Details

sample79.0ms

Algorithm

intervals

Results

29.0ms	84×	body	1280	valid
17.0ms	56×	body	10240	exit
13.0ms	41×	body	640	valid
5.0ms	95×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	9
1	9
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1))
3.7b	(- (exp x) 1)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 80

Calls

2 calls:

14.0ms	(/ (exp x) (- (exp x) 1))
10.0ms	(- (exp x) 1)

series64.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1))
33.0ms	(- (exp x) 1)

simplify4.0s

Counts

86 → 86

Iterations

Iter	Nodes
4	6277
3	1634
2	570
1	249
0	126

prune436.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) 1)
0.2b	(/ (expm1 (+ x x)) (+ (exp x) 1))
0.3b	(/ (exp x) (/ (expm1 (+ x x)) (+ (exp x) 1)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
98×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
17×	`distribute-lft-out`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`add-exp-log`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `div-sub` `expm1-udef`

Counts

3 → 148

Calls

3 calls:

8.0ms	(+ (exp x) 1)
15.0ms	(/ (expm1 (+ x x)) (+ (exp x) 1))
16.0ms	(/ (exp x) (/ (expm1 (+ x x)) (+ (exp x) 1)))

series106.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (exp x) 1)
43.0ms	(/ (expm1 (+ x x)) (+ (exp x) 1))
54.0ms	(/ (exp x) (/ (expm1 (+ x x)) (+ (exp x) 1)))

simplify1.9s

Counts

157 → 157

Iterations

Iter	Nodes
2	2042
1	548
0	220

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma x 1/12 1/2) (/ 1 x))
0.1b	(fma x 1/12 1/2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+` `div-inv`

Counts

2 → 31

Calls

2 calls:

6.0ms	(+ (fma x 1/12 1/2) (/ 1 x))
0.0ms	(fma x 1/12 1/2)

series84.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (fma x 1/12 1/2) (/ 1 x))
54.0ms	(fma x 1/12 1/2)

simplify5.4s

Counts

37 → 37

Iterations

Iter	Nodes
4	7137
3	1496
2	338
1	103
0	45

prune209.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x 1/2) (/ 1 x))
0.1b	(fma 1/12 x 1/2)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+` `div-inv`

Counts

2 → 31

Calls

2 calls:

12.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
1.0ms	(fma 1/12 x 1/2)

series58.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
38.0ms	(fma 1/12 x 1/2)

simplify5.4s

Counts

37 → 37

Iterations

Iter	Nodes
4	7123
3	1816
2	421
1	115
0	44

prune285.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes46.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	2292×	body	1280	valid
1.1s	2471×	body	10240	exit
570.0ms	1611×	body	640	valid
227.0ms	2861×	body	80	valid
170.0ms	819×	body	320	valid
55.0ms	419×	body	160	valid