Details

sample81.0ms

Algorithm

intervals

Results

29.0ms	56×	body	1280	valid
17.0ms	50×	body	640	valid
13.0ms	190×	body	80	valid
8.0ms	31×	body	320	valid
2.0ms	14×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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)

series72.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- (exp x) 1) x)
17.0ms	(- (exp x) 1)

simplify1.3s

Counts

70 → 70

Iterations

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

prune580.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

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:

44.0ms	(* x (+ (* 1/6 x) 1/2))
11.0ms	(* 1/6 x)

series154.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(* x (+ (* 1/6 x) 1/2))
29.0ms	(* 1/6 x)

simplify5.6s

Counts

48 → 48

Iterations

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

prune346.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ (* 1/6 x) 1/2) (* x x)) x)
0.0b	(* (+ (* 1/6 x) 1/2) (* x x))
0.3b	(* 1/6 x)
3.8b	(/ (+ (* (+ (* 1/6 x) 1/2) (* x x)) x) x)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

21.0ms	(+ (* (+ (* 1/6 x) 1/2) (* x x)) x)
33.0ms	(* (+ (* 1/6 x) 1/2) (* x x))
11.0ms	(* 1/6 x)
47.0ms	(/ (+ (* (+ (* 1/6 x) 1/2) (* x x)) x) x)

series207.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (+ (* 1/6 x) 1/2) (* x x)) x)
107.0ms	(* (+ (* 1/6 x) 1/2) (* x x))
16.0ms	(* 1/6 x)
52.0ms	(/ (+ (* (+ (* 1/6 x) 1/2) (* x x)) x) x)

simplify2.0s

Counts

95 → 95

Iterations

Iter	Nodes
3	4912
2	1040
1	332
0	134

prune714.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

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))
4.0b	(- (* (exp x) (exp x)) (* 1 1))

rewrite143.0ms

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)
79.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
26.0ms	(* (exp x) (exp x))
24.0ms	(- (* (exp x) (exp x)) (* 1 1))

series172.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (exp x) 1)
108.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
26.0ms	(* (exp x) (exp x))
27.0ms	(- (* (exp x) (exp x)) (* 1 1))

simplify2.9s

Counts

103 → 103

Iterations

Iter	Nodes
3	5811
2	1366
1	421
0	149

prune781.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes32.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.1b

bsearch41.0ms

Steps

Iters	Range		Point
9	-0.0008162261515098681	-6.511446174461762e-09	-0.0001556646497825041

simplify6.0ms

Iterations

Iter	Nodes
2	27
1	27
0	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	2318×	body	1280	valid
627.0ms	1609×	body	640	valid
363.0ms	5394×	body	80	valid
199.0ms	816×	body	320	valid
55.0ms	420×	body	160	valid