Details

sample125.0ms

Algorithm

intervals

Results

37.0ms	191×	body	80	valid
30.0ms	41×	body	2560	valid
15.0ms	28×	body	1280	valid
11.0ms	93×	body	80	nan
6.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify170.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize48.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
0.8b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

Slowest

90.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
46.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(- (* b b) (* (* c a) 4))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
104.0ms	(sqrt (- (* b b) (* (* c a) 4)))
87.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
60.0ms	(- (* b b) (* (* c a) 4))

simplify2.0s

Counts: 88 → 88

prune861.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize38.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
0.8b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1/2 a))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`insert-posit16` `difference-of-squares`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

Slowest

115.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1/2 a))
37.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
11.0ms	(sqrt (- (* b b) (* (* c a) 4)))
10.0ms	(- (* b b) (* (* c a) 4))

series387.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
112.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1/2 a))
97.0ms	(sqrt (- (* b b) (* (* c a) 4)))
60.0ms	(- (* b b) (* (* c a) 4))

simplify1.9s

Counts: 97 → 97

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize47.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* c a) 4)))
23.1b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
1.0b	(- (* b b) (* (* c a) 4))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

Slowest

17.0ms	(- (* b b) (* (* c a) 4))
8.0ms	(- (* b b) (* (* c a) 4))
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

424.0ms	(- (* b b) (* (* c a) 4))
96.0ms	(sqrt (- (* b b) (* (* c a) 4)))
80.0ms	(sqrt (- (* b b) (* (* c a) 4)))
71.0ms	(- (* b b) (* (* c a) 4))

simplify567.0ms

Counts: 70 → 70

prune743.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize32.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* c a) 4)))
23.1b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
1.0b	(- (* b b) (* (* c a) 4))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

Slowest

8.0ms	(sqrt (- (* b b) (* (* c a) 4)))
7.0ms	(- (* b b) (* (* c a) 4))
7.0ms	(- (* b b) (* (* c a) 4))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(sqrt (- (* b b) (* (* c a) 4)))
73.0ms	(sqrt (- (* b b) (* (* c a) 4)))
49.0ms	(- (* b b) (* (* c a) 4))
48.0ms	(- (* b b) (* (* c a) 4))

simplify445.0ms

Counts: 70 → 70

prune716.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

regimes236.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.6b

bsearch142.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	1143×	body	2560	valid
644.0ms	5839×	body	80	valid
477.0ms	888×	body	1280	valid
278.0ms	2933×	body	80	nan
163.0ms	450×	body	640	valid
149.0ms	115×	body	5120	valid
55.0ms	203×	body	320	valid
20.0ms	108×	body	160	valid