Details

sample84.0ms

Algorithm

intervals

Results

45.0ms	277×	body	80	valid
10.0ms	105×	body	80	nan

simplify220.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	20	38
1	39	38
2	79	37
3	143	37
4	179	37
5	189	37
6	193	37
done	193	37

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize160.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

59.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
126.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

163 → 163

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	179	6238
1	441	4232
2	1815	3344
done	5001	2696

prune884.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize171.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-log-exp`
9×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `flip3-+` `fma-neg` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

13.0ms	(- (* b b) (* (* 4.0 a) c))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	104	1247
1	278	1120
2	1323	1017
done	5000	1010

prune674.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.9b

localize167.0ms

Local error

Found 4 expressions with local error:

6.6b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
8×	`add-log-exp`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 72

Calls

4 calls:

20.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

84 → 84

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	152	1636
1	405	1538
2	1795	1342
done	5000	1306

prune935.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.9b

localize199.0ms

Local error

Found 4 expressions with local error:

21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

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` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 66

Calls

4 calls:

32.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
140.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts

78 → 78

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	94	1238
1	224	1122
2	750	1028
3	3976	1022
done	5000	1019

prune778.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.9b

regimes330.0ms

Accuracy

93.2% (0.8b remaining)

Error of 8.0b against oracle of 7.1b and baseline of 19.5b

bsearch368.0ms

Steps

Iters	Range		Point
9	9.357224410271438e+98	8.450543925883448e+104	1.8826250280731126e+103
10	-1.9836462979030918e+161	-7.955079132577946e+149	-1.3389186356061464e+154

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	122
1	52	122
done	52	122

end0.0ms

sample2.2s

Algorithm

intervals

Results

986.0ms	8729×	body	80	valid
721.0ms	2885×	body	80	nan