Details

sample45.0ms

Algorithm

intervals

Results

19.0ms	276×	body	80	valid
5.0ms	79×	body	80	nan

simplify132.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	179
6	179
5	175
4	163
3	136
2	78
1	38
0	20

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize140.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite105.0ms

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:

37.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
120.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
134.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify655.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1037
1	255
0	100

prune783.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize154.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b	(/ (* 2.0 c) (+ (* b -2) (/ (* 2.0 a) (/ b c))))
4.0b	(/ (* 2.0 a) (/ b c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(/ (* 2.0 c) (+ (* b -2) (/ (* 2.0 a) (/ b c))))
20.0ms	(/ (* 2.0 a) (/ b c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
258.0ms	(/ (* 2.0 c) (+ (* b -2) (/ (* 2.0 a) (/ b c))))
34.0ms	(/ (* 2.0 a) (/ b c))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	3851
1	665
0	243

prune903.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize184.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b	(/ (* 2.0 c) (+ (* b -2) (/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))))
4.1b	(/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(/ (* 2.0 c) (+ (* b -2) (/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))))
70.0ms	(/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
358.0ms	(/ (* 2.0 c) (+ (* b -2) (/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))))
59.0ms	(/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))
133.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify502.0ms

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
1	894
0	309

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize160.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))
13.6b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

58×	`times-frac`
36×	`add-exp-log`
35×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-/r*` `add-cbrt-cube`
18×	`cbrt-prod`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`pow1` `sqrt-prod`
4×	`sqrt-div`
3×	`flip3--` `div-inv` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`
1×	`associate--l-` `neg-sub0` `clear-num` `sub-neg` `frac-2neg` `neg-log` `associate-/r/` `associate-/l*` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

68.0ms	(/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))
17.0ms	(- (- 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))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (* (* (* a 2.0) (cbrt c)) (cbrt c)) (/ b (cbrt c)))
117.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
106.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify491.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
1	754
0	259

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

regimes576.0ms

Accuracy

89.7% (1.7b remaining)

Error of 7.8b against oracle of 6.2b and baseline of 22.2b

bsearch471.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	5.97656052905875e+77
9	-6.622314338184697e+74	-3.7162343696193017e+68	-3.6945990134744297e+74

simplify18.0ms

Iterations

Iter	Nodes
done	78
2	78
1	77
0	60

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	8719×	body	80	valid
330.0ms	2811×	body	80	nan