Details

sample416.0ms

Algorithm

intervals

Results

226.0ms	97×	body	2560	valid
127.0ms	85×	body	1280	valid
28.0ms	44×	body	640	valid
10.0ms	20×	body	320	valid
9.0ms	256×	pre	80	true
2.0ms	9×	body	160	valid
0.0ms	1×	body	80	valid

simplify30.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize46.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
33×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 262

Calls

2 calls:

Slowest

40.0ms	(- (/ 1 x) (/ 1 (tan x)))
13.0ms	(/ 1 (tan x))

series119.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

73.0ms	(- (/ 1 x) (/ 1 (tan x)))
45.0ms	(/ 1 (tan x))

simplify400.0ms

Counts: 471 → 268

prune2.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))
0.1b	(fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))
0.1b	(* (* x x) x)
0.1b	(* (pow x 5) 2/945)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
14×	`add-sqr-sqrt` `add-exp-log`
11×	`add-cbrt-cube`
8×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`pow-plus` `associate-r` `prod-exp` `pow-prod-up`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`pow2` `pow-sqr` `*-commutative` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow3` `pow-exp`

Counts

4 → 81

Calls

4 calls:

Slowest

18.0ms	(* (* x x) x)
9.0ms	(* (pow x 5) 2/945)
0.0ms	(fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))
0.0ms	(fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))

series337.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))
74.0ms	(* (pow x 5) 2/945)
65.0ms	(fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))
47.0ms	(* (* x x) x)

simplify741.0ms

Counts: 94 → 93

prune883.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
0.5b	(* (cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))) (cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))))

rewrite14.0ms

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

11.0ms	(* (cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))) (cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))))
1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))

series830.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

217.0ms	(* (cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))) (cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945)))))
216.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
208.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
189.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))

simplify695.0ms

Counts: 111 → 97

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
0.7b	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

Slowest

1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
1.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

235.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
200.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
192.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))
186.0ms	(cbrt (fma 1/3 x (fma 1/45 (* (* x x) x) (* (pow x 5) 2/945))))

simplify792.0ms

Counts: 76 → 68

prune767.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.2b

regimes101.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample16.2s

Algorithm

intervals

Results

10.4s	3258×	body	2560	valid
3.7s	2532×	body	1280	valid
1.1s	1242×	body	640	valid
385.0ms	625×	body	320	valid
353.0ms	8000×	pre	80	true
115.0ms	309×	body	160	valid
6.0ms	34×	body	80	valid