Details

sample103.0ms

Algorithm

intervals

Results

19.0ms	32×	body	2560	valid
17.0ms	171×	body	80	valid
17.0ms	34×	body	1280	valid
10.0ms	105×	body	80	nan
5.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	10×	body	160	valid
1.0ms	5×	body	320	valid

simplify281.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	138
7	138
6	136
5	131
4	126
3	107
2	61
1	28
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

133.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
60.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
89.0ms	(- (* b b) (* 4.0 (* a c)))
172.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
137.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify5.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4826
2	1269
1	409
0	157

prune854.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* c (* 4.0 a))))) (* 2.0 a))
1.0b	(- (* b b) (* c (* 4.0 a)))
2.4b	(- (- b) (sqrt (- (* b b) (* c (* 4.0 a)))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

141.0ms	(/ (- (- b) (sqrt (- (* b b) (* c (* 4.0 a))))) (* 2.0 a))
26.0ms	(- (* b b) (* c (* 4.0 a)))
48.0ms	(- (- b) (sqrt (- (* b b) (* c (* 4.0 a)))))
18.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series591.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (- (- b) (sqrt (- (* b b) (* c (* 4.0 a))))) (* 2.0 a))
106.0ms	(- (* b b) (* c (* 4.0 a)))
166.0ms	(- (- b) (sqrt (- (* b b) (* c (* 4.0 a)))))
130.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify2.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1311
1	414
0	159

prune845.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite297.0ms

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×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

206.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms	(- (* b b) (* 4.0 (* a c)))
49.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
83.0ms	(- (* b b) (* 4.0 (* a c)))
139.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1679
1	474
0	183

prune783.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

localize15.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.1b

regimes731.0ms

Accuracy

85.4% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 34.2b

bsearch190.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	6.0605931798902975e+143
8	-1.9399997713196595e-50	-4.155540846280759e-54	-9.446364120144488e-54

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	5836×	body	80	valid
915.0ms	1056×	body	2560	valid
511.0ms	909×	body	1280	valid
502.0ms	2825×	body	80	nan
169.0ms	449×	body	640	valid
71.0ms	103×	body	5120	valid
69.0ms	230×	body	320	valid
23.0ms	127×	body	160	valid