Details

sample106.0ms

Algorithm

intervals

Results

50.0ms	76×	body	1280	valid
16.0ms	41×	body	640	valid
14.0ms	29×	body	2560	valid
5.0ms	19×	body	320	valid
5.0ms	80×	body	80	valid
2.0ms	11×	body	160	valid

simplify24.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (sqrt (+ (* x x) 1.0)))
2.7b	(log (+ x (sqrt (+ (* x x) 1.0))))
19.1b	(sqrt (+ (* x x) 1.0))

rewrite74.0ms

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:

18.0ms	(+ x (sqrt (+ (* x x) 1.0)))
44.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms	(sqrt (+ (* x x) 1.0))

series413.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(+ x (sqrt (+ (* x x) 1.0)))
257.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
63.0ms	(sqrt (+ (* x x) 1.0))

simplify1.4s

Counts: 51 → 51

prune230.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite195.0ms

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:

150.0ms

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

series238.0ms

Counts

1 → 3

Calls

1 calls:

237.0ms

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

simplify1.5s

Counts: 273 → 273

prune670.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 0.25 x) x)
0.1b	(* 0.09375 (/ 1 (pow x 4)))
0.3b	(/ 1 (pow x 4))
5.8b	(- (- (* 0.09375 (/ 1 (pow x 4))) (log x)) (/ (/ 0.25 x) x))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
101×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
77×	`add-cube-cbrt`
38×	`add-exp-log`
25×	`associate-r`
23×	`unpow-prod-down`
16×	`add-cbrt-cube` `associate-/l*`
15×	`div-exp`
10×	`prod-exp` `associate-/r*`
9×	`sqr-pow`
8×	`add-log-exp`
7×	`div-inv` `unswap-sqr`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp`
5×	`cbrt-undiv`
3×	`diff-log` `associate-l` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `associate--l+` `clear-num` `frac-sub` `flip--` `cbrt-unprod`
1×	`associate--l-` `pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `associate-/l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 203

Calls

4 calls:

13.0ms	(/ (/ 0.25 x) x)
42.0ms	(* 0.09375 (/ 1 (pow x 4)))
16.0ms	(/ 1 (pow x 4))
164.0ms	(- (- (* 0.09375 (/ 1 (pow x 4))) (log x)) (/ (/ 0.25 x) x))

series248.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ 0.25 x) x)
62.0ms	(* 0.09375 (/ 1 (pow x 4)))
30.0ms	(/ 1 (pow x 4))
126.0ms	(- (- (* 0.09375 (/ 1 (pow x 4))) (log x)) (/ (/ 0.25 x) x))

simplify1.2s

Counts: 215 → 215

prune809.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 2 x) (* 0.125 (/ 1 (pow x 3))))
0.0b	(+ (- (* 2 x) (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))
0.2b	(/ 1 (pow x 3))
11.2b	(log (+ (- (* 2 x) (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

9.0ms	(- (* 2 x) (* 0.125 (/ 1 (pow x 3))))
47.0ms	(+ (- (* 2 x) (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))
10.0ms	(/ 1 (pow x 3))
37.0ms	(log (+ (- (* 2 x) (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (* 2 x) (* 0.125 (/ 1 (pow x 3))))
63.0ms	(+ (- (* 2 x) (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))
57.0ms	(/ 1 (pow x 3))
250.0ms	(log (+ (- (* 2 x) (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))

simplify909.0ms

Counts: 132 → 132

prune392.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes187.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.9b

bsearch135.0ms

Steps

Iters	Range		Point
8	0.0026080803058150265	15.61478477777618	0.8937069043444494
10	-380908646326105.1	-0.06705623481545048	-1.0296652542029618

simplify481.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	2341×	body	1280	valid
563.0ms	1538×	body	640	valid
389.0ms	409×	body	160	valid
347.0ms	774×	body	2560	valid
197.0ms	769×	body	320	valid
123.0ms	2169×	body	80	valid