Details

sample72.0ms

Algorithm

intervals

Results

38.0ms	82×	body	1280	valid
10.0ms	36×	body	640	valid
7.0ms	23×	body	2560	valid
3.0ms	87×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ x (sqrt (+ (* x x) 1.0)))
2.5b	(log (+ x (sqrt (+ (* x x) 1.0))))
16.6b	(sqrt (+ (* x x) 1.0))

rewrite58.0ms

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:

31.0ms	(+ x (sqrt (+ (* x x) 1.0)))
17.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms	(sqrt (+ (* x x) 1.0))

series300.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(+ x (sqrt (+ (* x x) 1.0)))
178.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms	(sqrt (+ (* x x) 1.0))

simplify167.0ms

Counts: 51 → 51

prune157.0ms

Pruning

5 alts after pruning (5 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)))

rewrite112.0ms

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:

87.0ms

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

series144.0ms

Counts

1 → 3

Calls

1 calls:

144.0ms

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

simplify81.0ms

Counts: 273 → 273

prune382.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.0b	(+ x (/ 0.5 x))
0.1b	(/ 0.125 (pow x 3))
10.0b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
11×	`add-log-exp`
10×	`add-exp-log`
6×	`log-prod` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `difference-of-squares` `sqr-pow`
4×	`cube-mult` `unpow3` `distribute-lft-out--`
3×	`flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`log-div` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `associate--l+` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 117

Calls

4 calls:

98.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
10.0ms	(+ x (/ 0.5 x))
8.0ms	(/ 0.125 (pow x 3))
160.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
45.0ms	(+ x (/ 0.5 x))
39.0ms	(/ 0.125 (pow x 3))
168.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify58.0ms

Counts: 129 → 129

prune255.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (sqrt (+ x (sqrt (+ (* x x) 1.0)))))
2.6b	(log (sqrt (+ x (sqrt (+ (* x x) 1.0)))))
16.6b	(sqrt (+ (* x x) 1.0))
16.6b	(sqrt (+ (* x x) 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

14×	`log-prod` `*-un-lft-identity` `sqrt-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

19.0ms	(log (sqrt (+ x (sqrt (+ (* x x) 1.0)))))
19.0ms	(log (sqrt (+ x (sqrt (+ (* x x) 1.0)))))
13.0ms	(sqrt (+ (* x x) 1.0))
10.0ms	(sqrt (+ (* x x) 1.0))

series464.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(log (sqrt (+ x (sqrt (+ (* x x) 1.0)))))
188.0ms	(log (sqrt (+ x (sqrt (+ (* x x) 1.0)))))
42.0ms	(sqrt (+ (* x x) 1.0))
46.0ms	(sqrt (+ (* x x) 1.0))

simplify87.0ms

Counts: 82 → 82

prune237.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch81.0ms

Steps

Iters	Range		Point
8	0.00035048323440066366	1.494961173861339	0.8824016443345339
9	-8327.681910469391	-0.031006959526126927	-1.0031499381962932

simplify1.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	2367×	body	1280	valid
501.0ms	1529×	body	640	valid
369.0ms	2144×	body	80	valid
275.0ms	778×	body	2560	valid
122.0ms	789×	body	320	valid
36.0ms	393×	body	160	valid