Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	56×	body	1280	valid
7.0ms	134×	body	80	valid
7.0ms	33×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	6×	body	160	valid

simplify157.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
1.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
48×	`times-frac`
47×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
16×	`distribute-lft-out`
15×	`add-cube-cbrt`
14×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-sub` `flip-+` `div-inv`

Counts

2 → 83

Calls

2 calls:

17.0ms	(/ (+ x 1) (- x 1))
45.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series110.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ (+ x 1) (- x 1))
85.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify600.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	2000
2	869
1	327
0	141

prune244.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1))
6.8b	(- (/ x (+ x 1)) (* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1)))
15.0b	(/ (+ x 1) (- (* x x) (* 1 1)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
33×	`times-frac`
28×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
22×	`associate-l`
10×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
9×	`difference-of-squares`
5×	`pow1` `flip3-+` `frac-sub` `flip-+` `add-log-exp`
4×	`frac-times` `associate-/r` `associate-r` `associate-r/` `associate-/r/` `associate-/l*`
3×	`flip3--` `insert-posit16` `flip--`
2×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate--r+` `unswap-sqr` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

3 → 110

Calls

3 calls:

50.0ms	(* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1))
32.0ms	(- (/ x (+ x 1)) (* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1)))
20.0ms	(/ (+ x 1) (- (* x x) (* 1 1)))

series230.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1))
143.0ms	(- (/ x (+ x 1)) (* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1)))
39.0ms	(/ (+ x 1) (- (* x x) (* 1 1)))

simplify496.0ms

Counts

119 → 119

Iterations

Iter	Nodes
done	2000
1	683
0	192

prune385.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- x 1))
0.1b	(* (/ 1 (- x 1)) (+ x 1))
6.8b	(- (/ x (+ x 1)) (* (/ 1 (- x 1)) (+ x 1)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
44×	`times-frac`
27×	`associate-l` `add-cube-cbrt`
16×	`add-exp-log`
14×	`difference-of-squares`
10×	`add-cbrt-cube`
7×	`associate-/r*` `difference-of-sqr-1` `distribute-lft-out--`
6×	`pow1`
5×	`frac-sub` `add-log-exp`
4×	`frac-times` `flip3-+` `div-exp` `associate-r` `prod-exp` `associate-*r/` `associate-/r/` `flip-+`
3×	`flip3--` `insert-posit16` `flip--` `associate-/l*` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `associate--r+`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `distribute-lft-out` `inv-pow`

Counts

3 → 127

Calls

3 calls:

13.0ms	(/ 1 (- x 1))
41.0ms	(* (/ 1 (- x 1)) (+ x 1))
47.0ms	(- (/ x (+ x 1)) (* (/ 1 (- x 1)) (+ x 1)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 1 (- x 1))
33.0ms	(* (/ 1 (- x 1)) (+ x 1))
101.0ms	(- (/ x (+ x 1)) (* (/ 1 (- x 1)) (+ x 1)))

simplify488.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	2001
1	680
0	202

prune405.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ -3 (* x (* x x)))
0.1b	(* x (* x x))
0.5b	(/ -1 (* x x))
7.2b	(+ (+ (/ -3 (* x (* x x))) (/ -3 x)) (/ -1 (* x x)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ -3 (* x (* x x)))
13.0ms	(* x (* x x))
6.0ms	(/ -1 (* x x))
232.0ms	(+ (+ (/ -3 (* x (* x x))) (/ -3 x)) (/ -1 (* x x)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ -3 (* x (* x x)))
45.0ms	(* x (* x x))
28.0ms	(/ -1 (* x x))
26.0ms	(+ (+ (/ -3 (* x (* x x))) (/ -3 x)) (/ -1 (* x x)))

simplify651.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2002
2	1508
1	437
0	161

prune224.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 29.5b

bsearch114.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	10678.074230429429
10	-121993772661.31783	-0.0015977726548224043	-11573.705281839704

simplify8.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample2.1s

Algorithm

intervals

Results

710.0ms	1260×	body	640	valid
699.0ms	1748×	body	1280	valid
371.0ms	4092×	body	80	valid
180.0ms	626×	body	320	valid
59.0ms	274×	body	160	valid