Details

sample95.0ms

Algorithm

intervals

Results

17.0ms	36×	body	2560	valid
16.0ms	188×	body	80	valid
15.0ms	108×	body	80	nan
10.0ms	24×	body	1280	valid
5.0ms	17×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify145.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

107.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
19.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
68.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

118 → 118

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	195	2476
1	521	2183
2	2396	1862
done	5000	1794

prune464.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

77.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
10.0ms	(- (* b b) (* (* 4.0 a) c))
55.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
58.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

164 → 164

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	261	4025
1	674	3498
2	3313	3147
done	5001	3070

prune883.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize32.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

73.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
66.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
118.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

128 → 128

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	113	2856
1	295	2330
2	1225	1950
done	5001	1810

prune625.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize47.0ms

Local error

Found 4 expressions with local error:

22.3b	(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
125.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

73 → 73

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	71	1269
1	174	1005
2	677	906
3	3809	906
done	5000	903

prune450.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.1b

regimes221.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.0b against oracle of 5.3b and baseline of 33.8b

bsearch143.0ms

Steps

Iters	Range		Point
9	4.939518845348872e-48	4.7173742985844417e-39	1.4070882317677973e-46
10	-2.8734245235493903e+48	-2.602501271628617e+37	-2.8472042802820317e+48

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.0s

Algorithm

intervals

Results

811.0ms	1074×	body	2560	valid
558.0ms	5856×	body	80	valid
553.0ms	903×	body	1280	valid
253.0ms	2902×	body	80	nan
195.0ms	451×	body	640	valid
53.0ms	112×	body	5120	valid
43.0ms	223×	body	320	valid
15.0ms	111×	body	160	valid