Details

sample128.0ms

Algorithm

intervals

Results

81.0ms	269×	body	80	valid
18.0ms	88×	body	80	nan

simplify198.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	160
7	160
6	159
5	152
4	140
3	108
2	63
1	36
0	20

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize170.0ms

Local error

Found 4 expressions with local error:

1.6b	(fma -4 (* c a) (* b b))
1.6b	(fma -4 (* c a) (* b b))
24.4b	(sqrt (fma -4 (* c a) (* b b)))
24.4b	(sqrt (fma -4 (* c a) (* b b)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(fma -4 (* c a) (* b b))
0.0ms	(fma -4 (* c a) (* b b))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
5.0ms	(sqrt (fma -4 (* c a) (* b b)))

series833.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma -4 (* c a) (* b b))
90.0ms	(fma -4 (* c a) (* b b))
108.0ms	(sqrt (fma -4 (* c a) (* b b)))
566.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify7.4s

Counts

66 → 66

Iterations

Iter	Nodes
5	9819
4	1681
3	403
2	122
1	61
0	41

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.9b

localize165.0ms

Local error

Found 4 expressions with local error:

11.3b	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
24.4b	(sqrt (fma -4 (* c a) (* b b)))
24.4b	(sqrt (fma -4 (* c a) (* b b)))
24.4b	(sqrt (fma -4 (* c a) (* b b)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

21.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
93.0ms	(sqrt (fma -4 (* c a) (* b b)))
111.0ms	(sqrt (fma -4 (* c a) (* b b)))
115.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.5s

Counts

98 → 98

Iterations

Iter	Nodes
4	4009
3	1390
2	496
1	207
0	97

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.9b

localize193.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (fma -4 (* c a) (* b b)))
25.2b	(cbrt (fma -4 (* c a) (* b b)))
25.2b	(cbrt (fma -4 (* c a) (* b b)))
25.2b	(cbrt (fma -4 (* c a) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (fma -4 (* c a) (* b b)))
316.0ms	(cbrt (fma -4 (* c a) (* b b)))
226.0ms	(cbrt (fma -4 (* c a) (* b b)))
265.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify3.0s

Counts

70 → 70

Iterations

Iter	Nodes
5	6393
4	1999
3	677
2	258
1	122
0	68

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.9b

localize195.0ms

Local error

Found 4 expressions with local error:

25.2b	(cbrt (fma -4 (* c a) (* b b)))
25.2b	(cbrt (fma -4 (* c a) (* b b)))
25.2b	(cbrt (fma -4 (* c a) (* b b)))
25.2b	(cbrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
14.0ms	(cbrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))

series926.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (fma -4 (* c a) (* b b)))
229.0ms	(cbrt (fma -4 (* c a) (* b b)))
204.0ms	(cbrt (fma -4 (* c a) (* b b)))
293.0ms	(cbrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))

simplify3.0s

Counts

67 → 67

Iterations

Iter	Nodes
5	6368
4	1935
3	644
2	244
1	115
0	64

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.9b

regimes312.0ms

Accuracy

87.3% (0.9b remaining)

Error of 13.6b against oracle of 12.6b and baseline of 19.8b

bsearch118.0ms

Steps

Iters	Range		Point
6	2.332248586404817e+54	2.734436825826664e+55	2.6656023684116586e+55

simplify21.0ms

Iterations

Iter	Nodes
2	42
1	42
0	36

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8753×	body	80	valid
562.0ms	2909×	body	80	nan