Details

sample102.0ms

Algorithm

intervals

Results

60.0ms	101×	body	1280	valid
18.0ms	124×	body	80	valid
8.0ms	17×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify18.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize30.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`sqrt-prod`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1`
4×	`insert-posit16` `difference-of-squares`
3×	`associate-/r` `associate-/l` `distribute-lft-out--`
2×	`sqrt-div` `distribute-lft-out`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 73

Calls

4 calls:

Slowest

34.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
16.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
6.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)

series151.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

76.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
62.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
10.0ms	(/ 1/2 (hypot 1 x))
2.0ms	(hypot 1 x)

simplify546.0ms

Counts: 105 → 85

prune755.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 80

Calls

4 calls:

Slowest

5.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
3.0ms	(/ 1/2 (hypot 1 x))
3.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)

series60.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

34.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
14.0ms	(/ 1/2 (hypot 1 x))
10.0ms	(/ 1/2 (hypot 1 x))
1.0ms	(hypot 1 x)

simplify441.0ms

Counts: 116 → 92

prune902.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize79.0ms

Local error

Found 4 expressions with local error:

1.3b	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
0.1b	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
0.0b	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
0.0b	(* (hypot 1 x) (hypot 1 x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
7×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `insert-posit16`
3×	`pow2` `cbrt-undiv` `times-frac` `swap-sqr` `div-exp` `pow-sqr` `associate-/l*`
2×	`*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow3` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

Slowest

28.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
26.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
19.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
5.0ms	(* (hypot 1 x) (hypot 1 x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
51.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
45.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
24.0ms	(* (hypot 1 x) (hypot 1 x))

simplify397.0ms

Counts: 114 → 106

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.3b	(- 1/8 (/ 1/8 (* (* (* (hypot 1 x) (cbrt (hypot 1 x))) (* (hypot 1 x) (cbrt (hypot 1 x)))) (cbrt (hypot 1 x)))))
0.2b	(cbrt (hypot 1 x))
0.2b	(cbrt (hypot 1 x))
0.2b	(cbrt (hypot 1 x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 51

Calls

4 calls:

Slowest

53.0ms	(- 1/8 (/ 1/8 (* (* (* (hypot 1 x) (cbrt (hypot 1 x))) (* (hypot 1 x) (cbrt (hypot 1 x)))) (cbrt (hypot 1 x)))))
1.0ms	(cbrt (hypot 1 x))
1.0ms	(cbrt (hypot 1 x))
1.0ms	(cbrt (hypot 1 x))

series556.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(cbrt (hypot 1 x))
177.0ms	(cbrt (hypot 1 x))
112.0ms	(cbrt (hypot 1 x))
79.0ms	(- 1/8 (/ 1/8 (* (* (* (hypot 1 x) (cbrt (hypot 1 x))) (* (hypot 1 x) (cbrt (hypot 1 x)))) (cbrt (hypot 1 x)))))

simplify616.0ms

Counts: 72 → 63

prune980.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

regimes131.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch6.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	2933×	body	1280	valid
891.0ms	4014×	body	80	valid
255.0ms	591×	body	640	valid
80.0ms	303×	body	320	valid
65.0ms	159×	body	160	valid