Details

sample82.0ms

Algorithm

intervals

Results

43.0ms	280×	body	80	valid
7.0ms	88×	body	80	nan

simplify165.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	166
6	166
5	164
4	150
3	116
2	66
1	35
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize153.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

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`
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 → 63

Calls

4 calls:

18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
120.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1036
1	254
0	100

prune646.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.0b

localize184.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

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` `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:

10.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify849.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	982
1	236
0	90

prune798.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.0b

localize209.0ms

Local error

Found 4 expressions with local error:

24.4b	(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)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
177.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
132.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3628
2	700
1	211
0	90

prune868.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.0b

localize198.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
7.1b	(/ (* a c) b)
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
8×	`times-frac` `add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r*` `div-exp` `sqrt-prod` `distribute-lft-out`
3×	`distribute-rgt-neg-in`
2×	`neg-sub0` `clear-num` `frac-2neg` `flip3--` `sqrt-div` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`associate--l-` `rem-sqrt-square` `associate-+r-` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 83

Calls

4 calls:

20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
23.0ms	(/ (* a c) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
42.0ms	(/ (* a c) b)
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

95 → 95

Iterations

Iter	Nodes
done	5002
2	2551
1	500
0	187

prune800.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

regimes549.0ms

Accuracy

89.9% (1.3b remaining)

Error of 7.8b against oracle of 6.4b and baseline of 19.7b

bsearch695.0ms

Steps

Iters	Range		Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
7	-9.685109581380507e+154	-1.5171851739610474e+153	-2.0256498248166784e+153

simplify28.0ms

Iterations

Iter	Nodes
done	63
1	63
0	52

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	8758×	body	80	valid
376.0ms	2839×	body	80	nan