Details

sample165.0ms

Algorithm

intervals

Results

35.0ms	35×	body	2560	valid
31.0ms	184×	body	80	valid
27.0ms	28×	body	1280	valid
25.0ms	15×	body	640	valid
13.0ms	86×	body	80	nan
5.0ms	4×	body	5120	valid
4.0ms	8×	body	320	valid
2.0ms	5×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.6b	(fma (* a c) -4 (* b b))
1.7b	(- (sqrt (fma (* a c) -4 (* b b))) b)
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite39.0ms

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:

24.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
11.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
67.0ms	(fma (* a c) -4 (* b b))
113.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
128.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify986.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2003
2	718
1	319
0	156

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fma (* a c) -4 (* b b))) a)
0.6b	(fma (* a c) -4 (* b b))
8.4b	(- (/ (sqrt (fma (* a c) -4 (* b b))) a) (/ b a))
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
286×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
22×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-/r*`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `div-exp` `frac-sub` `fma-udef` `flip--` `sub-div`

Counts

4 → 405

Calls

4 calls:

9.0ms	(/ (sqrt (fma (* a c) -4 (* b b))) a)
0.0ms	(fma (* a c) -4 (* b b))
27.0ms	(- (/ (sqrt (fma (* a c) -4 (* b b))) a) (/ b a))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (sqrt (fma (* a c) -4 (* b b))) a)
92.0ms	(fma (* a c) -4 (* b b))
144.0ms	(- (/ (sqrt (fma (* a c) -4 (* b b))) a) (/ b a))
103.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify969.0ms

Counts

417 → 417

Iterations

Iter	Nodes
2	2100
1	970
0	453

prune5.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 29.2b

localize57.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (fma (* a c) -4 (* b b))) b)
24.6b	(sqrt (fma (* a c) -4 (* b b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`prod-diff`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
7.0ms	(sqrt (fma (* a c) -4 (* b b)))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
93.0ms	(sqrt (fma (* a c) -4 (* b b)))
98.0ms	(sqrt (fma (* a c) -4 (* b b)))
114.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
4	2519
3	919
2	298
1	158
0	86

prune1.7s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 29.2b

localize48.0ms

Local error

Found 3 expressions with local error:

0.6b	(fma (* a c) -4 (* b b))
21.2b	(fma (sqrt (fma (* a c) -4 (* b b))) (/ 1 a) (- (/ b a)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 38

Calls

3 calls:

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

series307.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(fma (* a c) -4 (* b b))
155.0ms	(fma (sqrt (fma (* a c) -4 (* b b))) (/ 1 a) (- (/ b a)))
87.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.5s

Counts

47 → 47

Iterations

Iter	Nodes
4	2484
3	633
2	190
1	92
0	60

prune596.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 29.0b

regimes617.0ms

Accuracy

79.5% (1.3b remaining)

Error of 29.8b against oracle of 28.4b and baseline of 35.0b

bsearch122.0ms

Steps

Iters	Range		Point
7	3.2477440454532417e+94	1.208571928248366e+96	4.307246706626464e+94

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	19

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.2s	915×	body	1280	valid
1.0s	1126×	body	2560	valid
911.0ms	5836×	body	80	valid
490.0ms	2976×	body	80	nan
232.0ms	417×	body	640	valid
114.0ms	119×	body	5120	valid
89.0ms	236×	body	320	valid
25.0ms	115×	body	160	valid