Details

sample104.0ms

Algorithm

intervals

Results

34.0ms	132×	body	320	valid
16.0ms	482×	pre	80	true
13.0ms	226×	body	80	nan
10.0ms	88×	body	160	valid
4.0ms	17×	body	640	valid
1.0ms	19×	body	80	valid

simplify129.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.3b

localize20.0ms

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))
27.1b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite90.0ms

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:

3.0ms	(sqrt (fma -3 (* c a) (* b b)))
1.0ms	(fma -3 (* c a) (* b b))
58.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
24.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series755.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (fma -3 (* c a) (* b b)))
63.0ms	(fma -3 (* c a) (* b b))
127.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
466.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.5s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	3990
2	940
1	347
0	152

prune622.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 51.8b

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))
54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite21.0ms

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:

1.0ms	(fma -3 (* c a) (* b b))
1.0ms	(fma -3 (* c a) (* b b))
17.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.3s

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma -3 (* c a) (* b b))
90.0ms	(fma -3 (* c a) (* b b))
708.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
443.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify2.6s

Counts

69 → 69

Iterations

Iter	Nodes
done	5002
3	2382
2	672
1	231
0	112

prune639.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 51.8b

localize82.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`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×	`times-frac` `fma-udef`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt (/ (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))
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))

series1.8s

Counts

4 → 12

Calls

4 calls:

564.0ms	(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
408.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
385.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
456.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify2.3s

Counts

64 → 64

Iterations

Iter	Nodes
done	5015
3	3068
2	842
1	288
0	143

prune955.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 51.8b

localize133.0ms

Local error

Found 4 expressions with local error:

54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
54.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
54.6b	(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

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

series1.8s

Counts

4 → 12

Calls

4 calls:

457.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
431.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
428.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
451.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.9s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
4	2686
3	638
2	201
1	88
0	48

prune637.0ms

Pruning

39 alts after pruning (38 fresh and 1 done)

Merged error: 51.8b

regimes1.2s

Accuracy

0% (2.6b remaining)

Error of 52.2b against oracle of 49.6b and baseline of 52.2b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.2s	16100×	pre	80	true
1.1s	3638×	body	320	valid
884.0ms	3008×	body	160	valid
786.0ms	8100×	body	80	nan
155.0ms	867×	body	80	valid
150.0ms	487×	body	640	valid