Details

sample127.0ms

Algorithm

intervals

Results

64.0ms	76×	body	1280	valid
28.0ms	50×	body	640	valid
10.0ms	15×	body	2560	valid
7.0ms	24×	body	320	valid
6.0ms	71×	body	80	valid
3.0ms	20×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	9
1	9
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize20.0ms

Local error

Found 3 expressions with local error:

1.6b	(+ x (sqrt (+ (* x x) 1)))
3.8b	(log (+ x (sqrt (+ (* x x) 1))))
14.0b	(sqrt (+ (* x x) 1))

rewrite57.0ms

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:

38.0ms	(+ x (sqrt (+ (* x x) 1)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series281.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ x (sqrt (+ (* x x) 1)))
152.0ms	(log (+ x (sqrt (+ (* x x) 1))))
43.0ms	(sqrt (+ (* x x) 1))

simplify1.7s

Counts

54 → 54

Iterations

Iter	Nodes
4	3922
3	1654
2	660
1	271
0	121

prune610.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* x x) x)
0.1b	(* -1/6 (* (* x x) x))
17.2b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

29.0ms	(* (* x x) x)
31.0ms	(* (* x x) x)
43.0ms	(* -1/6 (* (* x x) x))
82.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x x) x)
65.0ms	(* (* x x) x)
53.0ms	(* -1/6 (* (* x x) x))
233.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

simplify2.8s

Counts

104 → 104

Iterations

Iter	Nodes
3	5081
2	907
1	256
0	88

prune688.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ 1/8 x) (* x x)) (+ x x))
0.0b	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
0.1b	(/ (/ 1/8 x) (* x x))
10.7b	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `times-frac`
19×	`add-cube-cbrt`
18×	`add-log-exp`
17×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`frac-sub`
13×	`associate-/l*`
12×	`distribute-lft-out--`
8×	`log-prod`
7×	`diff-log` `difference-of-squares`
6×	`cbrt-undiv` `log-div` `div-exp`
5×	`pow1` `flip3--` `flip--`
4×	`insert-posit16`
3×	`sub-neg` `flip3-+` `flip-+` `div-inv` `distribute-lft-out` `associate--r+`
2×	`sum-log` `prod-exp` `cbrt-unprod`
1×	`clear-num` `associate-/r*` `frac-2neg` `rem-log-exp` `log-pow` `associate--r-` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

49.0ms	(- (/ (/ 1/8 x) (* x x)) (+ x x))
96.0ms	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
10.0ms	(/ (/ 1/8 x) (* x x))
79.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (/ (/ 1/8 x) (* x x)) (+ x x))
58.0ms	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
69.0ms	(/ (/ 1/8 x) (* x x))
150.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

simplify11.6s

Counts

132 → 132

Iterations

Iter	Nodes
3	8868
2	1891
1	660
0	263

prune843.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/8 x) (* x x))
0.1b	(* (* x x) x)
12.4b	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
18.8b	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

10.0ms	(/ (/ 1/8 x) (* x x))
15.0ms	(* (* x x) x)
117.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
186.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (/ 1/8 x) (* x x))
44.0ms	(* (* x x) x)
166.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
70.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify804.0ms

Counts

129 → 129

Iterations

Iter	Nodes
2	2025
1	623
0	242

prune994.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.2b

bsearch121.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.9645338519110289
9	-24078.920296370652	-0.35383103211093586	-1.061520745717705

simplify7.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	2354×	body	1280	valid
844.0ms	1532×	body	640	valid
535.0ms	784×	body	2560	valid
519.0ms	2135×	body	80	valid
292.0ms	784×	body	320	valid
98.0ms	411×	body	160	valid