Details

sample115.0ms

Algorithm

intervals

Results

43.0ms	37×	body	2560	valid
20.0ms	194×	body	80	valid
15.0ms	28×	body	1280	valid
8.0ms	86×	body	80	nan
8.0ms	18×	body	640	valid
4.0ms	5×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.9b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b	(- (* b b) (* 4 (* a c)))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

41.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(- (* b b) (* 4 (* a c)))
8.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
96.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
52.0ms	(- (* b b) (* 4 (* a c)))
100.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
3	2002
2	1255
1	400
0	154

prune505.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

13.0ms	(- (* b b) (* 4 (* a c)))
8.0ms	(sqrt (- (* b b) (* 4 (* a c))))
8.0ms	(sqrt (- (* b b) (* 4 (* a c))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* b b) (* 4 (* a c)))
91.0ms	(sqrt (- (* b b) (* 4 (* a c))))
93.0ms	(sqrt (- (* b b) (* 4 (* a c))))
113.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	2005
4	2005
3	1783
2	454
1	156
0	61

prune656.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

8.0ms	(- (* b b) (* 4 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b b) (* 4 (* a c)))
94.0ms	(sqrt (- (* b b) (* 4 (* a c))))
101.0ms	(sqrt (- (* b b) (* 4 (* a c))))
116.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	2005
4	2005
3	1783
2	454
1	156
0	61

prune623.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.6b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
10.9b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite58.0ms

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:

19.0ms	(- (* b b) (* 4 (* a c)))
14.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b b) (* 4 (* a c)))
82.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
104.0ms	(sqrt (- (* b b) (* 4 (* a c))))
75.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify794.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2010
3	2010
2	737
1	253
0	100

prune313.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.5b

regimes569.0ms

Accuracy

82.7% (4.6b remaining)

Error of 9.8b against oracle of 5.2b and baseline of 31.7b

bsearch183.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	2.5703497435733685e+102
10	-1.094129558870314e-56	-1.2317994276347943e-74	-1.8774910265390396e-73

simplify6.0ms

Iterations

Iter	Nodes
done	38
2	38
1	32
0	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

968.0ms	1095×	body	2560	valid
905.0ms	948×	body	1280	valid
827.0ms	5820×	body	80	valid
718.0ms	2996×	body	80	nan
309.0ms	445×	body	640	valid
103.0ms	98×	body	5120	valid
97.0ms	225×	body	320	valid
26.0ms	116×	body	160	valid