Details

sample84.0ms

Algorithm

intervals

Results

34.0ms	69×	body	1280	valid
18.0ms	48×	body	640	valid
11.0ms	160×	body	80	valid
6.0ms	26×	body	320	valid
3.0ms	20×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
5.9b	(- (exp x) 1)

rewrite67.0ms

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:

49.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

series87.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- (exp x) 1) x)
26.0ms	(- (exp x) 1)

simplify1.7s

Counts

70 → 70

Iterations

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

prune299.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ 1/2 (* 1/6 x)))
0.3b	(* 1/6 x)

rewrite33.0ms

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:

22.0ms	(* x (+ 1/2 (* 1/6 x)))
10.0ms	(* 1/6 x)

series148.0ms

Counts

2 → 6

Calls

2 calls:

120.0ms	(* x (+ 1/2 (* 1/6 x)))
28.0ms	(* 1/6 x)

simplify3.6s

Counts

48 → 48

Iterations

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

prune157.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1)
0.0b	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
0.0b	(* (exp x) (exp x))
5.8b	(- (* (exp x) (exp x)) (* 1 1))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

13.0ms	(+ (exp x) 1)
71.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
31.0ms	(* (exp x) (exp x))
17.0ms	(- (* (exp x) (exp x)) (* 1 1))

series189.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp x) 1)
114.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
14.0ms	(* (exp x) (exp x))
47.0ms	(- (* (exp x) (exp x)) (* 1 1))

simplify1.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5008
2	1826
1	434
0	149

prune390.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 1 1) (* x (+ (exp x) 1)))
0.0b	(* (exp x) (exp x))
0.0b	(/ (* (exp x) (exp x)) (* x (+ (exp x) 1)))
4.8b	(- (/ (* (exp x) (exp x)) (* x (+ (exp x) 1))) (/ (* 1 1) (* x (+ (exp x) 1))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
30×	`add-cbrt-cube`
18×	`add-sqr-sqrt` `exp-prod` `prod-exp`
16×	`*-un-lft-identity`
14×	`div-exp` `add-cube-cbrt`
11×	`pow1`
9×	`cbrt-unprod`
8×	`cbrt-undiv` `1-exp` `associate-*r/` `associate-/r/`
6×	`add-log-exp`
4×	`flip3-+` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+` `insert-posit16` `div-inv`
3×	`distribute-rgt-out--` `swap-sqr` `associate-r` `associate-l`
2×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-/l`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

31.0ms	(/ (* 1 1) (* x (+ (exp x) 1)))
26.0ms	(* (exp x) (exp x))
43.0ms	(/ (* (exp x) (exp x)) (* x (+ (exp x) 1)))
89.0ms	(- (/ (* (exp x) (exp x)) (* x (+ (exp x) 1))) (/ (* 1 1) (* x (+ (exp x) 1))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* 1 1) (* x (+ (exp x) 1)))
25.0ms	(* (exp x) (exp x))
102.0ms	(/ (* (exp x) (exp x)) (* x (+ (exp x) 1)))
136.0ms	(- (/ (* (exp x) (exp x)) (* x (+ (exp x) 1))) (/ (* 1 1) (* x (+ (exp x) 1))))

simplify1.9s

Counts

121 → 121

Iterations

Iter	Nodes
done	5075
2	2923
1	570
0	186

prune476.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.3b

bsearch46.0ms

Steps

Iters	Range		Point
10	-0.0018335887134067947	-3.3545779559118727e-13	-0.00019562550875617412

simplify8.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	2251×	body	1280	valid
520.0ms	1603×	body	640	valid
329.0ms	5402×	body	80	valid
187.0ms	859×	body	320	valid
53.0ms	423×	body	160	valid