Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
9.0ms	178×	body	80	valid
6.0ms	24×	body	1280	valid
5.0ms	104×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize22.0ms

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)))

rewrite143.0ms

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--` `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 → 84

Calls

4 calls:

64.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
6.0ms	(- (* b b) (* (* 4.0 a) c))
57.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
65.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1142
1	388
0	158

prune683.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize35.0ms

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)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `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 → 85

Calls

4 calls:

196.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
12.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
95.0ms	(- (* b b) (* (* 4.0 a) c))
123.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1413
1	453
0	178

prune647.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

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×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 162

Calls

4 calls:

54.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
6.0ms	(- (* b b) (* (* 4.0 a) c))
53.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
82.0ms	(- (* b b) (* (* 4.0 a) c))
99.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	1998
1	636
0	262

prune973.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

localize44.0ms

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)))

rewrite133.0ms

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` `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 → 93

Calls

4 calls:

22.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) a)
6.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) a) (/ b a))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) a)
75.0ms	(- (* b b) (* (* 4.0 a) c))
139.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) a) (/ b a))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5033
3	4195
2	1113
1	406
0	177

prune551.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

regimes466.0ms

Accuracy

83.7% (4.7b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 34.1b

bsearch191.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

819.0ms	5812×	body	80	valid
558.0ms	1027×	body	2560	valid
399.0ms	885×	body	1280	valid
205.0ms	2885×	body	80	nan
166.0ms	505×	body	640	valid
101.0ms	118×	body	5120	valid
38.0ms	217×	body	320	valid
14.0ms	120×	body	160	valid