Details

sample92.0ms

Algorithm

intervals

Results

44.0ms	70×	body	1280	valid
16.0ms	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

Iter	Nodes
done	9
1	9
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize10.0ms

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))

rewrite73.0ms

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:

37.0ms	(+ x (sqrt (+ (* x x) 1.0)))
26.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms	(sqrt (+ (* x x) 1.0))

series362.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(+ x (sqrt (+ (* x x) 1.0)))
239.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
54.0ms	(sqrt (+ (* x x) 1.0))

simplify697.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
2	1377
1	320
0	134

prune290.0ms

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
106×	`times-frac`
76×	`associate-l`
51×	`*-un-lft-identity` `add-cube-cbrt`
44×	`sqrt-prod`
25×	`add-exp-log`
22×	`unpow-prod-down` `cube-prod`
18×	`unswap-sqr`
13×	`add-cbrt-cube` `associate-r`
10×	`div-exp` `sqr-pow`
8×	`prod-exp`
6×	`cube-mult` `unpow3`
4×	`cbrt-undiv` `cbrt-unprod`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `add-log-exp`

Counts

1 → 131

Calls

1 calls:

62.0ms

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

series104.0ms

Counts

1 → 3

Calls

1 calls:

104.0ms

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

simplify1.6s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	2721
1	544
0	175

prune738.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite149.0ms

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:

30.0ms	(- (* x 2) (/ 0.125 (pow x 3)))
13.0ms	(/ 0.125 (pow x 3))
100.0ms	(log (+ (/ 0.5 x) (- (* x 2) (/ 0.125 (pow x 3)))))

series422.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(- (* x 2) (/ 0.125 (pow x 3)))
52.0ms	(/ 0.125 (pow x 3))
232.0ms	(log (+ (/ 0.5 x) (- (* x 2) (/ 0.125 (pow x 3)))))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2124
1	474
0	199

prune488.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

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))

rewrite24.0ms

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:

3.0ms	(log (+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0))))))
5.0ms	(+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
4.0ms	(cbrt (+ (* x x) 1.0))
10.0ms	(cbrt (+ (* x x) 1.0))

series667.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(log (+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0))))))
99.0ms	(+ x (* (fabs (cbrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
241.0ms	(cbrt (+ (* x x) 1.0))
215.0ms	(cbrt (+ (* x x) 1.0))

simplify898.0ms

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
2	1730
1	432
0	167

prune403.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch106.0ms

Steps

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

simplify4.0ms

Iterations

Iter	Nodes
done	40
1	40
0	35

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	2422×	body	1280	valid
449.0ms	801×	body	2560	valid
428.0ms	1486×	body	640	valid
394.0ms	2073×	body	80	valid
136.0ms	810×	body	320	valid
41.0ms	408×	body	160	valid