Details

sample143.0ms

Algorithm

intervals

Results

28.0ms	179×	body	80	valid
28.0ms	29×	body	2560	valid
25.0ms	31×	body	1280	valid
16.0ms	24×	body	640	valid
15.0ms	102×	body	80	nan
3.0ms	6×	body	320	valid
2.0ms	5×	body	160	valid
1.0ms	1×	body	5120	valid

simplify159.0ms

Counts: 1 → 1

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.7b

localize27.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma c (* -3 a) (* b b)))
1.2b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.1b	(fma c (* -3 a) (* b b))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

Slowest

23.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
7.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))
0.0ms	(fma c (* -3 a) (* b b))

series444.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
111.0ms	(sqrt (fma c (* -3 a) (* b b)))
111.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
73.0ms	(fma c (* -3 a) (* b b))

simplify1.6s

Counts: 114 → 114

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 30.9b

localize40.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma c (* -3 a) (* b b)))
1.2b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)
0.1b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
28×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 213

Calls

4 calls:

Slowest

38.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)
32.0ms	(/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)
15.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
3.0ms	(sqrt (fma c (* -3 a) (* b b)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)
129.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)
109.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
94.0ms	(sqrt (fma c (* -3 a) (* b b)))

simplify872.0ms

Counts: 225 → 225

prune2.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.9b

localize32.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma c (* a -3) (* b b)))
1.2b	(- (sqrt (fma c (* a -3) (* b b))) b)
0.4b	(/ 1/3 a)
0.2b	(* (- (sqrt (fma c (* a -3) (* b b))) b) (/ 1/3 a))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
19×	`times-frac`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `flip3--` `flip--` `associate-/l`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 130

Calls

4 calls:

Slowest

36.0ms	(* (- (sqrt (fma c (* a -3) (* b b))) b) (/ 1/3 a))
15.0ms	(- (sqrt (fma c (* a -3) (* b b))) b)
7.0ms	(/ 1/3 a)
3.0ms	(sqrt (fma c (* a -3) (* b b)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

485.0ms	(sqrt (fma c (* a -3) (* b b)))
125.0ms	(* (- (sqrt (fma c (* a -3) (* b b))) b) (/ 1/3 a))
123.0ms	(- (sqrt (fma c (* a -3) (* b b))) b)
27.0ms	(/ 1/3 a)

simplify1.6s

Counts: 142 → 142

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.9b

localize45.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma c (* -3 a) (* b b)))
1.2b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.3b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (cbrt 3))
0.2b	(/ (/ 1 (* (cbrt 3) (cbrt 3))) (/ a (/ (- (sqrt (fma c (* -3 a) (* b b))) b) (cbrt 3))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

3113×	`times-frac`
1685×	`add-sqr-sqrt`
1380×	`*-un-lft-identity`
1076×	`add-cube-cbrt`
453×	`cbrt-prod`
304×	`difference-of-squares`
167×	`sqrt-prod`
160×	`div-inv`
152×	`distribute-lft-out--`
131×	`associate-/r*`
84×	`add-exp-log`
55×	`div-exp`
32×	`add-cbrt-cube`
25×	`cbrt-undiv`
18×	`prod-diff`
13×	`associate-/l*`
9×	`prod-exp` `associate-/r/`
6×	`rec-exp` `fma-neg` `1-exp` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 1176

Calls

4 calls:

Slowest

55.0ms	(/ (/ 1 (* (cbrt 3) (cbrt 3))) (/ a (/ (- (sqrt (fma c (* -3 a) (* b b))) b) (cbrt 3))))
22.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (cbrt 3))
7.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

463.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (cbrt 3))
362.0ms	(/ (/ 1 (* (cbrt 3) (cbrt 3))) (/ a (/ (- (sqrt (fma c (* -3 a) (* b b))) b) (cbrt 3))))
116.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
105.0ms	(sqrt (fma c (* -3 a) (* b b)))

simplify4.3s

Counts: 1188 → 1188

prune19.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.8b

regimes476.0ms

Accuracy

91.4% (0.5b remaining)

Error of 28.7b against oracle of 28.2b and baseline of 33.9b

bsearch188.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.0s	927×	body	1280	valid
971.0ms	5862×	body	80	valid
757.0ms	1031×	body	2560	valid
447.0ms	3018×	body	80	nan
211.0ms	469×	body	640	valid
138.0ms	105×	body	5120	valid
98.0ms	224×	body	320	valid
24.0ms	110×	body	160	valid