Details

sample52.0ms

Algorithm

intervals

Results

23.0ms	277×	body	80	valid
5.0ms	70×	body	80	nan

simplify188.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize146.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* c a) (* b b))
1.0b	(fma -4 (* c a) (* b b))
19.1b	(sqrt (fma -4 (* c a) (* b b)))
19.1b	(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)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma -4 (* c a) (* b b))
77.0ms	(fma -4 (* c a) (* b b))
94.0ms	(sqrt (fma -4 (* c a) (* b b)))
154.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
4	2097
3	454
2	127
1	61
0	41

prune522.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.0b

localize163.0ms

Local error

Found 4 expressions with local error:

19.1b	(sqrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))
19.9b	(cbrt (fma -4 (* c a) (* b b)))
19.9b	(cbrt (fma -4 (* c a) (* b b)))
19.9b	(cbrt (fma -4 (* c a) (* b b)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 69

Calls

4 calls:

36.0ms	(sqrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (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)))
2.0ms	(cbrt (fma -4 (* c a) (* b b)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))
238.0ms	(cbrt (fma -4 (* c a) (* b b)))
276.0ms	(cbrt (fma -4 (* c a) (* b b)))
263.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5012
4	3221
3	878
2	305
1	150
0	86

prune733.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.0b

localize164.0ms

Local error

Found 4 expressions with local error:

8.2b	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
19.1b	(sqrt (fma -4 (* c a) (* b b)))
19.1b	(sqrt (fma -4 (* c a) (* b b)))
19.1b	(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)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
100.0ms	(sqrt (fma -4 (* c a) (* b b)))
126.0ms	(sqrt (fma -4 (* c a) (* b b)))
132.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify4.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
4	4920
3	1432
2	519
1	207
0	97

prune811.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.0b

localize246.0ms

Local error

Found 4 expressions with local error:

19.9b	(cbrt (fma -4 (* c a) (* b b)))
19.9b	(cbrt (fma -4 (* c a) (* b b)))
19.9b	(cbrt (fma -4 (* c a) (* b b)))
19.9b	(cbrt (fma -4 (* c a) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`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`

Counts

4 → 56

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

series1.1s

Counts

4 → 12

Calls

4 calls:

278.0ms	(cbrt (fma -4 (* c a) (* b b)))
277.0ms	(cbrt (fma -4 (* c a) (* b b)))
295.0ms	(cbrt (fma -4 (* c a) (* b b)))
248.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5004
4	3122
3	788
2	254
1	103
0	53

prune897.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.0b

regimes387.0ms

Accuracy

87.2% (0.9b remaining)

Error of 13.4b against oracle of 12.5b and baseline of 19.5b

bsearch100.0ms

Steps

Iters	Range		Point
6	4.8498614244770303e+48	2.0602804194761557e+49	2.0410715251838527e+49

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	8721×	body	80	valid
374.0ms	2938×	body	80	nan