Details

sample103.0ms

Algorithm

intervals

Results

31.0ms	44×	body	2560	valid
22.0ms	183×	body	80	valid
14.0ms	24×	body	1280	valid
9.0ms	87×	body	80	nan
3.0ms	8×	body	640	valid
3.0ms	8×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	1×	body	5120	valid

simplify244.0ms

Counts: 1 → 1

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize39.0ms

Local error

Found 3 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
2.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.1b	(/ (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2) a)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

168×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
159×	`times-frac`
115×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `add-log-exp`
5×	`div-inv`
4×	`pow1`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `flip--` `associate-/l/`

Counts

3 → 229

Calls

3 calls:

Slowest

29.0ms	(/ (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2) a)
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

121.0ms	(/ (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2) a)
119.0ms	(sqrt (fma (* -4 a) c (* b b)))
112.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify993.0ms

Counts: 238 → 238

prune3.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.8b

localize42.0ms

Local error

Found 3 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
2.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1/2 a))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
60×	`prod-diff`
53×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
10×	`times-frac` `fma-neg`
8×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `associate-l` `add-log-exp`
6×	`pow1`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`frac-times` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

3 → 150

Calls

3 calls:

Slowest

51.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1/2 a))
18.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series346.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

134.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1/2 a))
118.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
94.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.3s

Counts: 159 → 159

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize51.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
2.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.2b	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2)))
0.1b	(/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
630×	`add-sqr-sqrt`
629×	`*-un-lft-identity`
433×	`add-cube-cbrt`
105×	`associate-/r*`
98×	`distribute-lft-out--` `difference-of-squares`
82×	`sqrt-prod`
70×	`distribute-rgt-neg-in`
60×	`prod-diff`
30×	`add-exp-log`
22×	`div-inv`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `div-exp`
10×	`fma-neg`
9×	`cbrt-undiv`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `associate-/r/` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `pow-flip` `flip--` `inv-pow`

Counts

4 → 579

Calls

4 calls:

Slowest

43.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2)))
23.0ms	(/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2))
21.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

294.0ms	(/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2))
136.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) 2)))
126.0ms	(sqrt (fma (* -4 a) c (* b b)))
121.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify1.2s

Counts: 591 → 591

prune8.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

localize35.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
2.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.3b	(* (sqrt 2) (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))))
0.3b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

316×	`times-frac`
312×	`add-sqr-sqrt`
285×	`*-un-lft-identity`
181×	`add-cube-cbrt`
155×	`sqrt-prod`
143×	`associate-r`
60×	`prod-diff`
52×	`distribute-lft-out--` `difference-of-squares`
47×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`add-log-exp` `unswap-sqr`
7×	`pow1` `neg-mul-1` `associate-/l*`
6×	`associate-/r` `associate-l*`
5×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `neg-log` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 356

Calls

4 calls:

Slowest

42.0ms	(* (sqrt 2) (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))))
33.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))
22.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

573.0ms	(* (sqrt 2) (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))))
194.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))
128.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
119.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.3s

Counts: 368 → 368

prune5.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

regimes319.0ms

Accuracy

83.5% (4.5b remaining)

Error of 10.5b against oracle of 6.0b and baseline of 33.1b

bsearch329.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.3s	889×	body	1280	valid
1.0s	1021×	body	2560	valid
973.0ms	5905×	body	80	valid
506.0ms	2867×	body	80	nan
309.0ms	437×	body	640	valid
136.0ms	124×	body	5120	valid
92.0ms	223×	body	320	valid
31.0ms	120×	body	160	valid