Details

sample136.0ms

Algorithm

intervals

Results

89.0ms	279×	body	80	valid
19.0ms	91×	body	80	nan

simplify145.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	152
7	152
6	151
5	144
4	132
3	101
2	62
1	35
0	20

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize167.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.9b	(sqrt (- (* b b) (* (* 4 a) c)))
21.9b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 67

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
123.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
122.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
146.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts

79 → 79

Iterations

Iter	Nodes
3	2437
2	760
1	248
0	102

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize167.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

25.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
114.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
147.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
135.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.0s

Counts

70 → 70

Iterations

Iter	Nodes
4	6322
3	1876
2	580
1	200
0	89

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize179.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (- (* b b) (* (* 4 a) c)))
21.9b	(sqrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
125.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
113.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.3s

Counts

72 → 72

Iterations

Iter	Nodes
4	6322
3	1876
2	580
1	200
0	89

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize182.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
20.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
142.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
137.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
153.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.2s

Counts

70 → 70

Iterations

Iter	Nodes
4	6322
3	1876
2	580
1	200
0	89

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

regimes559.0ms

Accuracy

92.2% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 19.4b

bsearch403.0ms

Steps

Iters	Range		Point
9	1.7155709022758137e+74	7.648947555279674e+80	3.6885722464483736e+80
8	-6.435448379097954e+123	-1.4863434806956936e+121	-4.694684309811035e+121

simplify13.0ms

Iterations

Iter	Nodes
2	52
1	52
0	43

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.0s	8775×	body	80	valid
566.0ms	2919×	body	80	nan