Details

sample189.0ms

Algorithm

intervals

Results

83.0ms	195×	body	80	valid
29.0ms	34×	body	1280	valid
11.0ms	18×	body	2560	valid
10.0ms	107×	body	80	nan
5.0ms	13×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	96
7	96
6	95
5	93
4	85
3	70
2	42
1	24
0	14

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) a)
0.8b	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
1.0b	(- (* b b) (* (* a 4.0) c))
21.8b	(sqrt (- (* b b) (* (* a 4.0) c)))

rewrite720.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

311.0ms	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) a)
107.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
261.0ms	(- (* b b) (* (* a 4.0) c))
21.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

series1.4s

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) a)
436.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
216.0ms	(- (* b b) (* (* a 4.0) c))
435.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

simplify6.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1142
1	390
0	158

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* a 4.0) c))) b)))
0.8b	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
1.0b	(- (* b b) (* (* a 4.0) c))
21.8b	(sqrt (- (* b b) (* (* a 4.0) c)))

rewrite928.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

595.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* a 4.0) c))) b)))
167.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
18.0ms	(- (* b b) (* (* a 4.0) c))
21.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ 1 (/ a (- (sqrt (- (* b b) (* (* a 4.0) c))) b)))
435.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
135.0ms	(- (* b b) (* (* a 4.0) c))
810.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

simplify9.6s

Counts

174 → 174

Iterations

Iter	Nodes
done	5004
2	2030
1	639
0	262

prune3.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize100.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
0.8b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
1.0b	(- (* b b) (* (* c a) 4.0))
21.8b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite430.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

264.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
121.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
15.0ms	(- (* b b) (* (* c a) 4.0))
18.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

364.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
324.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
178.0ms	(- (* b b) (* (* c a) 4.0))
220.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify5.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1185
1	391
0	158

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

localize123.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* a 4.0) c))
1.0b	(- (* b b) (* (* a 4.0) c))
21.8b	(sqrt (- (* b b) (* (* a 4.0) c)))
21.8b	(sqrt (- (* b b) (* (* a 4.0) c)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

11.0ms	(- (* b b) (* (* a 4.0) c))
16.0ms	(- (* b b) (* (* a 4.0) c))
24.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))
17.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

series1.1s

Counts

4 → 12

Calls

4 calls:

346.0ms	(- (* b b) (* (* a 4.0) c))
177.0ms	(- (* b b) (* (* a 4.0) c))
295.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))
281.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

simplify6.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	2216
2	534
1	159
0	62

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.9b

regimes999.0ms

Accuracy

82.3% (5.1b remaining)

Error of 10.6b against oracle of 5.5b and baseline of 34.6b

bsearch497.0ms

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
6	-4.525167845450207e+100	-9.36795079059543e+99	-2.7668189408748547e+100

simplify15.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample17.7s

Algorithm

intervals

Results

6.5s	1080×	body	2560	valid
4.2s	5755×	body	80	valid
2.8s	922×	body	1280	valid
2.2s	2818×	body	80	nan
524.0ms	483×	body	640	valid
447.0ms	97×	body	5120	valid
95.0ms	238×	body	320	valid
36.0ms	117×	body	160	valid