Details

sample110.0ms

Algorithm

intervals

Results

68.0ms	95×	body	1280	valid
16.0ms	133×	body	80	valid
7.0ms	15×	body	640	valid
2.0ms	8×	body	160	valid
2.0ms	5×	body	320	valid

simplify31.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(+ (/ 1/2 (hypot 1 x)) 1/2)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

Slowest

45.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
10.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
3.0ms	(/ 1/2 (hypot 1 x))

series156.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

63.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
43.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
43.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
6.0ms	(/ 1/2 (hypot 1 x))

simplify1.9s

Counts: 90 → 90

prune891.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.3b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

Slowest

22.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
3.0ms	(/ 1/2 (hypot 1 x))

series109.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

55.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
42.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
6.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))

simplify1.8s

Counts: 99 → 99

prune912.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize63.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
0.2b	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
49×	`times-frac`
45×	`*-un-lft-identity`
40×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
8×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`sqrt-prod`
1×	`pow2` `frac-times` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `flip--` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

Slowest

17.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
12.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
12.0ms	(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
5.0ms	(/ 1/2 (hypot 1 x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
73.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
36.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
11.0ms	(/ 1/2 (hypot 1 x))

simplify663.0ms

Counts: 137 → 137

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize72.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (* 1/2 1/2) (* (/ (/ (/ 1/2 (cbrt (hypot 1 x))) (cbrt (hypot 1 x))) (hypot 1 x)) (/ 1/2 (cbrt (hypot 1 x)))))
0.3b	(cbrt (hypot 1 x))
0.3b	(cbrt (hypot 1 x))
0.3b	(cbrt (hypot 1 x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `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--`

Counts

4 → 49

Calls

4 calls:

Slowest

7.0ms	(- (* 1/2 1/2) (* (/ (/ (/ 1/2 (cbrt (hypot 1 x))) (cbrt (hypot 1 x))) (hypot 1 x)) (/ 1/2 (cbrt (hypot 1 x)))))
1.0ms	(cbrt (hypot 1 x))
1.0ms	(cbrt (hypot 1 x))
1.0ms	(cbrt (hypot 1 x))

series483.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(cbrt (hypot 1 x))
135.0ms	(cbrt (hypot 1 x))
131.0ms	(cbrt (hypot 1 x))
65.0ms	(- (* 1/2 1/2) (* (/ (/ (/ 1/2 (cbrt (hypot 1 x))) (cbrt (hypot 1 x))) (hypot 1 x)) (/ 1/2 (cbrt (hypot 1 x)))))

simplify968.0ms

Counts: 61 → 61

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.0b

regimes126.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.5b and baseline of 14.7b

bsearch9.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.8s	2901×	body	1280	valid
350.0ms	4028×	body	80	valid
265.0ms	613×	body	640	valid
78.0ms	296×	body	320	valid
27.0ms	162×	body	160	valid