Details

sample178.0ms

Algorithm

intervals

Results

40.0ms	37×	body	2560	valid
35.0ms	186×	body	80	valid
25.0ms	28×	body	1280	valid
23.0ms	11×	body	320	valid
16.0ms	91×	body	80	nan
13.0ms	19×	body	640	valid
1.0ms	3×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize45.0ms

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))))

rewrite135.0ms

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:

90.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
17.0ms	(- (* b b) (* 4 (* a c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
60.0ms	(- (* b b) (* 4 (* a c)))
104.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
107.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.2s

Counts

93 → 93

Iterations

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

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize45.0ms

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)))

rewrite130.0ms

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:

59.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
16.0ms	(+ (* b b) (* (* -4 a) c))
38.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
13.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
68.0ms	(+ (* b b) (* (* -4 a) c))
110.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
91.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.3s

Counts

92 → 92

Iterations

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

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

localize42.0ms

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)))

rewrite107.0ms

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×	`sqrt-prod`
4×	`insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `distribute-rgt-neg-in` `flip3-+` `sqrt-div` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

72.0ms	(* (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (/ 1/2 a))
8.0ms	(+ (* b b) (* (* -4 a) c))
16.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
10.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (/ 1/2 a))
57.0ms	(+ (* b b) (* (* -4 a) c))
110.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
121.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	2002
3	2002
2	1720
1	466
0	179

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 6.0b

localize47.0ms

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)))

rewrite53.0ms

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

Counts

4 → 67

Calls

4 calls:

25.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
6.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
9.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
12.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
89.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
85.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
103.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify999.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2002
3	2002
2	648
1	211
0	88

prune1.2s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 6.0b

regimes465.0ms

Accuracy

79.7% (5.7b remaining)

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

bsearch223.0ms

Steps

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

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.2s	1101×	body	2560	valid
1.1s	915×	body	1280	valid
894.0ms	5836×	body	80	valid
488.0ms	194×	body	320	valid
382.0ms	2978×	body	80	nan
319.0ms	500×	body	640	valid
150.0ms	106×	body	5120	valid
29.0ms	117×	body	160	valid