Details

sample87.0ms

Algorithm

intervals

Results

41.0ms	287×	body	80	valid
12.0ms	108×	body	80	nan

simplify194.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	20	38
1	49	38
2	128	37
3	202	37
4	221	37
done	221	37

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.0b

localize129.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite136.0ms

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:

41.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts

163 → 163

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	179	6238
1	1182	3601
done	5001	3435

prune753.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize175.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.8b	(/ (* a c) b)
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`fma-def`
9×	`times-frac`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`distribute-rgt-neg-in`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u` `distribute-lft-out--`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `neg-log` `flip-+`

Counts

4 → 99

Calls

4 calls:

28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
20.0ms	(/ (* a c) b)
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
99.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
35.0ms	(/ (* a c) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.7s

Counts

111 → 111

Iterations

Useful iterations: done (4.7s)

Iter	Nodes	Cost
0	193	1632
1	1945	1524
done	5000	1330

prune773.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize151.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

71.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
68.0ms	(- (* b b) (* (* 4.0 a) c))
102.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

101 → 101

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	157	1641
1	1270	1500
done	5001	1347

prune627.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize160.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
125.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	87	1348
1	529	1188
done	5000	1112

prune839.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

regimes290.0ms

Accuracy

87.9% (1.8b remaining)

Error of 8.5b against oracle of 6.7b and baseline of 21.6b

bsearch209.0ms

Steps

Iters	Range		Point
9	1.7084993271036838e+35	8.915315724770326e+40	8.75372275402518e+40
8	-1.1598944120121166e+59	-1.8875019941432514e+54	-5.042692342260055e+58

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	46	142
1	57	142
done	57	142

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.6s	8706×	body	80	valid
284.0ms	2996×	body	80	nan