Details

sample132.0ms

Algorithm

intervals

Results

60.0ms	79×	body	1280	valid
31.0ms	41×	body	640	valid
16.0ms	26×	body	2560	valid
7.0ms	22×	body	320	valid
6.0ms	75×	body	80	valid
3.0ms	13×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ x (sqrt (+ (* x x) 1)))
2.7b	(log (+ x (sqrt (+ (* x x) 1))))
14.6b	(sqrt (+ (* x x) 1))

rewrite30.0ms

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:

11.0ms	(+ x (sqrt (+ (* x x) 1)))
10.0ms	(log (+ x (sqrt (+ (* x x) 1))))
8.0ms	(sqrt (+ (* x x) 1))

series214.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ x (sqrt (+ (* x x) 1)))
119.0ms	(log (+ x (sqrt (+ (* x x) 1))))
48.0ms	(sqrt (+ (* x x) 1))

simplify1.2s

Counts

54 → 54

Iterations

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

prune240.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* 3/40 (pow x 5))
0.1b	(* -1/6 (* (* x x) x))
21.0b	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

rewrite124.0ms

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:

24.0ms	(* (* x x) x)
13.0ms	(* 3/40 (pow x 5))
54.0ms	(* -1/6 (* (* x x) x))
31.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* x x) x)
73.0ms	(* 3/40 (pow x 5))
64.0ms	(* -1/6 (* (* x x) x))
85.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	2009
3	2009
2	1203
1	343
0	132

prune264.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ -1/16 (pow x 5))
0.5b	(/ 1/8 (* (* x x) x))
11.2b	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
19.1b	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

7.0ms	(/ -1/16 (pow x 5))
19.0ms	(/ 1/8 (* (* x x) x))
72.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
86.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ -1/16 (pow x 5))
48.0ms	(/ 1/8 (* (* x x) x))
141.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
68.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

simplify880.0ms

Counts

121 → 121

Iterations

Iter	Nodes
done	2003
2	2003
1	611
0	246

prune491.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
0.1b	(* (* x x) x)
0.5b	(/ 1/8 (* (* x x) x))
9.5b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
24×	`pow1`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`add-log-exp`
10×	`distribute-lft-out`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
5×	`sum-log`
4×	`insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `associate-+r-` `flip3-+` `pow-sqr` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `associate-+r+` `clear-num` `associate-/r` `frac-2neg` `diff-log` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

201.0ms	(+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
14.0ms	(* (* x x) x)
17.0ms	(/ 1/8 (* (* x x) x))
192.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
45.0ms	(* (* x x) x)
51.0ms	(/ 1/8 (* (* x x) x))
115.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2301
3	2301
2	1541
1	376
0	158

prune255.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch122.0ms

Steps

Iters	Range		Point
11	5.037382729650074e-10	1937402784720.5117	0.9496967329184121
7	-3.5555834389191174	-0.13673991589698092	-1.076228701950242

simplify14.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	2345×	body	1280	valid
747.0ms	1530×	body	640	valid
562.0ms	818×	body	2560	valid
257.0ms	802×	body	320	valid
184.0ms	2105×	body	80	valid
71.0ms	400×	body	160	valid