Details

sample128.0ms

Algorithm

intervals

Results

52.0ms	73×	body	1280	valid
25.0ms	60×	body	640	valid
19.0ms	31×	body	320	valid
12.0ms	22×	body	2560	valid
5.0ms	65×	body	80	valid
1.0ms	5×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (+ (* x x) 1.0)))
1.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b	(sqrt (+ (* x x) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

19.0ms	(+ x (sqrt (+ (* x x) 1.0)))
28.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
11.0ms	(sqrt (+ (* x x) 1.0))

series390.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(+ x (sqrt (+ (* x x) 1.0)))
227.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
61.0ms	(sqrt (+ (* x x) 1.0))

simplify1.3s

Counts: 51 → 51

prune234.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`unswap-sqr`
24×	`add-exp-log`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 270

Calls

1 calls:

109.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series220.0ms

Counts

1 → 3

Calls

1 calls:

220.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.6s

Counts: 273 → 273

prune565.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))
0.5b	(/ 1 (pow x 3))
10.2b	(log (+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
12×	`unpow-prod-down` `cube-prod` `associate-/r*` `add-log-exp`
6×	`div-exp` `distribute-lft-out`
5×	`log-prod` `sum-log` `add-cbrt-cube`
4×	`pow1` `cube-mult` `unpow3` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`log-div` `flip3-+` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `associate-+r-` `associate-+r+` `pow-flip` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `log-pow` `div-inv` `inv-pow`

Counts

3 → 106

Calls

3 calls:

96.0ms	(+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))
12.0ms	(/ 1 (pow x 3))
71.0ms	(log (+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))))

series322.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))
34.0ms	(/ 1 (pow x 3))
219.0ms	(log (+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))))

simplify838.0ms

Counts: 115 → 115

prune304.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0.0625) (pow x 5))
0.6b	(/ 0.125 (pow x 2))
12.9b	(log (+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5))))
20.2b	(+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac`
68×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
15×	`add-exp-log` `associate-/r*` `sqr-pow`
13×	`associate-/l*`
10×	`frac-add`
8×	`neg-mul-1` `add-cbrt-cube`
7×	`log-div`
6×	`div-exp` `add-log-exp`
5×	`pow1`
4×	`frac-times` `associate-+r+` `flip3--` `associate-*r/` `flip--` `unpow2`
3×	`log-prod`
2×	`cbrt-undiv` `neg-sub0` `distribute-rgt-in` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `div-sub` `associate-*l/` `pow-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `distribute-frac-neg` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 192

Calls

4 calls:

12.0ms	(/ (- 0.0625) (pow x 5))
8.0ms	(/ 0.125 (pow x 2))
65.0ms	(log (+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5))))
133.0ms	(+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (- 0.0625) (pow x 5))
49.0ms	(/ 0.125 (pow x 2))
290.0ms	(log (+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5))))
81.0ms	(+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5)))

simplify1.6s

Counts: 204 → 204

prune905.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.5b

bsearch99.0ms

Steps

Iters	Range		Point
10	1.3099675947624547e-09	64828.07766974042	0.9006433647360576
9	-1.9338314318659307	-5.99435871131559e-06	-1.019295534059107

simplify568.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.6s	2354×	body	1280	valid
588.0ms	1593×	body	640	valid
573.0ms	2163×	body	80	valid
319.0ms	757×	body	2560	valid
160.0ms	759×	body	320	valid
46.0ms	374×	body	160	valid