Details

sample85.0ms

Algorithm

intervals

Results

38.0ms	120×	body	1280	valid
15.0ms	74×	body	640	valid
13.0ms	286×	body	80	valid
4.0ms	37×	body	320	valid
2.0ms	19×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
4	34
3	30
2	24
1	14
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize10.0ms

Local error

Found 1 expressions with local error:

6.1b	(- (exp x) (exp (- x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

20.0ms

(- (exp x) (exp (- x)))

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

(- (exp x) (exp (- x)))

simplify891.0ms

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
2	671
1	170
0	73

prune111.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 5) 1/60 (* x (+ (* (* 1/3 x) x) 2)))
0.0b	(* x (+ (* (* 1/3 x) x) 2))
0.1b	(* (* 1/3 x) x)
0.3b	(* 1/3 x)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (pow x 5) 1/60 (* x (+ (* (* 1/3 x) x) 2)))
48.0ms	(* x (+ (* (* 1/3 x) x) 2))
13.0ms	(* (* 1/3 x) x)
7.0ms	(* 1/3 x)

series199.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma (pow x 5) 1/60 (* x (+ (* (* 1/3 x) x) 2)))
91.0ms	(* x (+ (* (* 1/3 x) x) 2))
27.0ms	(* (* 1/3 x) x)
16.0ms	(* 1/3 x)

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1761
1	307
0	109

prune427.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (* x x)) 1/27)
0.3b	(* 1/3 x)
0.3b	(* 1/3 x)
0.3b	(* 1/3 x)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`

Counts

4 → 83

Calls

4 calls:

39.0ms	(* (* x (* x x)) 1/27)
5.0ms	(* 1/3 x)
5.0ms	(* 1/3 x)
6.0ms	(* 1/3 x)

series116.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* x (* x x)) 1/27)
26.0ms	(* 1/3 x)
15.0ms	(* 1/3 x)
18.0ms	(* 1/3 x)

simplify973.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1064
1	189
0	75

prune591.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (exp (- x)) (exp (- x)))
0.0b	(* (exp x) (exp x))
6.0b	(- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

94×	`exp-prod`
53×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
24×	`distribute-rgt-neg-in`
20×	`distribute-lft-neg-in`
19×	`pow-prod-down`
18×	`pow1`
17×	`pow-sqr` `pow-prod-up`
8×	`neg-mul-1` `add-cbrt-cube` `add-log-exp`
7×	`exp-neg`
6×	`neg-sub0` `exp-diff` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-exp-log` `log1p-expm1-u`
3×	`fma-def`
2×	`pow2` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `fma-neg` `diff-log` `prod-diff` `un-div-inv` `flip-+` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 144

Calls

4 calls:

21.0ms	(+ (exp x) (exp (- x)))
41.0ms	(* (exp (- x)) (exp (- x)))
22.0ms	(* (exp x) (exp x))
30.0ms	(- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (exp x) (exp (- x)))
17.0ms	(* (exp (- x)) (exp (- x)))
19.0ms	(* (exp x) (exp x))
94.0ms	(- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))

simplify2.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	3591
1	505
0	181

prune680.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	3315×	body	1280	valid
1.1s	2534×	body	640	valid
342.0ms	8111×	body	80	valid
300.0ms	1268×	body	320	valid
97.0ms	615×	body	160	valid