Details

sample125.0ms

Algorithm

intervals

Results

30.0ms	37×	body	2560	valid
25.0ms	184×	body	80	valid
19.0ms	30×	body	1280	valid
12.0ms	95×	body	80	nan
9.0ms	18×	body	640	valid
5.0ms	5×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify162.0ms

Counts: 1 → 1

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.1b

localize28.0ms

Local error

Found 4 expressions with local error:

24.1b	(sqrt (fma c (* -3 a) (* b b)))
1.4b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.5b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.1b	(fma c (* -3 a) (* b b))

rewrite55.0ms

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

35.0ms	(/ (- (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)))
0.0ms	(fma c (* -3 a) (* b b))

series433.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
122.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
110.0ms	(sqrt (fma c (* -3 a) (* b b)))
77.0ms	(fma c (* -3 a) (* b b))

simplify2.1s

Counts: 114 → 114

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 29.0b

localize42.0ms

Local error

Found 4 expressions with local error:

24.1b	(sqrt (fma c (* -3 a) (* b b)))
1.4b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.4b	(/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))
0.2b	(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
66×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
30×	`add-exp-log`
22×	`sqrt-prod`
18×	`associate-/r*` `add-cbrt-cube` `prod-diff`
14×	`div-exp` `difference-of-squares`
11×	`associate-/r/`
7×	`cbrt-undiv` `distribute-lft-out--`
6×	`pow1` `flip3--` `fma-neg` `div-inv` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

Slowest

24.0ms	(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))
16.0ms	(/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))
8.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -3 a) (* b b)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

326.0ms	(/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))
180.0ms	(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))
104.0ms	(sqrt (fma c (* -3 a) (* b b)))
84.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)

simplify854.0ms

Counts: 181 → 181

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.6b

localize45.0ms

Local error

Found 4 expressions with local error:

24.1b	(sqrt (fma c (* -3 a) (* b b)))
1.4b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b	(/ 1/3 (/ a (- (sqrt (fma c (* -3 a) (* b b))) b)))
0.1b	(/ a (- (sqrt (fma c (* -3 a) (* b b))) b))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 219

Calls

4 calls:

Slowest

25.0ms	(/ 1/3 (/ a (- (sqrt (fma c (* -3 a) (* b b))) b)))
16.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
16.0ms	(/ a (- (sqrt (fma c (* -3 a) (* b b))) b))
3.0ms	(sqrt (fma c (* -3 a) (* b b)))

series731.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

331.0ms	(/ a (- (sqrt (fma c (* -3 a) (* b b))) b))
175.0ms	(/ 1/3 (/ a (- (sqrt (fma c (* -3 a) (* b b))) b)))
118.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
107.0ms	(sqrt (fma c (* -3 a) (* b b)))

simplify994.0ms

Counts: 231 → 231

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.6b

localize44.0ms

Local error

Found 4 expressions with local error:

24.1b	(sqrt (fma c (* -3 a) (* b b)))
1.4b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b	(/ 1/3 (/ a (- (sqrt (fma c (* -3 a) (* b b))) b)))
0.1b	(/ a (- (sqrt (fma c (* -3 a) (* b b))) b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 219

Calls

4 calls:

Slowest

13.0ms	(/ 1/3 (/ a (- (sqrt (fma c (* -3 a) (* b b))) b)))
12.0ms	(/ a (- (sqrt (fma c (* -3 a) (* b b))) b))
8.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

242.0ms	(/ a (- (sqrt (fma c (* -3 a) (* b b))) b))
176.0ms	(/ 1/3 (/ a (- (sqrt (fma c (* -3 a) (* b b))) b)))
124.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
105.0ms	(sqrt (fma c (* -3 a) (* b b)))

simplify969.0ms

Counts: 231 → 231

prune3.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.6b

regimes515.0ms

Accuracy

81% (3.9b remaining)

Error of 17.1b against oracle of 13.1b and baseline of 33.9b

bsearch102.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.4s	1105×	body	2560	valid
1.4s	5923×	body	80	valid
581.0ms	890×	body	1280	valid
522.0ms	2838×	body	80	nan
246.0ms	434×	body	640	valid
98.0ms	103×	body	5120	valid
82.0ms	220×	body	320	valid
25.0ms	100×	body	160	valid