Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	56×	body	1280	valid
25.0ms	127×	body	80	valid
16.0ms	39×	body	640	valid
7.0ms	24×	body	320	valid
2.0ms	10×	body	160	valid

simplify12.4s

Counts

1 → 1

Iterations

Iter	Nodes
9	9728
8	1956
7	573
6	233
5	101
4	49
3	28
2	20
1	16
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
2.8b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 150

Calls

3 calls:

8.0ms	(+ 1 (exp (* -2 x)))
16.0ms	(/ 2 (+ 1 (exp (* -2 x))))
64.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series125.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1 (exp (* -2 x)))
28.0ms	(/ 2 (+ 1 (exp (* -2 x))))
82.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.5s

Counts

159 → 159

Iterations

Iter	Nodes
3	2094
2	889
1	406
0	183

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* -2 x)) 1)
0.0b	(/ 2 (+ (exp (* -2 x)) 1))
2.8b	(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 150

Calls

3 calls:

9.0ms	(+ (exp (* -2 x)) 1)
24.0ms	(/ 2 (+ (exp (* -2 x)) 1))
129.0ms	(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

series109.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ (exp (* -2 x)) 1)
21.0ms	(/ 2 (+ (exp (* -2 x)) 1))
77.0ms	(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

simplify1.4s

Counts

159 → 159

Iterations

Iter	Nodes
3	2127
2	853
1	397
0	180

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* (* x x) x)
20.6b	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

rewrite32.0ms

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)
30.0ms	(* (* x x) x)
1.0ms	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

series239.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(fma (pow x 5) 2/15 x)
36.0ms	(* (* x x) x)
76.0ms	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

simplify2.6s

Counts

62 → 62

Iterations

Iter	Nodes
4	5996
3	1256
2	350
1	130
0	70

prune601.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
0.2b	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
0.2b	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
2.7b	(fma (* (cbrt (/ 2 (+ 1 (exp (* -2 x))))) (cbrt (/ 2 (+ 1 (exp (* -2 x)))))) (cbrt (/ 2 (+ 1 (exp (* -2 x))))) -1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
46×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`distribute-lft-out`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`fma-udef`

Counts

4 → 101

Calls

4 calls:

5.0ms	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
8.0ms	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
10.0ms	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
1.0ms	(fma (* (cbrt (/ 2 (+ 1 (exp (* -2 x))))) (cbrt (/ 2 (+ 1 (exp (* -2 x)))))) (cbrt (/ 2 (+ 1 (exp (* -2 x))))) -1)

series1.2s

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
204.0ms	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
172.0ms	(cbrt (/ 2 (+ 1 (exp (* -2 x)))))
648.0ms	(fma (* (cbrt (/ 2 (+ 1 (exp (* -2 x))))) (cbrt (/ 2 (+ 1 (exp (* -2 x)))))) (cbrt (/ 2 (+ 1 (exp (* -2 x))))) -1)

simplify4.4s

Counts

113 → 113

Iterations

Iter	Nodes
4	6712
3	1748
2	573
1	234
0	124

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes546.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch2.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	34
1	34
0	30

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	1687×	body	1280	valid
668.0ms	4089×	body	80	valid
542.0ms	1223×	body	640	valid
187.0ms	670×	body	320	valid
57.0ms	331×	body	160	valid