Details

sample131.0ms

Algorithm

intervals

Results

30.0ms	228×	body	80	nan
26.0ms	85×	body	320	valid
23.0ms	124×	body	160	valid
22.0ms	484×	pre	80	true
6.0ms	16×	body	640	valid
3.0ms	31×	body	80	valid

simplify147.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
30.4b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

2.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
37.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
12.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series425.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (fma -3 (* c a) (* b b)))
80.0ms	(fma -3 (* c a) (* b b))
107.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
117.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.2s

Counts

114 → 114

Iterations

Iter	Nodes
3	3443
2	937
1	330
0	152

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 47.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.1b	(fma -3 (* c a) (* b b))
0.3b	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `fma-udef` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 57

Calls

4 calls:

0.0ms	(fma -3 (* c a) (* b b))
0.0ms	(fma -3 (* c a) (* b b))
6.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma -3 (* c a) (* b b))
63.0ms	(fma -3 (* c a) (* b b))
561.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
390.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.0s

Counts

69 → 69

Iterations

Iter	Nodes
3	2180
2	613
1	231
0	112

prune849.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 47.5b

localize76.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.7s

Counts

4 → 12

Calls

4 calls:

509.0ms	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
412.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
417.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
399.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.3s

Counts

59 → 59

Iterations

Iter	Nodes
3	2168
2	589
1	216
0	105

prune1.1s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 47.5b

localize123.0ms

Local error

Found 4 expressions with local error:

50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
50.2b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.7s

Counts

4 → 12

Calls

4 calls:

431.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
412.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
439.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
408.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify751.0ms

Counts

56 → 56

Iterations

Iter	Nodes
4	2119
3	585
2	195
1	88
0	48

prune938.0ms

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 47.5b

regimes1.0s

Accuracy

0% (2.6b remaining)

Error of 51.6b against oracle of 49.0b and baseline of 51.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	3589×	body	320	valid
1.2s	2989×	body	160	valid
996.0ms	8133×	body	80	nan
920.0ms	16133×	pre	80	true
248.0ms	504×	body	640	valid
103.0ms	918×	body	80	valid