Details

sample153.0ms

Algorithm

intervals

Results

53.0ms	189×	body	80	valid
33.0ms	34×	body	2560	valid
18.0ms	23×	body	1280	valid
11.0ms	80×	body	80	nan
7.0ms	12×	body	640	valid
4.0ms	3×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify176.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize26.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))

rewrite190.0ms

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

99.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
65.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms	(- (* b b) (* (* c a) 4))
11.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
103.0ms	(sqrt (- (* b b) (* (* c a) 4)))
97.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
53.0ms	(- (* b b) (* (* c a) 4))

simplify2.3s

Counts: 88 → 88

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b	(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

Slowest

59.0ms	(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))
43.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms	(- (* b b) (* (* c a) 4))
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))
105.0ms	(sqrt (- (* b b) (* (* c a) 4)))
98.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
58.0ms	(- (* b b) (* (* c a) 4))

simplify760.0ms

Counts: 134 → 134

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize39.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b	(/ 1 (/ 2 (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac`
438×	`add-sqr-sqrt`
363×	`*-un-lft-identity`
289×	`add-cube-cbrt`
74×	`difference-of-squares`
71×	`associate-/r*`
40×	`sqrt-prod`
37×	`distribute-lft-out--`
25×	`add-exp-log`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
4×	`insert-posit16`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 358

Calls

4 calls:

Slowest

40.0ms	(/ 1 (/ 2 (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)))
34.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
12.0ms	(sqrt (- (* b b) (* (* c a) 4)))
8.0ms	(- (* b b) (* (* c a) 4))

series413.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(/ 1 (/ 2 (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)))
123.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
91.0ms	(sqrt (- (* b b) (* (* c a) 4)))
57.0ms	(- (* b b) (* (* c a) 4))

simplify955.0ms

Counts: 370 → 370

prune5.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* c a) 4)))
1.0b	(- (* b b) (* (* c a) 4))
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b	(* (/ 1/2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

Slowest

137.0ms	(* (/ 1/2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
42.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms	(- (* b b) (* (* c a) 4))
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(* (/ 1/2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
119.0ms	(sqrt (- (* b b) (* (* c a) 4)))
106.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
68.0ms	(- (* b b) (* (* c a) 4))

simplify2.2s

Counts: 101 → 101

prune979.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

regimes331.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.0b against oracle of 5.3b and baseline of 33.5b

bsearch207.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	5796×	body	80	valid
980.0ms	1094×	body	2560	valid
746.0ms	860×	body	1280	valid
422.0ms	2811×	body	80	nan
254.0ms	481×	body	640	valid
153.0ms	103×	body	5120	valid
133.0ms	251×	body	320	valid
62.0ms	130×	body	160	valid