Details

sample102.0ms

Algorithm

intervals

Results

21.0ms	37×	body	2560	valid
17.0ms	182×	body	80	valid
15.0ms	31×	body	1280	valid
8.0ms	22×	body	640	valid
8.0ms	89×	body	80	nan
2.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	5120	valid

simplify180.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite131.0ms

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:

89.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
118.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(- (* b b) (* 4.0 (* a c)))
93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1618
1	411
0	155

prune515.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize37.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
4.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.9b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
20×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
10×	`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 → 138

Calls

4 calls:

14.0ms	(- (* b b) (* 4.0 (* a c)))
151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
79.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* 4.0 (* a c)))
233.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
281.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
123.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	3701
1	654
0	249

prune914.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize62.0ms

Local error

Found 4 expressions with local error:

9.7b	(- (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

179.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
96.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
109.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	4970
2	846
1	211
0	80

prune470.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
15.9b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`cbrt-undiv` `times-frac` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-*r/` `associate-/r/` `difference-of-squares` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

36.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
77.0ms	(- (* b b) (* 4.0 (* a c)))
229.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	3371
1	480
0	170

prune480.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.0b

regimes484.0ms

Accuracy

83.3% (4.5b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 32.8b

bsearch170.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	4.8254787200880607e+107
9	-1.0952546209266604e-55	-7.034794544076098e-65	-9.332433396832084e-58

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample3.2s

Algorithm

intervals

Results

858.0ms	892×	body	1280	valid
824.0ms	5891×	body	80	valid
512.0ms	1016×	body	2560	valid
275.0ms	2883×	body	80	nan
133.0ms	461×	body	640	valid
56.0ms	220×	body	320	valid
51.0ms	98×	body	5120	valid
48.0ms	118×	body	160	valid