Details

sample76.0ms

Algorithm

intervals

Results

31.0ms	284×	body	80	valid
8.0ms	85×	body	80	nan

simplify500.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	151
7	151
6	150
5	143
4	131
3	103
2	61
1	35
0	20

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize152.0ms

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))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite149.0ms

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:

60.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
169.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
170.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.4s

Counts

79 → 79

Iterations

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

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize268.0ms

Local error

Found 4 expressions with local error:

11.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `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`
1×	`neg-sub0` `+-commutative` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 62

Calls

4 calls:

29.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
154.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
149.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5010
3	2847
2	727
1	231
0	88

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize286.0ms

Local error

Found 4 expressions with local error:

9.3b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

20.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
179.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
143.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
152.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2587
2	672
1	225
0	92

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.7b

localize613.0ms

Local error

Found 4 expressions with local error:

21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

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:

24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
174.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
250.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
227.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts

72 → 72

Iterations

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

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.7b

regimes1.2s

Accuracy

86.5% (1.7b remaining)

Error of 9.2b against oracle of 7.5b and baseline of 19.9b

bsearch371.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-1.3122553888834108e+154

simplify20.0ms

Iterations

Iter	Nodes
done	49
1	49
0	41

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	8783×	body	80	valid
367.0ms	2988×	body	80	nan