Details

sample61.0ms

Algorithm

intervals

Results

23.0ms	56×	body	1280	valid
11.0ms	134×	body	80	valid
10.0ms	33×	body	640	valid
6.0ms	27×	body	320	valid
1.0ms	6×	body	160	valid

simplify194.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1266×	`*-un-lft-identity`
972×	`times-frac`
831×	`add-sqr-sqrt`
612×	`prod-diff`
511×	`add-cube-cbrt`
247×	`distribute-lft-out`
158×	`difference-of-squares`
108×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
54×	`div-inv`
36×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
7×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`

Counts

2 → 717

Calls

2 calls:

18.0ms	(/ (+ x 1) (- x 1))
93.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series123.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (+ x 1) (- x 1))
92.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.1s

Counts

723 → 723

Iterations

Iter	Nodes
done	2001
1	1328
0	565

prune2.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ (+ x 1) (- x 1))
1.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
31.2b	(fma (/ -1 (- x 1)) (+ x 1) (/ (+ x 1) (- x 1)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

1312×	`*-un-lft-identity`
1000×	`times-frac`
866×	`add-sqr-sqrt`
612×	`prod-diff`
526×	`add-cube-cbrt`
255×	`distribute-lft-out`
168×	`difference-of-squares`
110×	`associate-/r/`
95×	`distribute-lft-out--`
82×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`fma-neg`
14×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef`

Counts

4 → 786

Calls

4 calls:

27.0ms	(/ (+ x 1) (- x 1))
18.0ms	(/ (+ x 1) (- x 1))
71.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0ms	(fma (/ -1 (- x 1)) (+ x 1) (/ (+ x 1) (- x 1)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ x 1) (- x 1))
35.0ms	(/ (+ x 1) (- x 1))
407.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
142.0ms	(fma (/ -1 (- x 1)) (+ x 1) (/ (+ x 1) (- x 1)))

simplify1.3s

Counts

798 → 798

Iterations

Iter	Nodes
done	2001
1	1352
0	580

prune2.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 3 (* x (* x x)))
0.1b	(* x (* x x))
0.5b	(/ 1 (* x x))
9.0b	(+ (/ 3 (* x (* x x))) (/ 1 (* x x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
26×	`pow1`
23×	`add-cbrt-cube`
16×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`times-frac` `add-cube-cbrt`
9×	`prod-exp`
7×	`fma-def` `div-exp` `cbrt-unprod`
6×	`pow-prod-up` `pow-flip` `associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-l` `distribute-lft-out`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `1-exp` `pow-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `cube-unmult` `associate-r` `frac-add` `*-commutative` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

26.0ms	(/ 3 (* x (* x x)))
15.0ms	(* x (* x x))
9.0ms	(/ 1 (* x x))
57.0ms	(+ (/ 3 (* x (* x x))) (/ 1 (* x x)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 3 (* x (* x x)))
47.0ms	(* x (* x x))
26.0ms	(/ 1 (* x x))
122.0ms	(+ (/ 3 (* x (* x x))) (/ 1 (* x x)))

simplify609.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2002
2	1054
1	349
0	142

prune443.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.5b	(/ 1 (* x x))
1.5b	(log (exp (+ (/ 3 (* x (* x x))) (/ 1 (* x x)))))
9.0b	(+ (/ 3 (* x (* x x))) (/ 1 (* x x)))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
21×	`*-un-lft-identity`
20×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
10×	`times-frac`
7×	`fma-def` `log-pow`
6×	`exp-prod` `prod-exp` `pow-prod-up` `pow-flip` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `div-exp` `pow-prod-down` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-l` `associate-/l*`
2×	`pow2` `cbrt-undiv` `rec-exp` `pow-plus` `1-exp` `pow-sqr`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `cube-unmult` `rem-log-exp` `associate-r` `exp-sum` `frac-add` `-commutative` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

23.0ms	(* x (* x x))
18.0ms	(/ 1 (* x x))
198.0ms	(log (exp (+ (/ 3 (* x (* x x))) (/ 1 (* x x)))))
69.0ms	(+ (/ 3 (* x (* x x))) (/ 1 (* x x)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* x (* x x))
18.0ms	(/ 1 (* x x))
108.0ms	(log (exp (+ (/ 3 (* x (* x x))) (/ 1 (* x x)))))
105.0ms	(+ (/ 3 (* x (* x x))) (/ 1 (* x x)))

simplify854.0ms

Counts

121 → 121

Iterations

Iter	Nodes
done	2002
2	872
1	310
0	137

prune451.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch169.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	13418.220827984447
10	-121993772661.31783	-0.0015977726548224043	-10835.479300405816

simplify21.0ms

Iterations

Iter	Nodes
done	52
4	52
3	50
2	47
1	39
0	26

end0.0ms

sample2.0s

Algorithm

intervals

Results

823.0ms	1748×	body	1280	valid
524.0ms	1260×	body	640	valid
360.0ms	4092×	body	80	valid
145.0ms	626×	body	320	valid
42.0ms	274×	body	160	valid