Details

sample128.0ms

Algorithm

intervals

Results

43.0ms	84×	body	1280	valid
39.0ms	87×	body	10240	exit
20.0ms	54×	body	640	valid
6.0ms	80×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	13×	body	160	valid

simplify46.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

46.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize17.0ms

Local error

Found 2 expressions with local error:

4.2b	(- (exp x) 1)
0.5b	(/ (exp x) (- (exp x) 1))

rewrite24.0ms

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

13.0ms	(/ (exp x) (- (exp x) 1))
10.0ms	(- (exp x) 1)

series51.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

36.0ms	(/ (exp x) (- (exp x) 1))
15.0ms	(- (exp x) 1)

simplify3.5s

Counts

96 → 69

Calls

96 calls:

Slowest

455.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
355.0ms	(/ (exp x) (- (pow (exp x) 3) (pow 1 3)))
243.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
163.0ms	(* (* (/ (exp x) (- (exp x) 1)) (/ (exp x) (- (exp x) 1))) (/ (exp x) (- (exp x) 1)))
162.0ms	(* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1))

prune497.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 1 expressions with local error:

0.3b	(* 1/12 x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

1 → 19

Calls

1 calls:

Slowest

8.0ms

(* 1/12 x)

series21.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

21.0ms

(* 1/12 x)

simplify544.0ms

Counts

22 → 22

Calls

22 calls:

Slowest

247.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
164.0ms	(* (* (* 1/12 x) (* 1/12 x)) (* 1/12 x))
13.0ms	(exp (* 1/12 x))
10.0ms	(* (sqrt 1/12) (sqrt x))
9.0ms	(* 1/12 x)

prune207.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt 1/12) (* (sqrt 1/12) x))
0.4b	(* (sqrt 1/12) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-l`
11×	`add-sqr-sqrt`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

2 → 45

Calls

2 calls:

Slowest

30.0ms	(* (sqrt 1/12) (* (sqrt 1/12) x))
7.0ms	(* (sqrt 1/12) x)

series163.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

102.0ms	(* (sqrt 1/12) (* (sqrt 1/12) x))
61.0ms	(* (sqrt 1/12) x)

simplify2.2s

Counts

51 → 51

Calls

51 calls:

Slowest

423.0ms	(* (* (* (sqrt 1/12) (sqrt 1/12)) (sqrt 1/12)) (* (* (* (sqrt 1/12) x) (* (sqrt 1/12) x)) (* (sqrt 1/12) x)))
370.0ms	(* (* (* (sqrt 1/12) (* (sqrt 1/12) x)) (* (sqrt 1/12) (* (sqrt 1/12) x))) (* (sqrt 1/12) (* (sqrt 1/12) x)))
201.0ms	(* (* (* (sqrt 1/12) x) (* (sqrt 1/12) x)) (* (sqrt 1/12) x))
188.0ms	(* (* (* (sqrt 1/12) (sqrt 1/12)) (sqrt 1/12)) (* (* (* (sqrt 1/12) (sqrt 1/12)) (sqrt 1/12)) (* (* x x) x)))
174.0ms	(exp (* (sqrt 1/12) (* (sqrt 1/12) x)))

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize51.0ms

Local error

Found 3 expressions with local error:

59.8b	(posit16->real (real->posit16 (* (sqrt 1/12) x)))
0.4b	(* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x))))
0.4b	(* (sqrt 1/12) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`associate-l`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-prod`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r`
4×	`unswap-sqr`
3×	`insert-posit16` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`remove-posit16`

Counts

3 → 55

Calls

3 calls:

Slowest

10.0ms	(* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x))))
7.0ms	(* (sqrt 1/12) x)
1.0ms	(posit16->real (real->posit16 (* (sqrt 1/12) x)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

116.0ms	(* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x))))
69.0ms	(* (sqrt 1/12) x)
57.0ms	(posit16->real (real->posit16 (* (sqrt 1/12) x)))

simplify2.5s

Counts

65 → 64

Calls

65 calls:

Slowest

407.0ms	(* (* (* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x)))) (* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x))))) (* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x)))))
282.0ms	(* (* (* (sqrt 1/12) (sqrt 1/12)) (sqrt 1/12)) (* (* (posit16->real (real->posit16 (* (sqrt 1/12) x))) (posit16->real (real->posit16 (* (sqrt 1/12) x)))) (posit16->real (real->posit16 (* (sqrt 1/12) x)))))
232.0ms	(* (* (posit16->real (real->posit16 (* (sqrt 1/12) x))) (posit16->real (real->posit16 (* (sqrt 1/12) x)))) (posit16->real (real->posit16 (* (sqrt 1/12) x))))
208.0ms	(* (* (* (sqrt 1/12) x) (* (sqrt 1/12) x)) (* (sqrt 1/12) x))
201.0ms	(exp (* (sqrt 1/12) (posit16->real (real->posit16 (* (sqrt 1/12) x)))))

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes166.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 21.2b

bsearch4.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	2286×	body	1280	valid
1.0s	2561×	body	10240	exit
514.0ms	1695×	body	640	valid
298.0ms	2833×	body	80	valid
230.0ms	779×	body	320	valid
51.0ms	409×	body	160	valid