Details

sample95.0ms

Algorithm

intervals

Results

31.0ms	44×	body	1280	valid
23.0ms	45×	body	640	valid
15.0ms	136×	body	80	valid
9.0ms	25×	body	320	valid
1.0ms	6×	body	160	valid

simplify13.7s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
2.1b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite125.0ms

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` `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 → 147

Calls

3 calls:

11.0ms	(+ 1 (exp (* -2 x)))
18.0ms	(/ 2 (+ 1 (exp (* -2 x))))
92.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series135.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ 1 (exp (* -2 x)))
30.0ms	(/ 2 (+ 1 (exp (* -2 x))))
94.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.2s

Counts

156 → 156

Iterations

Iter	Nodes
3	2046
2	861
1	403
0	180

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
2.1b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite86.0ms

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` `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 → 147

Calls

3 calls:

6.0ms	(+ 1 (exp (* -2 x)))
10.0ms	(/ 2 (+ 1 (exp (* -2 x))))
68.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series104.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(+ 1 (exp (* -2 x)))
21.0ms	(/ 2 (+ 1 (exp (* -2 x))))
70.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.2s

Counts

156 → 156

Iterations

Iter	Nodes
3	2046
2	861
1	403
0	180

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ (sqrt 2) (+ 1 (exp (* -2 x))))
29.1b	(fma (/ (sqrt 2) 1) (/ (sqrt 2) (+ 1 (exp (* -2 x)))) -1)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`sqrt-prod`
8×	`distribute-lft-out`
6×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`associate-/r*`
3×	`expm1-log1p-u` `pow1` `fma-def` `log1p-expm1-u`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

3 → 77

Calls

3 calls:

5.0ms	(+ 1 (exp (* -2 x)))
11.0ms	(/ (sqrt 2) (+ 1 (exp (* -2 x))))
0.0ms	(fma (/ (sqrt 2) 1) (/ (sqrt 2) (+ 1 (exp (* -2 x)))) -1)

series194.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ 1 (exp (* -2 x)))
54.0ms	(/ (sqrt 2) (+ 1 (exp (* -2 x))))
129.0ms	(fma (/ (sqrt 2) 1) (/ (sqrt 2) (+ 1 (exp (* -2 x)))) -1)

simplify1.0s

Counts

86 → 86

Iterations

Iter	Nodes
3	2118
2	808
1	278
0	130

prune906.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* -1/3 (* (* x x) x)))
0.1b	(* (* x x) x)
0.1b	(* -1/3 (* (* x x) x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `pow-plus` `pow-prod-up` `add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`pow2` `pow-sqr` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `pow3` `flip-+` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

6.0ms	(+ x (* -1/3 (* (* x x) x)))
19.0ms	(* (* x x) x)
63.0ms	(* -1/3 (* (* x x) x))

series203.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(+ x (* -1/3 (* (* x x) x)))
35.0ms	(* (* x x) x)
57.0ms	(* -1/3 (* (* x x) x))

simplify1.5s

Counts

78 → 78

Iterations

Iter	Nodes
3	2843
2	686
1	220
0	83

prune541.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes448.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 28.8b

bsearch1.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	30
1	30
0	25

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	1684×	body	1280	valid
540.0ms	1210×	body	640	valid
389.0ms	4157×	body	80	valid
161.0ms	624×	body	320	valid
88.0ms	325×	body	160	valid