Details

sample152.0ms

Algorithm

intervals

Results

79.0ms	84×	body	1280	valid
26.0ms	42×	body	640	valid
14.0ms	18×	body	2560	valid
12.0ms	31×	body	320	valid
6.0ms	65×	body	80	valid
4.0ms	16×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.9b

localize47.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ x (sqrt (+ (* x x) 1)))
3.6b	(log (+ x (sqrt (+ (* x x) 1))))
15.4b	(sqrt (+ (* x x) 1))

rewrite51.0ms

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:

15.0ms	(+ x (sqrt (+ (* x x) 1)))
22.0ms	(log (+ x (sqrt (+ (* x x) 1))))
14.0ms	(sqrt (+ (* x x) 1))

series273.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(+ x (sqrt (+ (* x x) 1)))
165.0ms	(log (+ x (sqrt (+ (* x x) 1))))
41.0ms	(sqrt (+ (* x x) 1))

simplify1.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	2000
4	2000
3	1978
2	707
1	273
0	121

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.1b	(* -1/6 (* (* x x) x))
17.7b	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

14.0ms	(* 3/40 (pow x 5))
14.0ms	(* (* x x) x)
38.0ms	(* -1/6 (* (* x x) x))
19.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 3/40 (pow x 5))
50.0ms	(* (* x x) x)
52.0ms	(* -1/6 (* (* x x) x))
89.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

simplify1.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	2020
3	2020
2	1177
1	344
0	132

prune297.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1/8 (* (* x x) x))
0.1b	(* (* x x) x)
10.7b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite235.0ms

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-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
5×	`distribute-lft-out`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`pow2` `log-div` `pow-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3-+` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 71

Calls

3 calls:

14.0ms	(/ 1/8 (* (* x x) x))
19.0ms	(* (* x x) x)
201.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series280.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ 1/8 (* (* x x) x))
62.0ms	(* (* x x) x)
152.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify1.0s

Counts

80 → 80

Iterations

Iter	Nodes
done	2000
3	2000
2	880
1	314
0	135

prune237.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(/ -1/16 (pow x 5))
13.1b	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
21.6b	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
24×	`pow1`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
21×	`times-frac`
15×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
9×	`add-log-exp`
8×	`frac-add`
7×	`associate-/r*`
6×	`pow-plus` `pow-prod-up` `distribute-lft-out`
5×	`log-div` `log-prod`
4×	`flip3-+` `flip-+` `insert-posit16` `sqr-pow`
3×	`sum-log` `div-exp` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`pow2` `pow-sqr`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `pow-exp` `log-pow` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

16.0ms	(* (* x x) x)
9.0ms	(/ -1/16 (pow x 5))
63.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
65.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* x x) x)
67.0ms	(/ -1/16 (pow x 5))
104.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
80.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	2029
3	2029
2	1963
1	564
0	229

prune411.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.0b

bsearch108.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	48819.349325626084	0.9441797120105823
9	-6838974.188497498	-0.005838610583870787	-1.0580774043529224

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	2395×	body	1280	valid
1.1s	1561×	body	640	valid
550.0ms	797×	body	2560	valid
313.0ms	767×	body	320	valid
192.0ms	2085×	body	80	valid
91.0ms	395×	body	160	valid