Details

sample142.0ms

Algorithm

intervals

Results

65.0ms	81×	body	1280	valid
32.0ms	52×	body	640	valid
18.0ms	28×	body	2560	valid
7.0ms	22×	body	320	valid
5.0ms	62×	body	80	valid
2.0ms	11×	body	160	valid

simplify4.0ms

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: 53.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ x (sqrt (+ (* x x) 1)))
2.8b	(log (+ x (sqrt (+ (* x x) 1))))
16.2b	(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:

36.0ms	(+ x (sqrt (+ (* x x) 1)))
13.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series238.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (+ (* x x) 1)))
136.0ms	(log (+ x (sqrt (+ (* x x) 1))))
41.0ms	(sqrt (+ (* x x) 1))

simplify1.9s

Counts

54 → 54

Iterations

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

prune606.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))
19.7b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

rewrite172.0ms

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:

28.0ms	(* (* x x) x)
26.0ms	(* (* x x) x)
67.0ms	(* -1/6 (* (* x x) x))
49.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* x x) x)
43.0ms	(* (* x x) x)
41.0ms	(* -1/6 (* (* x x) x))
187.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

simplify3.4s

Counts

104 → 104

Iterations

Iter	Nodes
3	5081
2	907
1	256
0	88

prune746.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ (/ 1/8 x) (* x x))
15.1b	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
20.1b	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite369.0ms

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:

29.0ms	(* (* x x) x)
19.0ms	(/ (/ 1/8 x) (* x x))
146.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
173.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x x) x)
64.0ms	(/ (/ 1/8 x) (* x x))
163.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
93.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify11.6s

Counts

129 → 129

Iterations

Iter	Nodes
3	11604
2	1992
1	609
0	242

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ 1/8 x) (* x x))
13.1b	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

32×	`times-frac`
26×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`log-prod`
6×	`cbrt-undiv` `log-div` `div-exp` `frac-sub`
5×	`distribute-lft-out--`
3×	`pow1` `div-inv`
2×	`flip3--` `prod-exp` `cbrt-unprod` `insert-posit16` `flip--` `add-log-exp` `difference-of-squares`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

2 → 71

Calls

2 calls:

11.0ms	(/ (/ 1/8 x) (* x x))
74.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

series167.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (/ 1/8 x) (* x x))
101.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

simplify4.3s

Counts

77 → 77

Iterations

Iter	Nodes
3	7001
2	1708
1	596
0	226

prune603.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch125.0ms

Steps

Iters	Range		Point
11	1.0334628320549359e-08	2.7368728718549235e+26	0.9440471341056946
9	-128555.04713805256	-0.18430940072566707	-1.0816386065582386

simplify9.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	2338×	body	1280	valid
730.0ms	1571×	body	640	valid
509.0ms	788×	body	2560	valid
258.0ms	800×	body	320	valid
155.0ms	2112×	body	80	valid
119.0ms	391×	body	160	valid