Details

sample123.0ms

Algorithm

intervals

Results

28.0ms	186×	body	80	valid
22.0ms	29×	body	2560	valid
22.0ms	32×	body	1280	valid
13.0ms	23×	body	640	valid
12.0ms	96×	body	80	nan
3.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify78.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

Slowest

49.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
20.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))
88.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
50.0ms	(- (* b_2 b_2) (* a c))

simplify1.2s

Counts: 107 → 107

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize52.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b_2 b_2) (* a c)))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))
10.3b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

Slowest

10.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))
60.0ms	(- (* b_2 b_2) (* a c))

simplify794.0ms

Counts: 73 → 73

prune880.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

localize44.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b_2 b_2) (* a c)))
9.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
1.0b	(- (* b_2 b_2) (* a c))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 188

Calls

4 calls:

Slowest

104.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
74.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series671.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

295.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
248.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
47.0ms	(- (* b_2 b_2) (* a c))

simplify1.0s

Counts: 200 → 200

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.6b

localize21.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b_2 b_2) (* a c)))
14.4b	(/ (* a c) a)
1.0b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

Slowest

50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(/ (* a c) a)
11.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
50.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(/ (* a c) a)

simplify1.1s

Counts: 79 → 79

prune901.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.6b

regimes315.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.5b

bsearch320.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.1s	5855×	body	80	valid
868.0ms	1059×	body	2560	valid
650.0ms	904×	body	1280	valid
594.0ms	454×	body	640	valid
339.0ms	2930×	body	80	nan
105.0ms	128×	body	5120	valid
75.0ms	238×	body	320	valid
26.0ms	113×	body	160	valid