Details

sample235.0ms

Algorithm

intervals

Results

27.0ms	195×	body	80	valid
20.0ms	24×	body	2560	valid
20.0ms	30×	body	1280	valid
19.0ms	100×	body	80	nan
7.0ms	14×	body	640	valid
4.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify88.0ms

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize35.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(- (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

99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series438.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
122.0ms	(sqrt (- (* b_2 b_2) (* a c)))
102.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(- (* b_2 b_2) (* a c))

simplify527.0ms

Counts: 182 → 134

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize20.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 200

Calls

4 calls:

Slowest

54.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series417.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

193.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
110.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))
40.0ms	(- (* b_2 b_2) (* a c))

simplify407.0ms

Counts: 312 → 212

prune2.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.8b

localize24.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`prod-diff`
51×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-l` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 162

Calls

4 calls:

Slowest

97.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

188.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
47.0ms	(- (* b_2 b_2) (* a c))

simplify277.0ms

Counts: 246 → 174

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize24.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite179.0ms

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

90.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series392.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(- (* b_2 b_2) (* a c))

simplify1.0s

Counts: 182 → 134

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

regimes301.0ms

Accuracy

82.8% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 33.3b

bsearch232.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	1051×	body	2560	valid
765.0ms	5842×	body	80	valid
605.0ms	888×	body	1280	valid
379.0ms	2921×	body	80	nan
274.0ms	489×	body	640	valid
108.0ms	108×	body	5120	valid
105.0ms	222×	body	320	valid
25.0ms	116×	body	160	valid