Details

sample144.0ms

Algorithm

intervals

Results

46.0ms	23×	body	1280	valid
30.0ms	42×	body	2560	valid
22.0ms	176×	body	80	valid
12.0ms	23×	body	640	valid
11.0ms	98×	body	80	nan
4.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify151.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize50.0ms

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)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite86.0ms

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:

47.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
8.0ms	(- (* b b) (* 4 (* a c)))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
86.0ms	(- (* b b) (* 4 (* a c)))
124.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
93.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

93 → 93

Iterations

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

prune458.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
0.6b	(- (* b b) (* 4 (* a c)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

36.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
8.0ms	(- (* b b) (* 4 (* a c)))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
65.0ms	(- (* b b) (* 4 (* a c)))
114.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
104.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.4s

Counts

141 → 141

Iterations

Iter	Nodes
done	2002
3	2002
2	1799
1	571
0	229

prune633.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1/2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
0.6b	(- (* b b) (* 4 (* a c)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

99.0ms	(* (/ 1/2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
8.0ms	(- (* b b) (* 4 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (/ 1/2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
60.0ms	(- (* b b) (* 4 (* a c)))
105.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
108.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	2001
3	2001
2	1599
1	463
0	174

prune584.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* -4 a) c)
0.6b	(+ (* b b) (* (* -4 a) c))
0.7b	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
21.9b	(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

14.0ms	(* (* -4 a) c)
14.0ms	(+ (* b b) (* (* -4 a) c))
20.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
6.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* -4 a) c)
65.0ms	(+ (* b b) (* (* -4 a) c))
120.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
108.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	2004
3	2004
2	1104
1	331
0	130

prune358.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.3b

regimes420.0ms

Accuracy

83.1% (4.7b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.3b

bsearch207.0ms

Steps

Iters	Range		Point
7	6.52945691119865e+99	1.3360629297740576e+102	6.384705165981893e+101
9	-3.929467862544791e-84	-4.77908653107304e-89	-5.961198324014865e-88

simplify10.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1077×	body	2560	valid
989.0ms	5862×	body	80	valid
906.0ms	903×	body	1280	valid
537.0ms	2940×	body	80	nan
288.0ms	471×	body	640	valid
231.0ms	109×	body	5120	valid
99.0ms	219×	body	320	valid
37.0ms	117×	body	160	valid