Details

sample74.0ms

Algorithm

intervals

Results

28.0ms	72×	body	1280	valid
18.0ms	47×	body	640	valid
10.0ms	169×	body	80	valid
7.0ms	36×	body	320	valid
1.0ms	13×	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: 40.7b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.7b	(- (exp x) 1)

rewrite49.0ms

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:

27.0ms	(/ (- (exp x) 1) x)
15.0ms	(- (exp x) 1)

series83.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- (exp x) 1) x)
25.0ms	(- (exp x) 1)

simplify1.6s

Counts

70 → 70

Iterations

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

prune244.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (* x (+ 1/2 (* 1/6 x))))
0.0b	(+ 1/2 (* 1/6 x))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`associate-l`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt` `add-log-exp`
6×	`+-commutative` `distribute-lft-out`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `insert-posit16`
3×	`flip3-+` `flip-+`
2×	`sum-log` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

168.0ms	(+ 1 (* x (+ 1/2 (* 1/6 x))))
15.0ms	(+ 1/2 (* 1/6 x))
72.0ms	(* x (+ 1/2 (* 1/6 x)))
13.0ms	(* 1/6 x)

series189.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ 1 (* x (+ 1/2 (* 1/6 x))))
54.0ms	(+ 1/2 (* 1/6 x))
78.0ms	(* x (+ 1/2 (* 1/6 x)))
22.0ms	(* 1/6 x)

simplify1.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	929
1	302
0	107

prune304.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (+ 1/2 (* 1/6 x))) 1)
0.0b	(+ 1/2 (* 1/6 x))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite457.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`associate-l`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt` `add-log-exp`
6×	`+-commutative` `distribute-lft-out`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `insert-posit16`
3×	`flip3-+` `flip-+`
2×	`sum-log` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

364.0ms	(+ (* x (+ 1/2 (* 1/6 x))) 1)
26.0ms	(+ 1/2 (* 1/6 x))
56.0ms	(* x (+ 1/2 (* 1/6 x)))
9.0ms	(* 1/6 x)

series200.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x (+ 1/2 (* 1/6 x))) 1)
40.0ms	(+ 1/2 (* 1/6 x))
97.0ms	(* x (+ 1/2 (* 1/6 x)))
25.0ms	(* 1/6 x)

simplify3.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	4057
2	914
1	301
0	107

prune260.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 x)
0.4b	(* 1/6 x)
0.4b	(* 1/6 x)
12.5b	(/ (- (* (* x (+ 1/2 (* 1/6 x))) (* x (+ 1/2 (* 1/6 x)))) 1) (- (* x (+ 1/2 (* 1/6 x))) 1))

rewrite6.6s

Algorithm

rewrite-expression-head

Rules

1228×	`add-sqr-sqrt`
465×	`unswap-sqr`
440×	`*-un-lft-identity`
363×	`times-frac`
352×	`difference-of-squares`
176×	`difference-of-sqr-1`
104×	`distribute-lft-out--`
79×	`associate-l`
72×	`swap-sqr`
56×	`add-cube-cbrt`
39×	`*-commutative`
33×	`associate-/l*`
12×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
10×	`pow1`
9×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 482

Calls

4 calls:

13.0ms	(* 1/6 x)
13.0ms	(* 1/6 x)
13.0ms	(* 1/6 x)
6.6s	(/ (- (* (* x (+ 1/2 (* 1/6 x))) (* x (+ 1/2 (* 1/6 x)))) 1) (- (* x (+ 1/2 (* 1/6 x))) 1))

series144.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* 1/6 x)
22.0ms	(* 1/6 x)
15.0ms	(* 1/6 x)
90.0ms	(/ (- (* (* x (+ 1/2 (* 1/6 x))) (* x (+ 1/2 (* 1/6 x)))) 1) (- (* x (+ 1/2 (* 1/6 x))) 1))

simplify2.4s

Counts

494 → 494

Iterations

Iter	Nodes
done	5001
2	2029
1	814
0	353

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes42.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.2b

bsearch45.0ms

Steps

Iters	Range		Point
6	-0.0005350557287305616	-5.532094628653386e-05	-9.8136436745457e-05

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	22

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	2277×	body	1280	valid
505.0ms	466×	body	160	valid
445.0ms	1638×	body	640	valid
303.0ms	5311×	body	80	valid
164.0ms	900×	body	320	valid