Details

sample168.0ms

Algorithm

intervals

Results

113.0ms	181×	body	1280	valid
15.0ms	43×	body	640	valid
13.0ms	251×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
10	2899
9	809
8	249
7	88
6	71
5	62
4	56
3	40
2	26
1	14
0	7

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp (- x)) 2.0)
3.9b	(+ (- (exp (- x)) 2.0) (exp x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
3×	`fma-neg` `distribute-lft-out--`
2×	`expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `flip3--` `associate-+l-` `flip-+` `flip--`

Counts

2 → 61

Calls

2 calls:

21.0ms	(- (exp (- x)) 2.0)
116.0ms	(+ (- (exp (- x)) 2.0) (exp x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (exp (- x)) 2.0)
73.0ms	(+ (- (exp (- x)) 2.0) (exp x))

simplify790.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1104
1	278
0	111

prune398.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))
0.0b	(fma (pow x 4) 1/12 (* x x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))
0.0ms	(fma (pow x 4) 1/12 (* x x))

series233.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))
167.0ms	(fma (pow x 4) 1/12 (* x x))

simplify1.1s

Counts

26 → 26

Iterations

Iter	Nodes
done	5002
3	1140
2	217
1	57
0	37

prune203.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 4) 1/12 (pow x 2))
0.0b	(fma (pow x 4) 1/12 (pow x 2))
28.5b	(sqrt (fma (pow x 4) 1/12 (pow x 2)))
28.5b	(sqrt (fma (pow x 4) 1/12 (pow x 2)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma (pow x 4) 1/12 (pow x 2))
0.0ms	(fma (pow x 4) 1/12 (pow x 2))
1.0ms	(sqrt (fma (pow x 4) 1/12 (pow x 2)))
1.0ms	(sqrt (fma (pow x 4) 1/12 (pow x 2)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(fma (pow x 4) 1/12 (pow x 2))
119.0ms	(fma (pow x 4) 1/12 (pow x 2))
109.0ms	(sqrt (fma (pow x 4) 1/12 (pow x 2)))
133.0ms	(sqrt (fma (pow x 4) 1/12 (pow x 2)))

simplify1.5s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
3	1846
2	370
1	108
0	55

prune527.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (exp (- x)) 2.0) (- (exp (- x)) 2.0))
0.0b	(pow (- (exp (- x)) 2.0) 3)
0.0b	(pow (exp x) 3)
3.8b	(+ (pow (exp x) 3) (pow (- (exp (- x)) 2.0) 3))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
19×	`unpow-prod-down` `cube-prod`
18×	`prod-diff`
13×	`pow1`
12×	`fma-def` `distribute-lft-out--`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`distribute-lft-out`
8×	`add-cbrt-cube`
7×	`flip3--` `swap-sqr` `add-exp-log` `flip--`
6×	`pow-unpow` `add-log-exp` `difference-of-squares`
5×	`pow-pow` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`cube-mult` `exp-prod` `unpow3` `sqr-pow`
2×	`cube-div` `pow-to-exp` `sub-neg` `associate-l/` `pow-exp` `associate-r/` `rem-cube-cbrt`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `sum-cubes` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

161.0ms	(* (- (exp (- x)) 2.0) (- (exp (- x)) 2.0))
27.0ms	(pow (- (exp (- x)) 2.0) 3)
4.0ms	(pow (exp x) 3)
122.0ms	(+ (pow (exp x) 3) (pow (- (exp (- x)) 2.0) 3))

series398.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (- (exp (- x)) 2.0) (- (exp (- x)) 2.0))
66.0ms	(pow (- (exp (- x)) 2.0) 3)
28.0ms	(pow (exp x) 3)
235.0ms	(+ (pow (exp x) 3) (pow (- (exp (- x)) 2.0) 3))

simplify594.0ms

Counts

171 → 171

Iterations

Iter	Nodes
done	5001
1	789
0	253

prune751.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.6s	5650×	body	1280	valid
954.0ms	8188×	body	80	valid
395.0ms	1220×	body	640	valid
110.0ms	636×	body	320	valid
36.0ms	333×	body	160	valid