Details

sample74.0ms

Algorithm

intervals

Results

30.0ms	285×	body	80	valid
8.0ms	85×	body	80	nan

simplify485.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
7	168
6	166
5	160
4	151
3	127
2	74
1	38
0	20

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize201.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite136.0ms

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:

48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
186.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.6s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
3	3032
2	772
1	249
0	103

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize223.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `distribute-rgt-neg-in` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 64

Calls

4 calls:

48.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2530
2	695
1	218
0	85

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize437.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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:

13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series812.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
202.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
266.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
200.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5003
3	1993
2	580
1	205
0	92

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize536.0ms

Local error

Found 4 expressions with local error:

22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

16.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series970.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
245.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
217.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
226.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify4.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	1640
2	460
1	154
0	66

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

regimes1.1s

Accuracy

83% (2.2b remaining)

Error of 9.7b against oracle of 7.5b and baseline of 20.2b

bsearch340.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
6	-2.971125736392027e+46	-1.937449214055594e+45	-2.900769547116861e+46

simplify45.0ms

Iterations

Iter	Nodes
done	63
1	63
0	50

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s	8738×	body	80	valid
290.0ms	2975×	body	80	nan