Details

sample136.0ms

Algorithm

intervals

Results

69.0ms	87×	body	1280	valid
24.0ms	46×	body	640	valid
14.0ms	23×	body	2560	valid
11.0ms	65×	body	80	valid
8.0ms	28×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ x (sqrt (+ (* x x) 1)))
1.7b	(log (+ x (sqrt (+ (* x x) 1))))
14.2b	(sqrt (+ (* x x) 1))

rewrite50.0ms

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-+` `insert-posit16`
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 → 45

Calls

3 calls:

31.0ms	(+ x (sqrt (+ (* x x) 1)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series261.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(+ x (sqrt (+ (* x x) 1)))
125.0ms	(log (+ x (sqrt (+ (* x x) 1))))
55.0ms	(sqrt (+ (* x x) 1))

simplify1.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	1978
2	707
1	273
0	121

prune203.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 1/6)
18.0b	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
23×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`associate-r`
12×	`prod-exp`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt` `add-log-exp`
6×	`pow-plus` `pow-prod-up`
5×	`associate-l`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `associate-+l+` `sum-log` `pow-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sub-neg` `flip3-+` `diff-log` `pow3` `pow-exp` `associate-+l-` `flip-+`

Counts

4 → 93

Calls

4 calls:

9.0ms	(* 3/40 (pow x 5))
18.0ms	(* (* x x) x)
78.0ms	(* (* (* x x) x) 1/6)
26.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* 3/40 (pow x 5))
59.0ms	(* (* x x) x)
58.0ms	(* (* (* x x) x) 1/6)
59.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

simplify2.7s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
3	3928
2	964
1	330
0	134

prune307.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1/16 (pow x 5))
0.5b	(/ 1/8 (* (* x x) x))
11.4b	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
21.5b	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`times-frac`
23×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`unpow-prod-down`
8×	`associate-/r*`
7×	`log-prod`
6×	`div-exp` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1` `log-div` `frac-sub` `sqr-pow`
4×	`cbrt-undiv` `insert-posit16` `distribute-lft-out--`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`clear-num` `frac-2neg` `div-inv`
1×	`pow-to-exp` `sub-neg` `diff-log` `rem-log-exp` `pow-exp` `log-pow`

Counts

4 → 111

Calls

4 calls:

5.0ms	(/ 1/16 (pow x 5))
14.0ms	(/ 1/8 (* (* x x) x))
96.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
42.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ 1/16 (pow x 5))
52.0ms	(/ 1/8 (* (* x x) x))
157.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
190.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

simplify1.3s

Counts

123 → 123

Iterations

Iter	Nodes
done	5199
2	2093
1	591
0	263

prune528.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.5b	(/ 1/8 (* (* x x) x))
10.0b	(log (+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
18×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`log-div` `log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`frac-add` `distribute-lft-out`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`pow2` `flip3-+` `pow-sqr` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3--` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `div-inv` `flip--` `unswap-sqr`

Counts

3 → 75

Calls

3 calls:

14.0ms	(* (* x x) x)
15.0ms	(/ 1/8 (* (* x x) x))
67.0ms	(log (+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x)))))

series180.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* (* x x) x)
43.0ms	(/ 1/8 (* (* x x) x))
95.0ms	(log (+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x)))))

simplify1.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5003
2	1512
1	470
0	182

prune304.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes185.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.6b

bsearch145.0ms

Steps

Iters	Range		Point
11	4.21785760657603e-35	57.56933376468871	0.9540314055762552
9	-34.11472770615283	-3.67231414207575e-08	-1.0840635159626253

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	32

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	2352×	body	1280	valid
824.0ms	1515×	body	640	valid
504.0ms	786×	body	2560	valid
250.0ms	2138×	body	80	valid
242.0ms	773×	body	320	valid
73.0ms	436×	body	160	valid