Details

sample124.0ms

Algorithm

intervals

Results

80.0ms	226×	body	10240	exit
10.0ms	203×	body	80	valid
5.0ms	20×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	18×	body	160	valid

simplify46.0ms

Counts: 1 → 1

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ 1 (+ wj 1))
0.0b	(* (- (/ x (exp wj)) wj) (/ 1 (+ wj 1)))
5.1b	(+ (* (- (/ x (exp wj)) wj) (/ 1 (+ wj 1))) wj)

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
36×	`times-frac`
30×	`add-cube-cbrt`
18×	`add-exp-log` `associate-r`
13×	`add-cbrt-cube`
7×	`pow1` `associate-/r*` `distribute-lft-out`
6×	`associate-l` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`prod-exp` `associate-/r/`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `distribute-lft-out--` `inv-pow`

Counts

4 → 123

Calls

4 calls:

12.0ms	(/ x (exp wj))
14.0ms	(/ 1 (+ wj 1))
158.0ms	(* (- (/ x (exp wj)) wj) (/ 1 (+ wj 1)))
99.0ms	(+ (* (- (/ x (exp wj)) wj) (/ 1 (+ wj 1))) wj)

series187.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ x (exp wj))
14.0ms	(/ 1 (+ wj 1))
64.0ms	(* (- (/ x (exp wj)) wj) (/ 1 (+ wj 1)))
68.0ms	(+ (* (- (/ x (exp wj)) wj) (/ 1 (+ wj 1))) wj)

simplify50.0ms

Counts: 135 → 135

prune462.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

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))

rewrite161.0ms

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:

19.0ms	(+ x (pow wj 2))
122.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
18.0ms	(* 2 (* wj x))

series141.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ x (pow wj 2))
56.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
23.0ms	(* 2 (* wj x))

simplify138.0ms

Counts: 53 → 53

prune156.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
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 → 95

Calls

4 calls:

86.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
7.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
10.0ms	(cbrt (+ x (pow wj 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

462.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
529.0ms	(cbrt (+ x (pow wj 2)))
466.0ms	(cbrt (+ x (pow wj 2)))
450.0ms	(cbrt (+ x (pow wj 2)))

simplify85.0ms

Counts: 107 → 107

prune442.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-div`
24×	`cbrt-prod`
14×	`flip3-+` `flip-+`
12×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `pow1/3` `associate-r/` `associate-l/` `add-cbrt-cube` `add-log-exp`
2×	`distribute-lft-out`

Counts

4 → 68

Calls

4 calls:

39.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
33.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
9.0ms	(cbrt (cbrt (+ x (pow wj 2))))
14.0ms	(cbrt (cbrt (+ x (pow wj 2))))

series1.8s

Counts

4 → 12

Calls

4 calls:

404.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
392.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
518.0ms	(cbrt (cbrt (+ x (pow wj 2))))
509.0ms	(cbrt (cbrt (+ x (pow wj 2))))

simplify128.0ms

Counts: 80 → 80

prune562.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes185.0ms

Accuracy

98.4% (0.0b remaining)

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

bsearch111.0ms

Steps

Iters	Range		Point
8	2.5492078154212987e-10	8.845201659255268e-06	9.705982152869648e-09
8	-3.4223688865970257e-07	-1.822584514918214e-10	-3.018517982554952e-09

simplify37.0ms

end0.0ms

sample6.4s

Algorithm

intervals

Results

5.1s	7734×	body	10240	exit
353.0ms	6325×	body	80	valid
137.0ms	807×	body	320	valid
111.0ms	421×	body	640	valid
58.0ms	536×	body	160	valid