Details

sample78.0ms

Algorithm

intervals

Results

33.0ms	72×	body	1280	valid
18.0ms	55×	body	640	valid
10.0ms	165×	body	80	valid
6.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	16
3	16
2	14
1	11
0	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.1b	(- (exp x) 1)

rewrite39.0ms

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:

28.0ms	(/ (- (exp x) 1) x)
9.0ms	(- (exp x) 1)

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

simplify2.9s

Counts

70 → 70

Iterations

Iter	Nodes
4	4417
3	1393
2	512
1	232
0	108

prune596.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

19.0ms	(* x (+ (* 1/6 x) 1/2))
6.0ms	(* 1/6 x)

series113.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(* x (+ (* 1/6 x) 1/2))
28.0ms	(* 1/6 x)

simplify5.3s

Counts

48 → 48

Iterations

Iter	Nodes
4	7450
3	1901
2	511
1	186
0	72

prune315.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (* x (+ (* 1/6 x) 1/2)))
0.0b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)
2.3b	(/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x)

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow1`
9×	`times-frac` `associate-l`
7×	`associate-r`
6×	`associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `-commutative` `flip-+` `associate-/l*`
2×	`unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 97

Calls

4 calls:

42.0ms	(* x (* x (+ (* 1/6 x) 1/2)))
39.0ms	(* x (+ (* 1/6 x) 1/2))
11.0ms	(* 1/6 x)
104.0ms	(/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x)

series310.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* x (* x (+ (* 1/6 x) 1/2)))
96.0ms	(* x (+ (* 1/6 x) 1/2))
29.0ms	(* 1/6 x)
75.0ms	(/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x)

simplify2.9s

Counts

109 → 109

Iterations

Iter	Nodes
3	6231
2	1235
1	370
0	151

prune835.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

2.3b	(/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x)
12.5b	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))
12.5b	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))
12.5b	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `insert-posit16` `div-inv` `add-log-exp`
3×	`cbrt-div` `associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+`

Counts

4 → 99

Calls

4 calls:

97.0ms	(/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x)
30.0ms	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))
17.0ms	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))
18.0ms	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))

series506.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x)
149.0ms	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))
153.0ms	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))
133.0ms	(cbrt (/ (+ (* x (* x (+ (* 1/6 x) 1/2))) x) x))

simplify1.5s

Counts

111 → 111

Iterations

Iter	Nodes
3	2806
2	675
1	253
0	126

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch51.0ms

Steps

Iters	Range		Point
8	-0.18430940072566707	-1.79411439440973e-05	-0.0002116977350152651

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

981.0ms	2213×	body	1280	valid
841.0ms	1695×	body	640	valid
340.0ms	5431×	body	80	valid
156.0ms	844×	body	320	valid
73.0ms	420×	body	160	valid