Details

sample100.0ms

Algorithm

intervals

Results

17.0ms	198×	body	80	valid
14.0ms	27×	body	2560	valid
11.0ms	26×	body	1280	valid
10.0ms	9×	body	160	valid
9.0ms	101×	body	80	nan
5.0ms	15×	body	640	valid
4.0ms	14×	body	320	valid
1.0ms	2×	body	5120	valid

simplify139.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite172.0ms

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--` `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 → 77

Calls

4 calls:

103.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms	(- (* b b) (* 4.0 (* a c)))
104.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1618
1	411
0	155

prune572.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

132.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
14.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
86.0ms	(- (* b b) (* 4.0 (* a c)))
114.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2387
1	485
0	181

prune553.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize85.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
12.4b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

7.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* b b) (* 4.0 (* a c)))
106.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1144
1	258
0	98

prune586.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

localize50.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.8b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

35.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
99.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
97.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
221.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
297.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.4s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	3611
1	648
0	250

prune813.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

regimes672.0ms

Accuracy

86.3% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 33.8b

bsearch210.0ms

Steps

Iters	Range		Point
3	5.437233749566996e+22	6.419404774371196e+22	6.358019085320933e+22
8	5.9238016895844435e-289	2.20999447876618e-286	5.992812285264993e-289
6	-0.042530208599811804	-0.005947574473424517	-0.03099989563658143

simplify9.0ms

Iterations

Iter	Nodes
done	45
1	45
0	38

end0.0ms

sample3.2s

Algorithm

intervals

Results

637.0ms	492×	body	640	valid
629.0ms	1023×	body	2560	valid
568.0ms	5935×	body	80	valid
417.0ms	864×	body	1280	valid
340.0ms	2964×	body	80	nan
140.0ms	112×	body	5120	valid
51.0ms	237×	body	320	valid
18.0ms	114×	body	160	valid