Details

sample88.0ms

Algorithm

intervals

Results

40.0ms	70×	body	1280	valid
18.0ms	50×	body	640	valid
9.0ms	20×	body	2560	valid
6.0ms	26×	body	320	valid
4.0ms	81×	body	80	valid
1.0ms	9×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ x (sqrt (+ (* x x) 1.0)))
2.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b	(sqrt (+ (* x x) 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

13.0ms	(+ x (sqrt (+ (* x x) 1.0)))
14.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms	(sqrt (+ (* x x) 1.0))

series738.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(+ x (sqrt (+ (* x x) 1.0)))
579.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
81.0ms	(sqrt (+ (* x x) 1.0))

simplify628.0ms

Counts

51 → 51

Iterations

Useful iterations: done (626.0ms)

Iter	Nodes	Cost
0	134	761
1	320	691
2	1377	618
done	5001	606

prune320.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 1 expressions with local error:

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`*-un-lft-identity` `add-cube-cbrt`
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` `add-cbrt-cube` `pow-exp`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 270

Calls

1 calls:

114.0ms

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

series151.0ms

Counts

1 → 3

Calls

1 calls:

151.0ms

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

simplify413.0ms

Counts

273 → 273

Iterations

Useful iterations: done (405.0ms)

Iter	Nodes	Cost
0	293	3830
1	854	2926
done	5001	2621

prune681.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* 2 x) (/ 0.125 (pow x 3)))
0.1b	(/ 0.125 (pow x 3))
12.6b	(log (+ (/ 0.5 x) (- (* 2 x) (/ 0.125 (pow x 3)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

15.0ms	(- (* 2 x) (/ 0.125 (pow x 3)))
6.0ms	(/ 0.125 (pow x 3))
53.0ms	(log (+ (/ 0.5 x) (- (* 2 x) (/ 0.125 (pow x 3)))))

series444.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(- (* 2 x) (/ 0.125 (pow x 3)))
49.0ms	(/ 0.125 (pow x 3))
237.0ms	(log (+ (/ 0.5 x) (- (* 2 x) (/ 0.125 (pow x 3)))))

simplify1.0s

Counts

103 → 103

Iterations

Useful iterations: 2 (417.0ms)

Iter	Nodes	Cost
0	198	1529
1	471	1313
2	2093	1251
done	5002	1251

prune394.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0))))))
4.0b	(+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
15.4b	(cbrt (+ (* x x) 1.0))
15.4b	(cbrt (+ (* x x) 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

5.0ms	(log (+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0))))))
8.0ms	(+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
9.0ms	(cbrt (+ (* x x) 1.0))
9.0ms	(cbrt (+ (* x x) 1.0))

series710.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log (+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0))))))
107.0ms	(+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
266.0ms	(cbrt (+ (* x x) 1.0))
248.0ms	(cbrt (+ (* x x) 1.0))

simplify797.0ms

Counts

63 → 63

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	167	1513
1	432	1416
2	1730	1239
done	5000	1218

prune366.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.5b

bsearch147.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.8895740307587359
7	-22.8286883066892	-0.10952899301968014	-1.0200493385609686

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	57
1	40	57
done	40	57

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	2422×	body	1280	valid
620.0ms	1486×	body	640	valid
517.0ms	810×	body	320	valid
437.0ms	801×	body	2560	valid
158.0ms	2073×	body	80	valid
55.0ms	408×	body	160	valid