Details

sample74.0ms

Algorithm

intervals

Results

35.0ms	77×	body	1280	valid
13.0ms	55×	body	640	valid
9.0ms	172×	body	80	valid
6.0ms	33×	body	320	valid
1.0ms	11×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	18
3	18
2	16
1	13
0	5

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.0b	(- (exp x) 1)

rewrite28.0ms

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:

18.0ms	(/ (- (exp x) 1) x)
8.0ms	(- (exp x) 1)

series73.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- (exp x) 1) x)
31.0ms	(- (exp x) 1)

simplify1.4s

Counts

70 → 70

Iterations

Iter	Nodes
4	3127
3	1236
2	514
1	234
0	108

prune586.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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))
9.0ms	(* 1/6 x)

series105.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(* x (+ (* 1/6 x) 1/2))
16.0ms	(* 1/6 x)

simplify5.5s

Counts

48 → 48

Iterations

Iter	Nodes
4	7621
3	1915
2	512
1	189
0	72

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (+ (* 1/6 x) 1/2)))
0.0b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)
4.4b	(log (exp (* x (+ (* 1/6 x) 1/2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

8.0ms	(exp (* x (+ (* 1/6 x) 1/2)))
21.0ms	(* x (+ (* 1/6 x) 1/2))
5.0ms	(* 1/6 x)
7.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(exp (* x (+ (* 1/6 x) 1/2)))
76.0ms	(* x (+ (* 1/6 x) 1/2))
28.0ms	(* 1/6 x)
112.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

simplify870.0ms

Counts

84 → 84

Iterations

Iter	Nodes
3	2652
2	602
1	239
0	106

prune638.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 x)
0.3b	(* 1/6 x)
0.3b	(* 1/6 x)
4.4b	(log (* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
16×	`add-sqr-sqrt` `add-exp-log`
15×	`log-pow`
10×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
9×	`pow1/3` `associate-r` `associate-l` `pow-prod-up`
8×	`pow-prod-down`
6×	`pow-plus` `prod-exp`
4×	`insert-posit16` `add-log-exp`
3×	`rem-log-exp` `pow-sqr` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2`
1×	`log-prod` `pow3`

Counts

4 → 84

Calls

4 calls:

10.0ms	(* 1/6 x)
10.0ms	(* 1/6 x)
9.0ms	(* 1/6 x)
60.0ms	(log (* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 1/6 x)
19.0ms	(* 1/6 x)
21.0ms	(* 1/6 x)
123.0ms	(log (* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))

simplify3.3s

Counts

96 → 96

Iterations

Iter	Nodes
5	6841
4	1636
3	560
2	215
1	110
0	58

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes25.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.9b

bsearch32.0ms

Steps

Iters	Range		Point
7	-0.00125944232679287	-5.041062903413811e-05	-0.00014547784294540906

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	2296×	body	1280	valid
510.0ms	1589×	body	640	valid
354.0ms	5498×	body	80	valid
183.0ms	823×	body	320	valid
50.0ms	391×	body	160	valid