Details

sample75.0ms

Algorithm

intervals

Results

37.0ms	278×	body	80	valid
8.0ms	92×	body	80	nan

simplify145.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize153.0ms

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))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

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:

11.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts: 72 → 72

prune480.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.7b

localize143.0ms

Local error

Found 4 expressions with local error:

7.5b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite67.0ms

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:

15.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
165.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
158.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts: 67 → 67

prune659.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.7b

localize152.0ms

Local error

Found 4 expressions with local error:

8.9b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

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` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

Calls

4 calls:

27.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
150.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
167.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts: 66 → 66

prune603.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.7b

localize168.0ms

Local error

Found 4 expressions with local error:

24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
186.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts: 70 → 70

prune751.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.7b

regimes272.0ms

Accuracy

92.6% (0.9b remaining)

Error of 8.5b against oracle of 7.5b and baseline of 20.2b

bsearch271.0ms

Steps

Iters	Range		Point
10	1.1938117014962488e+94	7.783906932586822e+104	1.5274426010927598e+96
7	-9.285931959904111e+157	-1.3338943710063638e+156	-1.3544632410955304e+156

simplify1.2s

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	8701×	body	80	valid
342.0ms	2847×	body	80	nan