Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	73×	body	1280	valid
16.0ms	168×	body	80	valid
11.0ms	54×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	16×	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: 39.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:

19.0ms	(/ (- (exp x) 1) x)
9.0ms	(- (exp x) 1)

series62.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1) x)
21.0ms	(- (exp x) 1)

simplify2.5s

Counts

70 → 70

Iterations

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

prune515.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

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:

32.0ms	(* x (+ (* 1/6 x) 1/2))
6.0ms	(* 1/6 x)

series120.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(* x (+ (* 1/6 x) 1/2))
17.0ms	(* 1/6 x)

simplify5.0s

Counts

48 → 48

Iterations

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

prune360.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)
5.4b	(log (exp (* x (+ (* 1/6 x) 1/2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

21.0ms	(* x (+ (* 1/6 x) 1/2))
6.0ms	(* 1/6 x)
4.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

series186.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(* x (+ (* 1/6 x) 1/2))
16.0ms	(* 1/6 x)
78.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

simplify1.1s

Counts

68 → 68

Iterations

Iter	Nodes
3	2514
2	559
1	222
0	98

prune594.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (exp (* x 3)) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
0.0b	(* (exp x) (+ 1 (exp x)))
0.0b	(exp (* x 3))
4.8b	(+ (exp (* x 3)) -1)

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log`
6×	`pow1` `distribute-lft-out`
5×	`difference-of-sqr--1` `associate-/l*`
4×	`flip3-+` `associate-r` `flip-+` `insert-posit16`
3×	`associate-/r` `associate-l*`
2×	`associate-*r/` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `exp-lft-cube` `exp-prod` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `exp-to-pow` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

68.0ms	(/ (+ (exp (* x 3)) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
42.0ms	(* (exp x) (+ 1 (exp x)))
8.0ms	(exp (* x 3))
19.0ms	(+ (exp (* x 3)) -1)

series134.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (+ (exp (* x 3)) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
29.0ms	(* (exp x) (+ 1 (exp x)))
10.0ms	(exp (* x 3))
21.0ms	(+ (exp (* x 3)) -1)

simplify3.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	3801
2	1242
1	415
0	157

prune854.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes73.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.3b

bsearch70.0ms

Steps

Iters	Range		Point
9	-0.35383103211093586	-7.139329650713034e-08	-9.443138140720151e-05

simplify10.0ms

Iterations

Iter	Nodes
2	42
1	42
0	30

end0.0ms

sample2.1s

Algorithm

intervals

Results

888.0ms	2284×	body	1280	valid
503.0ms	1615×	body	640	valid
367.0ms	5474×	body	80	valid
176.0ms	862×	body	320	valid
47.0ms	404×	body	160	valid