`
39×	`sqrt-prod`
29×	`associate-/r*`
23×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`associate-*r/`
12×	`associate-l`
10×	`div-inv`
9×	`frac-add`
8×	`cbrt-undiv` `div-exp` `associate-/l/`
7×	`flip3-+` `flip-+`
6×	`associate-/l*`
5×	`pow1` `associate-r`
4×	`unpow-prod-down` `cube-prod` `prod-exp` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r/` `cbrt-unprod` `distribute-lft-out` `sqr-pow`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp` `*-commutative`

Counts

4 → 213

Calls

4 calls:

187.0ms	(* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0)))
227.0ms	(/ (+ (* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0))) (/ (sqrt PI) 1.0))
14.0ms	(/ 1.0 (/ 5.0 (* (fabs x) (fabs x))))
2.0ms	(sqrt PI)

series620.0ms

Counts

4 → 10

Calls

4 calls:

99.0ms	(* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0)))
482.0ms	(/ (+ (* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0))) (/ (sqrt PI) 1.0))
39.0ms	(/ 1.0 (/ 5.0 (* (fabs x) (fabs x))))
0.0ms	(sqrt PI)

simplify1.4s

Counts

223 → 223

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	420	9772
done	5001	9234

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (fabs (cbrt PI)) (sqrt 1.0))) (/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (sqrt (cbrt PI)) (sqrt 1.0))))
0.4b	(/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (fabs (cbrt PI)) (sqrt 1.0)))
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

1502×	`times-frac`
1147×	`add-sqr-sqrt`
1026×	`sqrt-prod`
605×	`add-cube-cbrt` `*-un-lft-identity`
353×	`associate-r`
142×	`cbrt-prod`
137×	`associate-l`
105×	`unswap-sqr`
45×	`add-exp-log` `add-cbrt-cube`
22×	`associate-/r*` `div-inv`
21×	`cbrt-undiv` `div-exp`
13×	`associate-*r/`
9×	`prod-exp` `cbrt-unprod`
8×	`sqrt-div` `frac-add` `associate-/l/`
6×	`pow1` `flip3-+` `flip-+` `associate-/l*`
4×	`add-log-exp`
3×	`associate-*l/` `associate-/r/`
2×	`pow1/3`
1×	`frac-times` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 830

Calls

4 calls:

1.1s	(* (/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (fabs (cbrt PI)) (sqrt 1.0))) (/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (sqrt (cbrt PI)) (sqrt 1.0))))
113.0ms	(/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (fabs (cbrt PI)) (sqrt 1.0)))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series1.4s

Counts

4 → 8

Calls

4 calls:

951.0ms	(* (/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (fabs (cbrt PI)) (sqrt 1.0))) (/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (sqrt (cbrt PI)) (sqrt 1.0))))
491.0ms	(/ (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (fabs (cbrt PI)) (sqrt 1.0)))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify1.5s

Counts

838 → 838

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	941	79911
done	5001	72884

prune7.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (/ (sqrt PI) 1.0) (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0))))))
0.4b	(/ (/ (sqrt PI) 1.0) (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))))
0.7b	(/ 1.0 (/ 5.0 (* (fabs x) (fabs x))))
1.0b	(sqrt PI)

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

2835×	`times-frac`
1410×	`sqrt-prod`
1310×	`add-sqr-sqrt`
1309×	`add-cube-cbrt` `*-un-lft-identity`
157×	`associate-/r*`
108×	`associate-*r/`
72×	`sqrt-div` `frac-add`
66×	`associate-/r/`
63×	`div-inv`
54×	`flip3-+` `flip-+`
31×	`associate-/l*`
27×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/`
14×	`cbrt-undiv` `div-exp`
9×	`associate-/l/`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`

Counts

4 → 1283

Calls

4 calls:

299.0ms	(/ (sqrt (+ (* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (/ (sqrt PI) 1.0) (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0))))))
121.0ms	(/ (/ (sqrt PI) 1.0) (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))))
42.0ms	(/ 1.0 (/ 5.0 (* (fabs x) (fabs x))))
2.0ms	(sqrt PI)

series1.1s

Counts

4 → 10

Calls

4 calls:

469.0ms	(/ (sqrt (+ (* (pow (fabs x) 3) (+ (/ 1.0 (/ 5.0 (* (fabs x) (fabs x)))) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))) (/ (/ (sqrt PI) 1.0) (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0))))))
565.0ms	(/ (/ (sqrt PI) 1.0) (sqrt (+ (* (pow (fabs x) 3) (+ (* (/ 1.0 5.0) (pow (fabs x) 2)) (/ 2.0 3.0))) (* (fabs x) (+ (* (pow (fabs x) (* 2 3)) (/ 1.0 21.0)) 2.0)))))
52.0ms	(/ 1.0 (/ 5.0 (* (fabs x) (fabs x))))
0.0ms	(sqrt PI)

simplify1.7s

Counts

1293 → 1293

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	1465	169116
done	5000	153326

prune10.7s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes284.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	67
1	41	67
done	41	67

end0.0ms

sample3.4s

Algorithm

intervals

Results

3.0s

14083×

body

valid