Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	280×	body	80	valid
7.0ms	94×	body	80	nan

simplify154.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize129.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite93.0ms

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:

23.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts: 72 → 72

prune457.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.9b

localize103.0ms

Local error

Found 4 expressions with local error:

8.4b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:

16.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts: 70 → 70

prune541.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.9b

localize162.0ms

Local error

Found 4 expressions with local error:

9.7b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

19.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
170.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
163.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts: 67 → 67

prune637.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

localize145.0ms

Local error

Found 4 expressions with local error:

24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

11.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
125.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
120.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
126.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts: 64 → 64

prune701.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.9b

regimes280.0ms

Accuracy

92.1% (1.0b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 20.0b

bsearch300.0ms

Steps

Iters	Range		Point
10	1.1938117014962488e+94	7.783906932586822e+104	4.760113507749772e+96
7	-1.0008868913456756e+160	-1.5580059821118574e+158	-1.5837719412499088e+158

simplify560.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

997.0ms	8736×	body	80	valid
575.0ms	2858×	body	80	nan