Details

sample72.0ms

Algorithm

intervals

Results

24.0ms	61×	body	1280	valid
9.0ms	39×	body	640	valid
6.0ms	122×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
8	2490
7	682
6	240
5	101
4	51
3	30
2	22
1	18
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
2.7b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
63×	`times-frac`
61×	`add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-exp-log`
5×	`flip3-+` `flip-+` `div-inv`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `expm1-def` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

2 → 132

Calls

2 calls:

11.0ms	(/ 2 (+ 1 (exp (* -2 x))))
58.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series113.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(/ 2 (+ 1 (exp (* -2 x))))
92.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify2.9s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
3	2451
2	948
1	397
0	172

prune402.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* (* x x) x)
16.9b	(fma -1/3 (* (* x x) x) (fma (pow x 5) 2/15 x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/15 x)
17.0ms	(* (* x x) x)
0.0ms	(fma -1/3 (* (* x x) x) (fma (pow x 5) 2/15 x))

series340.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(fma (pow x 5) 2/15 x)
58.0ms	(* (* x x) x)
81.0ms	(fma -1/3 (* (* x x) x) (fma (pow x 5) 2/15 x))

simplify1.7s

Counts

62 → 62

Iterations

Iter	Nodes
done	5006
3	1700
2	388
1	136
0	70

prune262.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 8 (+ (exp (* x -2)) 1))
0.0b	(/ (/ 8 (+ (exp (* x -2)) 1)) (* (+ (exp (* x -2)) 1) (+ (exp (* x -2)) 1)))
0.0b	(fma (/ 2 (+ (exp (* x -2)) 1)) (/ 2 (+ (exp (* x -2)) 1)) (+ (/ 2 (+ (exp (* x -2)) 1)) 1))
2.7b	(- (/ (/ 8 (+ (exp (* x -2)) 1)) (* (+ (exp (* x -2)) 1) (+ (exp (* x -2)) 1))) 1)

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

183×	`times-frac`
144×	`*-un-lft-identity`
110×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
90×	`prod-diff`
54×	`associate-/r/`
37×	`flip3-+` `flip-+`
31×	`add-exp-log`
30×	`fma-neg`
22×	`distribute-lft-out`
21×	`associate-/l*`
20×	`frac-times`
18×	`add-cbrt-cube`
13×	`div-exp`
12×	`div-inv`
10×	`associate-l/` `associate-r/`
7×	`cbrt-undiv`
6×	`add-log-exp` `difference-of-squares`
5×	`expm1-def` `associate-/r*`
4×	`expm1-log1p-u` `pow1` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-sqr-1`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 264

Calls

4 calls:

26.0ms	(/ 8 (+ (exp (* x -2)) 1))
80.0ms	(/ (/ 8 (+ (exp (* x -2)) 1)) (* (+ (exp (* x -2)) 1) (+ (exp (* x -2)) 1)))
0.0ms	(fma (/ 2 (+ (exp (* x -2)) 1)) (/ 2 (+ (exp (* x -2)) 1)) (+ (/ 2 (+ (exp (* x -2)) 1)) 1))
235.0ms	(- (/ (/ 8 (+ (exp (* x -2)) 1)) (* (+ (exp (* x -2)) 1) (+ (exp (* x -2)) 1))) 1)

series322.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 8 (+ (exp (* x -2)) 1))
58.0ms	(/ (/ 8 (+ (exp (* x -2)) 1)) (* (+ (exp (* x -2)) 1) (+ (exp (* x -2)) 1)))
130.0ms	(fma (/ 2 (+ (exp (* x -2)) 1)) (/ 2 (+ (exp (* x -2)) 1)) (+ (/ 2 (+ (exp (* x -2)) 1)) 1))
98.0ms	(- (/ (/ 8 (+ (exp (* x -2)) 1)) (* (+ (exp (* x -2)) 1) (+ (exp (* x -2)) 1))) 1)

simplify3.0s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
2	2914
1	854
0	331

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes168.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch166.0ms

Steps

Iters	Range		Point
8	0.0004981816479932727	5.220773054910798	0.006963305059651398
10	-0.5767180207385502	-1.7878892965255107e-15	-0.006778948484773374

simplify9.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample2.2s

Algorithm

intervals

Results

821.0ms	1708×	body	1280	valid
580.0ms	4112×	body	80	valid
411.0ms	1233×	body	640	valid
121.0ms	625×	body	320	valid
40.0ms	322×	body	160	valid