Details

sample109.0ms

Algorithm

intervals

Results

40.0ms	76×	body	1280	valid
32.0ms	84×	body	10240	exit
17.0ms	54×	body	640	valid
6.0ms	98×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize14.0ms

Local error

Found 2 expressions with local error:

3.5b	(- (exp x) 1)
0.7b	(/ (exp x) (- (exp x) 1))

rewrite47.0ms

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

31.0ms	(/ (exp x) (- (exp x) 1))
14.0ms	(- (exp x) 1)

series58.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

39.0ms	(/ (exp x) (- (exp x) 1))
19.0ms	(- (exp x) 1)

simplify1.3s

Counts: 69 → 69

prune521.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 1/12 x)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0b	(+ (/ 1 x) 1/2)

rewrite53.0ms

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

36.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
8.0ms	(+ (/ 1 x) 1/2)
8.0ms	(* 1/12 x)

series50.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

17.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
17.0ms	(+ (/ 1 x) 1/2)
16.0ms	(* 1/12 x)

simplify693.0ms

Counts: 56 → 56

prune323.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

Slowest

50.0ms	(+ (* (sqrt 1/12) (* (sqrt 1/12) x)) (+ (/ 1 x) 1/2))
30.0ms	(* (sqrt 1/12) (* (sqrt 1/12) x))
9.0ms	(+ (/ 1 x) 1/2)
7.0ms	(* (sqrt 1/12) x)

series178.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

75.0ms	(* (sqrt 1/12) (* (sqrt 1/12) x))
46.0ms	(+ (* (sqrt 1/12) (* (sqrt 1/12) x)) (+ (/ 1 x) 1/2))
42.0ms	(* (sqrt 1/12) x)
15.0ms	(+ (/ 1 x) 1/2)

simplify1.3s

Counts: 85 → 85

prune668.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

Slowest

15.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

322.0ms	(* (cbrt x) (cbrt x))
298.0ms	(cbrt x)
296.0ms	(cbrt x)
283.0ms	(cbrt x)

simplify1.3s

Counts: 89 → 89

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes208.0ms

Accuracy

97.9% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 21.5b

bsearch6.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	2198×	body	1280	valid
1.2s	2686×	body	10240	exit
559.0ms	1680×	body	640	valid
231.0ms	2890×	body	80	valid
165.0ms	828×	body	320	valid
89.0ms	406×	body	160	valid