Details

sample142.0ms

Algorithm

intervals

Results

43.0ms	35×	body	2560	valid
28.0ms	184×	body	80	valid
22.0ms	28×	body	1280	valid
13.0ms	86×	body	80	nan
9.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify114.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
0.6b	(- (* b b) (* (* c a) 4))
1.7b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
24.6b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `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 → 88

Calls

4 calls:

90.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
15.0ms	(- (* b b) (* (* c a) 4))
55.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
63.0ms	(- (* b b) (* (* c a) 4))
104.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
100.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.6s

Counts

100 → 100

Iterations

Iter	Nodes
3	3565
2	1088
1	398
0	161

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
0.6b	(- (* b b) (* (* c a) 4))
8.4b	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
24.6b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

13.0ms	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
7.0ms	(- (* b b) (* (* c a) 4))
46.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
75.0ms	(- (* b b) (* (* c a) 4))
135.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
117.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.4s

Counts

109 → 109

Iterations

Iter	Nodes
3	3577
2	1188
1	411
0	179

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
0.6b	(- (* b b) (* (* c a) 4))
12.6b	(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
24.6b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

29.0ms	(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
7.0ms	(- (* b b) (* (* c a) 4))
22.0ms	(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
48.0ms	(- (* b b) (* (* c a) 4))
117.0ms	(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
84.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify3.7s

Counts

110 → 110

Iterations

Iter	Nodes
3	4164
2	1495
1	523
0	199

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* c a) 4))
16.0b	(- (* (sqrt (sqrt (- (* b b) (* (* c a) 4)))) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
24.6b	(sqrt (- (* b b) (* (* c a) 4)))
24.6b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-div`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `flip3--` `add-cube-cbrt` `sqrt-prod` `flip--`
5×	`frac-sub`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
2×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l/` `associate-r/`
1×	`sub-div`

Counts

4 → 64

Calls

4 calls:

7.0ms	(- (* b b) (* (* c a) 4))
31.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* c a) 4)))) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* c a) 4))
118.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* c a) 4)))) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
84.0ms	(sqrt (- (* b b) (* (* c a) 4)))
118.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
3	2999
2	1009
1	342
0	131

prune934.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

regimes280.0ms

Accuracy

84.7% (4.4b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 34.1b

bsearch202.0ms

Steps

Iters	Range		Point
10	8.296670056881522e-85	2.5972983117194536e-74	2.326372645943808e-74
7	-1.8217288728729631e+111	-6.606823090402082e+109	-5.148407540792454e+110

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	29

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	1126×	body	2560	valid
720.0ms	5836×	body	80	valid
718.0ms	2976×	body	80	nan
692.0ms	915×	body	1280	valid
275.0ms	417×	body	640	valid
107.0ms	119×	body	5120	valid
84.0ms	236×	body	320	valid
26.0ms	115×	body	160	valid