Details

sample113.0ms

Algorithm

intervals

Results

40.0ms	74×	body	1280	valid
34.0ms	91×	body	10240	exit
18.0ms	59×	body	640	valid
5.0ms	88×	body	80	valid
5.0ms	22×	body	320	valid
2.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

9.0ms

(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize17.0ms

Local error

Found 2 expressions with local error:

4.5b	(- (exp x) 1)
1.2b	(/ (exp x) (- (exp x) 1))

rewrite44.0ms

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-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

Slowest

27.0ms	(/ (exp x) (- (exp x) 1))
17.0ms	(- (exp x) 1)

series65.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

44.0ms	(/ (exp x) (- (exp x) 1))
20.0ms	(- (exp x) 1)

simplify1.7s

Counts

68 → 69

Calls

68 calls:

Slowest

408.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
181.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
58.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
48.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
33.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (- (exp x) 1)))

prune544.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 1/12 x)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0b	(+ (/ 1 x) 1/2)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`associate-r` `associate-l` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

Slowest

46.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
16.0ms	(+ (/ 1 x) 1/2)
10.0ms	(* 1/12 x)

series77.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

33.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
27.0ms	(* 1/12 x)
17.0ms	(+ (/ 1 x) 1/2)

simplify1.2s

Counts

23 → 56

Calls

23 calls:

Slowest

420.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
347.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
214.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
39.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
28.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune520.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 1/12 x)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0b	(+ (/ 1 x) 1/2)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`associate-r` `associate-l` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

Slowest

42.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
16.0ms	(+ (/ 1 x) 1/2)
5.0ms	(* 1/12 x)

series63.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

25.0ms	(* 1/12 x)
22.0ms	(+ (/ 1 x) 1/2)
16.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

simplify1.0s

Counts

23 → 56

Calls

23 calls:

Slowest

342.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
294.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
167.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
22.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune382.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 2 expressions with local error:

4.5b	(- (exp x) 1)
1.2b	(/ (exp x) (- (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-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

Slowest

16.0ms	(/ (exp x) (- (exp x) 1))
12.0ms	(- (exp x) 1)

series42.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

28.0ms	(/ (exp x) (- (exp x) 1))
15.0ms	(- (exp x) 1)

simplify1.6s

Counts

68 → 69

Calls

68 calls:

Slowest

412.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
225.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
56.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
44.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
42.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune540.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.1b

regimes126.0ms

Accuracy

99% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.2b

bsearch50.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	2604×	body	10240	exit
1.0s	2292×	body	1280	valid
640.0ms	1645×	body	640	valid
169.0ms	812×	body	320	valid
169.0ms	2832×	body	80	valid
77.0ms	420×	body	160	valid