Details

sample369.0ms

Algorithm

intervals

Results

72.0ms	93×	body	80	nan
42.0ms	41×	body	2560	valid
36.0ms	191×	body	80	valid
23.0ms	28×	body	1280	valid
7.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify89.0ms

Counts: 1 → 1

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize38.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

Slowest

86.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
82.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(- (* b_2 b_2) (* a c))

series372.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(- (* b_2 b_2) (* a c))

simplify1.4s

Counts: 134 → 134

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b_2 b_2) (* a c)))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (* b_2 b_2) (* a c))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

Slowest

22.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(sqrt (- (* b_2 b_2) (* a c)))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))
71.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (* b_2 b_2) (* a c))

simplify2.0s

Counts: 82 → 82

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize25.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b_2 b_2) (* a c)))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (* b_2 b_2) (* a c))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

Slowest

21.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(sqrt (- (* b_2 b_2) (* a c)))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
68.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (* b_2 b_2) (* a c))

simplify1.6s

Counts: 82 → 82

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize68.0ms

Local error

Found 4 expressions with local error:

23.8b	(cbrt (- (* b_2 b_2) (* a c)))
23.8b	(cbrt (- (* b_2 b_2) (* a c)))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))
6.4b	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`prod-diff` `sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log`

Counts

4 → 69

Calls

4 calls:

Slowest

32.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(cbrt (- (* b_2 b_2) (* a c)))
157.0ms	(cbrt (- (* b_2 b_2) (* a c)))
119.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts: 81 → 81

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.6b

regimes418.0ms

Accuracy

84.4% (4.4b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 33.9b

bsearch200.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

985.0ms	1143×	body	2560	valid
896.0ms	5839×	body	80	valid
679.0ms	452×	body	640	valid
523.0ms	888×	body	1280	valid
378.0ms	2927×	body	80	nan
93.0ms	116×	body	5120	valid
64.0ms	201×	body	320	valid
22.0ms	107×	body	160	valid