Details

sample69.0ms

Algorithm

intervals

Results

32.0ms	72×	body	1280	valid
13.0ms	54×	body	640	valid
5.0ms	17×	body	2560	valid
4.0ms	27×	body	320	valid
3.0ms	76×	body	80	valid
1.0ms	10×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ x (sqrt (+ (* x x) 1.0)))
2.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b	(sqrt (+ (* x x) 1.0))

rewrite50.0ms

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

series292.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ x (sqrt (+ (* x x) 1.0)))
180.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
51.0ms	(sqrt (+ (* x x) 1.0))

simplify138.0ms

Counts: 51 → 51

prune158.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite118.0ms

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:

99.0ms

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

series148.0ms

Counts

1 → 3

Calls

1 calls:

148.0ms

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

simplify85.0ms

Counts: 273 → 273

prune396.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ 0.5 x))
0.4b	(/ 0.125 (pow x 3))
8.0b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

12.0ms	(+ x (/ 0.5 x))
9.0ms	(/ 0.125 (pow x 3))
176.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series259.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ x (/ 0.5 x))
45.0ms	(/ 0.125 (pow x 3))
170.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify49.0ms

Counts: 103 → 103

prune204.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0.0625) (pow x 5))
0.4b	(/ 0.125 (pow x 3))
9.0b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.9b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
110×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
47×	`unpow-prod-down`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
19×	`associate-/r*`
17×	`sqr-pow`
15×	`add-exp-log`
14×	`cube-prod` `distribute-lft-out--`
13×	`associate-/l*`
12×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`neg-mul-1` `frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log` `associate--r+`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `div-inv` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 223

Calls

4 calls:

12.0ms	(/ (- 0.0625) (pow x 5))
9.0ms	(/ 0.125 (pow x 3))
228.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
252.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (- 0.0625) (pow x 5))
45.0ms	(/ 0.125 (pow x 3))
206.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
62.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify93.0ms

Counts: 235 → 235

prune631.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.4b

bsearch94.0ms

Steps

Iters	Range		Point
9	0.21963308938311268	137362616.0762091	0.8931378377170596
11	-2445851338.3862987	-4.2674702477225e-16	-1.0064602849522295

simplify1.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	2366×	body	1280	valid
562.0ms	762×	body	2560	valid
511.0ms	1566×	body	640	valid
119.0ms	757×	body	320	valid
115.0ms	2126×	body	80	valid
39.0ms	423×	body	160	valid