Details

sample134.0ms

Algorithm

intervals

Results

36.0ms	25×	body	1280	valid
34.0ms	210×	body	80	valid
21.0ms	23×	body	2560	valid
12.0ms	84×	body	80	nan
5.0ms	8×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.8b	(fma (* a c) -4 (* b b))
1.0b	(- (sqrt (fma (* a c) -4 (* b b))) b)
20.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

39.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
58.0ms	(fma (* a c) -4 (* b b))
98.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
103.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5008
3	2698
2	773
1	335
0	156

prune636.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (fma (* a c) -4 (* b b))) b))
0.8b	(fma (* a c) -4 (* b b))
1.0b	(- (sqrt (fma (* a c) -4 (* b b))) b)
20.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`associate-/r*` `add-cbrt-cube` `fma-neg` `add-exp-log` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `fma-udef` `div-inv`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/ a (- (sqrt (fma (* a c) -4 (* b b))) b))
0.0ms	(fma (* a c) -4 (* b b))
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ a (- (sqrt (fma (* a c) -4 (* b b))) b))
60.0ms	(fma (* a c) -4 (* b b))
125.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
108.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.1s

Counts

125 → 125

Iterations

Iter	Nodes
done	5002
3	2808
2	862
1	342
0	165

prune536.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
0.8b	(fma (* a c) -4 (* b b))
1.0b	(- (sqrt (fma (* a c) -4 (* b b))) b)
20.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 115

Calls

4 calls:

26.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
0.0ms	(fma (* a c) -4 (* b b))
12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
66.0ms	(fma (* a c) -4 (* b b))
128.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
102.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
3	2881
2	1007
1	397
0	175

prune664.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (fma b b (* (* a c) -4))) b) a)
1.0b	(fma b b (* (* a c) -4))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)
20.8b	(sqrt (fma b b (* (* a c) -4)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

20.0ms	(/ (- (sqrt (fma b b (* (* a c) -4))) b) a)
0.0ms	(fma b b (* (* a c) -4))
15.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (sqrt (fma b b (* (* a c) -4))) b) a)
66.0ms	(fma b b (* (* a c) -4))
118.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
111.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify2.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	3729
2	1007
1	421
0	179

prune534.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

regimes264.0ms

Accuracy

86.9% (3.6b remaining)

Error of 9.2b against oracle of 5.6b and baseline of 33.0b

bsearch236.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	6.105883600684466e+62
5	5.79842255379007e-265	2.1404603426561788e-264	8.90802686721313e-265
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify12.0ms

Iterations

Iter	Nodes
done	43
1	43
0	38

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	5870×	body	80	valid
931.0ms	1084×	body	2560	valid
613.0ms	907×	body	1280	valid
405.0ms	3007×	body	80	nan
251.0ms	447×	body	640	valid
154.0ms	101×	body	5120	valid
105.0ms	232×	body	320	valid
24.0ms	109×	body	160	valid