Details

sample130.0ms

Algorithm

intervals

Results

94.0ms	244×	body	10240	exit
9.0ms	208×	body	80	valid
4.0ms	16×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid

simplify830.0ms

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ wj 1))
0.0b	(/ wj (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
2.6b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite808.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

12.0ms	(/ x (+ wj 1))
18.0ms	(/ wj (+ wj 1))
44.0ms	(/ (/ x (+ wj 1)) (exp wj))
725.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ x (+ wj 1))
42.0ms	(/ wj (+ wj 1))
62.0ms	(/ (/ x (+ wj 1)) (exp wj))
85.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify1.2s

Counts: 188 → 188

prune727.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow wj 2))
0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate-r` `associate--l+` `*-commutative` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 44

Calls

3 calls:

9.0ms	(+ x (pow wj 2))
92.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
34.0ms	(* 2 (* wj x))

series146.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ x (pow wj 2))
55.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
31.0ms	(* 2 (* wj x))

simplify2.2s

Counts: 53 → 53

prune144.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.6b	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.6b	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.6b	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

424.0ms	(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
41.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
52.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
70.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

series1.8s

Counts

4 → 12

Calls

4 calls:

472.0ms	(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
451.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
443.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
449.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

simplify715.0ms

Counts: 99 → 99

prune467.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.6b	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.6b	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.9b	(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3--` `flip--`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

48.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
46.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
46.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
86.0ms	(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

series1.5s

Counts

4 → 12

Calls

4 calls:

407.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
421.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
462.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
193.0ms	(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

simplify673.0ms

Counts: 75 → 75

prune503.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes127.0ms

Accuracy

64.1% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.2b

bsearch49.0ms

Steps

Iters	Range		Point
9	1.3099675947624547e-09	0.00038687692640540744	9.422333290444804e-09

simplify763.0ms

end0.0ms

sample5.9s

Algorithm

intervals

Results

4.7s	7557×	body	10240	exit
369.0ms	6337×	body	80	valid
125.0ms	771×	body	320	valid
107.0ms	416×	body	640	valid
62.0ms	541×	body	160	valid