Details

sample126.0ms

Algorithm

intervals

Results

30.0ms	37×	body	2560	valid
27.0ms	28×	body	1280	valid
25.0ms	186×	body	80	valid
11.0ms	91×	body	80	nan
10.0ms	19×	body	640	valid
5.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify152.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.6b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

43.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
13.0ms	(- (* b b) (* 4 (* a c)))
25.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
49.0ms	(- (* b b) (* 4 (* a c)))
107.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
83.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify941.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2006
3	2006
2	1254
1	400
0	154

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
0.6b	(+ (* b b) (* (* -4 a) c))
1.1b	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
22.9b	(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `diff-log` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

61.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
8.0ms	(+ (* b b) (* (* -4 a) c))
21.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
10.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
50.0ms	(+ (* b b) (* (* -4 a) c))
83.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
83.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2000
3	2000
2	1344
1	412
0	156

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.6b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

83.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
13.0ms	(- (* b b) (* 4 (* a c)))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
81.0ms	(- (* b b) (* 4 (* a c)))
121.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
115.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	2015
3	2015
2	1553
1	452
0	177

prune939.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.0b

localize55.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 67

Calls

4 calls:

20.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4 (* a c))))
9.0ms	(sqrt (- (* b b) (* 4 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
78.0ms	(sqrt (- (* b b) (* 4 (* a c))))
97.0ms	(sqrt (- (* b b) (* 4 (* a c))))
96.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify893.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2001
3	2001
2	639
1	212
0	87

prune1.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.0b

regimes434.0ms

Accuracy

79.6% (5.7b remaining)

Error of 11.2b against oracle of 5.5b and baseline of 33.6b

bsearch252.0ms

Steps

Iters	Range		Point
8	6.45623811977989e+97	1.5556153764929518e+101	1.786204067849289e+100
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.2890050783826923e-183

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	1101×	body	2560	valid
935.0ms	5836×	body	80	valid
742.0ms	915×	body	1280	valid
659.0ms	500×	body	640	valid
446.0ms	2978×	body	80	nan
93.0ms	106×	body	5120	valid
72.0ms	194×	body	320	valid
32.0ms	117×	body	160	valid