Details

sample52.0ms

Algorithm

intervals

Results

19.0ms	275×	body	80	valid
13.0ms	76×	body	80	nan

simplify8.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize102.0ms

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))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(- (- b) (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)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Counts: 72 → 72

prune300.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize103.0ms

Local error

Found 4 expressions with local error:

8.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

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:

14.0ms	(+ (- 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)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify107.0ms

Counts: 70 → 70

prune366.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize112.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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:

9.0ms	(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)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
110.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Counts: 68 → 68

prune470.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize127.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

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

series428.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Counts: 64 → 64

prune528.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.6b

regimes209.0ms

Accuracy

93.8% (0.8b remaining)

Error of 8.6b against oracle of 7.8b and baseline of 20.1b

bsearch215.0ms

Steps

Iters	Range		Point
8	9.012561940608131e+125	4.309422734686771e+129	3.554764365478848e+126
10	-1.6145330241135586e+155	-4.1230913930237915e+136	-4.106334319949844e+145

simplify1.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	8765×	body	80	valid
293.0ms	2942×	body	80	nan