Details

sample67.0ms

Algorithm

intervals

Results

24.0ms	73×	body	1280	valid
18.0ms	47×	body	640	valid
10.0ms	194×	body	80	valid
4.0ms	24×	body	320	valid
2.0ms	15×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	13
0	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.2b	(- (exp x) 1)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

23.0ms	(/ (- (exp x) 1) x)
12.0ms	(- (exp x) 1)

series78.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- (exp x) 1) x)
20.0ms	(- (exp x) 1)

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	2009
4	2009
3	1887
2	592
1	239
0	108

prune253.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/6 x) 1/2)
0.0b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`insert-posit16`
2×	`flip3-+` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`

Counts

3 → 54

Calls

3 calls:

9.0ms	(+ (* 1/6 x) 1/2)
18.0ms	(* x (+ (* 1/6 x) 1/2))
5.0ms	(* 1/6 x)

series127.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* 1/6 x) 1/2)
64.0ms	(* x (+ (* 1/6 x) 1/2))
20.0ms	(* 1/6 x)

simplify862.0ms

Counts

63 → 63

Iterations

Iter	Nodes
done	2011
3	2011
2	707
1	227
0	80

prune213.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
4.2b	(- (* (exp x) (exp x)) (* 1 1))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

18×	`exp-prod`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `add-cbrt-cube`
8×	`add-exp-log`
5×	`add-log-exp`
4×	`times-frac` `pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l*`
3×	`swap-sqr` `associate-r` `associate-l` `insert-posit16` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`pow2` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `-commutative` `flip-+` `div-inv` `unswap-sqr`

Counts

3 → 78

Calls

3 calls:

15.0ms	(* (exp x) (exp x))
37.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
13.0ms	(- (* (exp x) (exp x)) (* 1 1))

series147.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(* (exp x) (exp x))
98.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
31.0ms	(- (* (exp x) (exp x)) (* 1 1))

simplify1.7s

Counts

87 → 87

Iterations

Iter	Nodes
done	2001
3	2001
2	1926
1	407
0	137

prune253.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(* (/ (+ (exp (+ x x)) -1) (+ (* (* (exp (+ x x)) (exp x)) x) x)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
4.2b	(+ (exp (+ x x)) -1)
4.2b	(- (* 1 1) (* (exp x) 1))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
39×	`associate-l`
31×	`times-frac`
27×	`add-cube-cbrt`
18×	`exp-prod`
13×	`pow1`
12×	`difference-of-sqr--1`
11×	`add-cbrt-cube`
9×	`add-exp-log`
8×	`add-log-exp`
6×	`distribute-lft1-in` `distribute-rgt-out` `associate-r` `exp-sum` `distribute-lft-out`
5×	`pow-prod-down`
4×	`flip3-+` `pow-sqr` `pow-prod-up` `flip-+` `insert-posit16`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-r/` `associate-/r/` `-commutative`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `pow-plus` `flip3--` `distribute-rgt-out--` `diff-log` `div-exp` `associate-*l/` `div-inv` `flip--`

Counts

4 → 126

Calls

4 calls:

13.0ms	(* (exp x) (exp x))
966.0ms	(* (/ (+ (exp (+ x x)) -1) (+ (* (* (exp (+ x x)) (exp x)) x) x)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
43.0ms	(+ (exp (+ x x)) -1)
15.0ms	(- (* 1 1) (* (exp x) 1))

series263.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (exp x) (exp x))
193.0ms	(* (/ (+ (exp (+ x x)) -1) (+ (* (* (exp (+ x x)) (exp x)) x) x)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
31.0ms	(+ (exp (+ x x)) -1)
20.0ms	(- (* 1 1) (* (exp x) 1))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	2005
2	2005
1	916
0	248

prune696.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.7b

bsearch76.0ms

Steps

Iters	Range		Point
8	-0.0009127344879205425	-1.3816842601692823e-07	-0.00010173923815578526

simplify6.0ms

Iterations

Iter	Nodes
done	44
1	44
0	29

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	2324×	body	1280	valid
482.0ms	1586×	body	640	valid
384.0ms	5476×	body	80	valid
185.0ms	802×	body	320	valid
74.0ms	402×	body	160	valid