Details

sample61.0ms

Algorithm

intervals

Results

34.0ms	287×	body	80	valid
5.0ms	87×	body	80	nan

simplify8.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize100.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Counts: 72 → 72

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize104.0ms

Local error

Found 4 expressions with local error:

12.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

11.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify107.0ms

Counts: 70 → 70

prune345.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize115.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Counts: 68 → 68

prune482.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

localize98.0ms

Local error

Found 4 expressions with local error:

7.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `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 → 60

Calls

4 calls:

12.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify101.0ms

Counts: 72 → 72

prune308.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.3b

regimes186.0ms

Accuracy

94.1% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 20.4b

bsearch155.0ms

Steps

Iters	Range		Point
4	9.012561940608131e+125	1.467599966670541e+126	1.2355926667992227e+126
9	-7.230061550164269e+155	-2.875458900305947e+147	-1.080857996826958e+154

simplify1.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8707×	body	80	valid
239.0ms	2916×	body	80	nan