Details

sample135.0ms

Algorithm

intervals

Results

83.0ms	182×	body	1280	valid
12.0ms	270×	body	80	valid
8.0ms	34×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid

simplify132.0ms

Counts: 1 → 1

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.1b

localize13.0ms

Local error

Found 2 expressions with local error:

4.1b	(+ (- (exp x) 2) (exp (- x)))
0.0b	(- (exp x) 2)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Counts

2 → 67

Calls

2 calls:

Slowest

37.0ms	(+ (- (exp x) 2) (exp (- x)))
9.0ms	(- (exp x) 2)

series74.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(+ (- (exp x) 2) (exp (- x)))
12.0ms	(- (exp x) 2)

simplify901.0ms

Counts: 73 → 73

prune870.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) (* x x))
0.2b	(* (* x x) (* x x))
0.1b	(* (* x x) (* (* x x) (* x x)))
0.0b	(fma (* (* x x) (* x x)) 1/12 (* x x))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

848×	`pow1`
370×	`pow-prod-up`
175×	`pow-prod-down`
153×	`pow-sqr`
140×	`pow-plus`
99×	`pow2`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`cube-unmult` `fma-udef`

Counts

4 → 337

Calls

4 calls:

Slowest

70.0ms	(* (* x x) (* (* x x) (* x x)))
37.0ms	(* (* x x) (* x x))
33.0ms	(* (* x x) (* x x))
0.0ms	(fma (* (* x x) (* x x)) 1/12 (* x x))

series278.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(fma (* (* x x) (* x x)) 1/12 (* x x))
75.0ms	(* (* x x) (* (* x x) (* x x)))
41.0ms	(* (* x x) (* x x))
38.0ms	(* (* x x) (* x x))

simplify1.5s

Counts: 349 → 349

prune3.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

33.1b	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
33.1b	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
33.1b	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
0.4b	(* (cbrt (fma (* (* x x) (* x x)) 1/12 (* x x))) (cbrt (fma (* (* x x) (* x x)) 1/12 (* x x))))

rewrite22.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `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 → 85

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (fma (* (* x x) (* x x)) 1/12 (* x x))) (cbrt (fma (* (* x x) (* x x)) 1/12 (* x x))))
2.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
2.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
1.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

222.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
216.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
190.0ms	(* (cbrt (fma (* (* x x) (* x x)) 1/12 (* x x))) (cbrt (fma (* (* x x) (* x x)) 1/12 (* x x))))
188.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))

simplify1.2s

Counts: 97 → 97

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize99.0ms

Local error

Found 4 expressions with local error:

33.1b	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
32.1b	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
32.1b	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
32.1b	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
2.0ms	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
2.0ms	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
1.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(cbrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
129.0ms	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
104.0ms	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))
102.0ms	(sqrt (fma (* (* x x) (* x x)) 1/12 (* x x)))

simplify2.5s

Counts: 74 → 74

prune981.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes72.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch1.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

4.0s	5666×	body	1280	valid
474.0ms	1203×	body	640	valid
450.0ms	8114×	body	80	valid
133.0ms	656×	body	320	valid
43.0ms	337×	body	160	valid