Details

sample72.0ms

Algorithm

intervals

Results

16.0ms	178×	body	80	valid
15.0ms	38×	body	2560	valid
8.0ms	24×	body	1280	valid
6.0ms	104×	body	80	nan
4.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify124.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	77
2	43
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 118

Calls

4 calls:

102.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
7.0ms	(- (* b b) (* (* 4.0 a) c))
58.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
59.0ms	(- (* b b) (* (* 4.0 a) c))
103.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1630
1	507
0	199

prune881.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 119

Calls

4 calls:

140.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
64.0ms	(- (* b b) (* (* 4.0 a) c))
115.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1620
1	572
0	219

prune847.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) a)
0.4b	(- (* b b) (* (* 4.0 a) c))
7.9b	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) a) (/ b a))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
287×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
23×	`fma-neg`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`associate-/r*`
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 → 411

Calls

4 calls:

19.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) a)
7.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) a) (/ b a))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) a)
86.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) a) (/ b a))
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

423 → 423

Iterations

Iter	Nodes
done	5000
2	2712
1	1146
0	501

prune2.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 a))
0.6b	(cbrt (/ 1 a))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
26×	`cbrt-prod`
18×	`times-frac` `prod-diff`
16×	`sqrt-prod`
6×	`fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`cbrt-div` `flip3--` `pow1/3` `sqrt-div` `div-inv` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 106

Calls

4 calls:

2.0ms	(cbrt (/ 1 a))
2.0ms	(cbrt (/ 1 a))
61.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt (/ 1 a))
282.0ms	(cbrt (/ 1 a))
142.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	5004
3	3681
2	1018
1	378
0	171

prune695.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.2b

regimes652.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 34.1b

bsearch194.0ms

Steps

Iters	Range		Point
10	2.044647849876085e-45	1.359053137570048e-33	8.272706925888016e-43
8	-8.579735130968805e+138	-4.109726801604347e+134	-5.836476522143193e+134

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample3.5s

Algorithm

intervals

Results

722.0ms	885×	body	1280	valid
685.0ms	5812×	body	80	valid
579.0ms	505×	body	640	valid
558.0ms	1027×	body	2560	valid
292.0ms	2885×	body	80	nan
139.0ms	118×	body	5120	valid
117.0ms	217×	body	320	valid
17.0ms	120×	body	160	valid