Details

sample59.0ms

Algorithm

intervals

Results

24.0ms	274×	body	80	valid
8.0ms	104×	body	80	nan

simplify219.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	158
7	158
6	157
5	150
4	138
3	110
2	62
1	36
0	20

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize159.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `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 → 151

Calls

4 calls:

31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
3	4518
2	1209
1	431
0	179

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize202.0ms

Local error

Found 4 expressions with local error:

15.2b	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	2002
2	534
1	182
0	76

prune912.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize200.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
123.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	2991
2	749
1	233
0	87

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize157.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(/ (* 2.0 c) (- (- b) (- b (* (/ a b) (* 2.0 c)))))
3.9b	(* (/ a b) (* 2.0 c))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms	(/ (* 2.0 c) (- (- b) (- b (* (/ a b) (* 2.0 c)))))
36.0ms	(* (/ a b) (* 2.0 c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
270.0ms	(/ (* 2.0 c) (- (- b) (- b (* (/ a b) (* 2.0 c)))))
42.0ms	(* (/ a b) (* 2.0 c))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	2105
1	573
0	206

prune936.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

regimes616.0ms

Accuracy

89.7% (1.5b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 19.9b

bsearch394.0ms

Steps

Iters	Range		Point
8	5.631099529881209e+40	2.2779562270647888e+45	2.2352971002606818e+45
10	-8.897020078895062e+156	-1.101416214509623e+146	-8.035809894237901e+152

simplify50.0ms

Iterations

Iter	Nodes
done	77
2	77
1	75
0	57

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.6s	8684×	body	80	valid
330.0ms	2885×	body	80	nan