Details

sample84.0ms

Algorithm

intervals

Results

49.0ms	277×	body	80	valid
13.0ms	77×	body	80	nan

simplify154.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	152
7	152
6	151
5	144
4	132
3	101
2	62
1	35
0	20

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize142.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite80.0ms

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×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 64

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4 a) c))
27.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b b) (* (* 4 a) c))
117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
94.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
3	2593
2	742
1	237
0	99

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize211.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
4.3b	(/ (* 2 c) (* (- (/ a (/ b c)) b) 2))
4.8b	(/ a (/ b c))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*`
3×	`flip3--` `associate-/r/` `sqrt-prod` `flip--`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-*l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 124

Calls

4 calls:

16.0ms	(- (* b b) (* (* 4 a) c))
58.0ms	(/ (* 2 c) (* (- (/ a (/ b c)) b) 2))
13.0ms	(/ a (/ b c))
16.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* (* 4 a) c))
89.0ms	(/ (* 2 c) (* (- (/ a (/ b c)) b) 2))
32.0ms	(/ a (/ b c))
125.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify886.0ms

Counts

136 → 136

Iterations

Iter	Nodes
2	2469
1	681
0	260

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize188.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ a (/ b c))
12.6b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `sqrt-prod`
5×	`div-inv`
4×	`sqrt-div` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`neg-sub0` `+-commutative` `clear-num` `frac-2neg` `flip3-+` `neg-log` `associate-/r/` `associate-+l-` `flip-+`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/ a (/ b c))
25.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
16.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ a (/ b c))
148.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

129 → 129

Iterations

Iter	Nodes
3	5767
2	1702
1	575
0	231

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize186.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
23.9b	(cbrt (- (* b b) (* (* 4 a) c)))
23.9b	(cbrt (- (* b b) (* (* 4 a) c)))
23.9b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite33.0ms

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` `insert-posit16` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
130.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
164.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
133.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify3.9s

Counts

70 → 70

Iterations

Iter	Nodes
4	6322
3	1876
2	580
1	200
0	89

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

regimes664.0ms

Accuracy

93.2% (1.1b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 21.0b

bsearch415.0ms

Steps

Iters	Range		Point
7	1.602087361235081e+82	9.448026055101687e+83	4.866803345215698e+83
8	-5.520406447692031e+155	-8.116303404487084e+152	-4.82289647433212e+153

simplify46.0ms

Iterations

Iter	Nodes
2	72
1	72
0	57

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.3s	8706×	body	80	valid
654.0ms	2907×	body	80	nan