Details

sample183.0ms

Algorithm

intervals

Results

54.0ms	522×	pre	80	true
42.0ms	150×	body	160	valid
31.0ms	266×	body	80	nan
24.0ms	62×	body	320	valid
6.0ms	44×	body	80	valid

simplify148.0ms

Counts: 1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 47.0b

localize27.0ms

Local error

Found 4 expressions with local error:

39.0b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b	(fma c (* -4 a) (* b b))
0.1b	(sqrt (fma c (* -4 a) (* b b)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

Slowest

16.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
9.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
0.0ms	(fma c (* -4 a) (* b b))

series447.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
127.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
92.0ms	(fma c (* -4 a) (* b b))
92.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify858.0ms

Counts: 191 → 191

prune2.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 43.4b

localize31.0ms

Local error

Found 4 expressions with local error:

46.4b	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.1b	(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.1b	(fma c (* -4 a) (* b b))
0.1b	(fma c (* -4 a) (* b b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/l*`
9×	`add-cbrt-cube` `add-exp-log`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-exp` `fma-udef`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 106

Calls

4 calls:

Slowest

8.0ms	(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms	(fma c (* -4 a) (* b b))
0.0ms	(fma c (* -4 a) (* b b))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

645.0ms	(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
459.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
93.0ms	(fma c (* -4 a) (* b b))
72.0ms	(fma c (* -4 a) (* b b))

simplify1.7s

Counts: 118 → 118

prune1.6s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 43.4b

localize65.0ms

Local error

Found 4 expressions with local error:

46.4b	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.6b	(cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))
0.5b	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
0.4b	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
5×	`fma-udef`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 87

Calls

4 calls:

Slowest

16.0ms	(cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))
15.0ms	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))
6.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
1.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series849.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

477.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
173.0ms	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))
105.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
94.0ms	(cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))

simplify2.0s

Counts: 99 → 99

prune1.9s

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 43.4b

localize78.0ms

Local error

Found 4 expressions with local error:

46.3b	(fma (sqrt (sqrt (pow (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) 1/3))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
3.7b	(pow (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) 1/3)
0.5b	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
0.4b	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
17×	`add-exp-log`
13×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
12×	`pow-pow`
11×	`add-cbrt-cube`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp`
6×	`associate-r`
5×	`pow2` `pow-sqr` `fma-udef`
4×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `pow-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `unpow-prod-down` `unpow1/3` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

Slowest

21.0ms	(pow (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) 1/3)
14.0ms	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))
6.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
1.0ms	(fma (sqrt (sqrt (pow (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) 1/3))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series979.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

465.0ms	(fma (sqrt (sqrt (pow (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) 1/3))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
232.0ms	(pow (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) 1/3)
201.0ms	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))
80.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))

simplify2.5s

Counts: 118 → 118

prune1.1s

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 43.4b

regimes809.0ms

Accuracy

0% (2.7b remaining)

Error of 43.2b against oracle of 40.5b and baseline of 43.2b

bsearch6.0ms

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.9s	4883×	body	160	valid
1.1s	16110×	pre	80	true
1.0s	8110×	body	80	nan
537.0ms	1379×	body	320	valid
241.0ms	1738×	body	80	valid