Details

sample137.0ms

Algorithm

intervals

Results

40.0ms	39×	body	2560	valid
26.0ms	180×	body	80	valid
23.0ms	29×	body	1280	valid
14.0ms	21×	body	640	valid
10.0ms	70×	body	80	nan
3.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify115.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.0b	(- (* b b) (* (* c a) 4))
19.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite190.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

102.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
55.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms	(- (* b b) (* (* c a) 4))
15.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
108.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
57.0ms	(- (* b b) (* (* c a) 4))
99.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify3.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5011
3	4767
2	1107
1	400
0	161

prune746.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
1.0b	(- (* b b) (* (* c a) 4))
5.4b	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
19.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `frac-sub` `sub-div`

Counts

4 → 97

Calls

4 calls:

28.0ms	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
15.0ms	(- (* b b) (* (* c a) 4))
69.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series829.0ms

Counts

4 → 12

Calls

4 calls:

540.0ms	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
56.0ms	(- (* b b) (* (* c a) 4))
120.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
114.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	5003
3	4532
2	1177
1	413
0	179

prune546.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
1.0b	(- (* b b) (* (* c a) 4))
10.1b	(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
19.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
132×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
82×	`add-cube-cbrt`
43×	`sqrt-prod`
24×	`associate-/r*`
15×	`add-exp-log`
14×	`difference-of-squares`
10×	`sqrt-div`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*` `distribute-lft-out--`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 181

Calls

4 calls:

32.0ms	(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
15.0ms	(- (* b b) (* (* c a) 4))
87.0ms	(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
58.0ms	(- (* b b) (* (* c a) 4))
151.0ms	(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
84.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.4s

Counts

193 → 193

Iterations

Iter	Nodes
done	5000
2	1944
1	746
0	295

prune811.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize49.0ms

Local error

Found 4 expressions with local error:

15.2b	(- (/ (/ 1 (/ 1 (sqrt (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4))))))) (/ a (sqrt (cbrt (- (* b b) (* (* c a) 4)))))) (/ b a))
19.9b	(cbrt (- (* b b) (* (* c a) 4)))
19.9b	(cbrt (- (* b b) (* (* c a) 4)))
19.9b	(cbrt (- (* b b) (* (* c a) 4)))

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

426×	`add-sqr-sqrt`
347×	`times-frac`
90×	`difference-of-squares`
88×	`*-un-lft-identity`
76×	`sqrt-prod`
31×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`pow1/3` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `frac-sub` `div-inv`

Counts

4 → 149

Calls

4 calls:

502.0ms	(- (/ (/ 1 (/ 1 (sqrt (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4))))))) (/ a (sqrt (cbrt (- (* b b) (* (* c a) 4)))))) (/ b a))
5.0ms	(cbrt (- (* b b) (* (* c a) 4)))
5.0ms	(cbrt (- (* b b) (* (* c a) 4)))
5.0ms	(cbrt (- (* b b) (* (* c a) 4)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (/ (/ 1 (/ 1 (sqrt (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4))))))) (/ a (sqrt (cbrt (- (* b b) (* (* c a) 4)))))) (/ b a))
100.0ms	(cbrt (- (* b b) (* (* c a) 4)))
100.0ms	(cbrt (- (* b b) (* (* c a) 4)))
114.0ms	(cbrt (- (* b b) (* (* c a) 4)))

simplify2.0s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
3	4569
2	1445
1	706
0	307

prune899.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.2b

regimes338.0ms

Accuracy

84.9% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 33.8b

bsearch161.0ms

Steps

Iters	Range		Point
9	1.542649851819534e-86	4.188981380654902e-77	1.2158870426682226e-82
6	-1.2115114540629089e+151	-9.504756559616229e+149	-7.397994825724217e+150

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	895×	body	1280	valid
775.0ms	1057×	body	2560	valid
739.0ms	5900×	body	80	valid
313.0ms	2938×	body	80	nan
186.0ms	455×	body	640	valid
101.0ms	211×	body	320	valid
95.0ms	106×	body	5120	valid
19.0ms	97×	body	160	valid