Details

sample61.0ms

Algorithm

intervals

Results

27.0ms	83×	body	1280	valid
13.0ms	50×	body	640	valid
8.0ms	171×	body	80	valid
4.0ms	27×	body	320	valid
1.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
2.8b	(- (exp x) 1)

rewrite43.0ms

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)
18.0ms	(- (exp x) 1)

series62.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (exp x) 1) x)
17.0ms	(- (exp x) 1)

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5004
3	1887
2	592
1	239
0	108

prune202.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

21.0ms	(* x (+ 1/2 (* 1/6 x)))
10.0ms	(* 1/6 x)

series117.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* x (+ 1/2 (* 1/6 x)))
30.0ms	(* 1/6 x)

simplify2.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
3	3789
2	664
1	205
0	72

prune173.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1)) x)
0.0b	(+ (* (+ (exp x) 1) (exp x)) 1)
0.0b	(exp (* 3 x))
2.8b	(+ -1 (exp (* 3 x)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
81×	`*-un-lft-identity`
55×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`associate-/l*`
13×	`distribute-lft-out`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`div-inv`
4×	`pow1` `insert-posit16`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`+-commutative` `sum-log`
1×	`exp-prod` `clear-num` `frac-2neg` `exp-to-pow` `rem-exp-log` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

86.0ms	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1)) x)
18.0ms	(+ (* (+ (exp x) 1) (exp x)) 1)
7.0ms	(exp (* 3 x))
5.0ms	(+ -1 (exp (* 3 x)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1)) x)
47.0ms	(+ (* (+ (exp x) 1) (exp x)) 1)
12.0ms	(exp (* 3 x))
20.0ms	(+ -1 (exp (* 3 x)))

simplify1.8s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	1744
1	578
0	235

prune613.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 3 x))
0.1b	(exp (+ (* 3 x) (* x 6)))
0.3b	(+ (* 3 x) (* x 6))
2.7b	(+ (exp (+ (* 3 x) (* x 6))) -1)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`pow1` `exp-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sum-log` `rem-exp-log`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`difference-of-sqr--1` `exp-to-pow` `exp-sum` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

7.0ms	(exp (* 3 x))
35.0ms	(exp (+ (* 3 x) (* x 6)))
14.0ms	(+ (* 3 x) (* x 6))
41.0ms	(+ (exp (+ (* 3 x) (* x 6))) -1)

series105.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* 3 x))
14.0ms	(exp (+ (* 3 x) (* x 6)))
45.0ms	(+ (* 3 x) (* x 6))
34.0ms	(+ (exp (+ (* 3 x) (* x 6))) -1)

simplify3.1s

Counts

63 → 63

Iterations

Iter	Nodes
done	5004
3	3280
2	807
1	251
0	90

prune358.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.4b

bsearch36.0ms

Steps

Iters	Range		Point
9	-34.11472770615283	-3.67231414207575e-08	-0.00017573658557392354

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	2233×	body	1280	valid
518.0ms	1648×	body	640	valid
396.0ms	5494×	body	80	valid
159.0ms	818×	body	320	valid
55.0ms	430×	body	160	valid