Details

sample166.0ms

Algorithm

intervals

Results

41.0ms	293×	body	80	nan
38.0ms	159×	body	160	valid
32.0ms	549×	pre	80	true
18.0ms	49×	body	320	valid
6.0ms	48×	body	80	valid

simplify100.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.3b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
39.3b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite29.0ms

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:

1.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
18.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series422.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (fma -3 (* c a) (* b b)))
90.0ms	(fma -3 (* c a) (* b b))
117.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
106.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
3	3402
2	935
1	329
0	152

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 40.7b

localize33.0ms

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))
43.7b	(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))
7.0ms	(/ (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))

series1.2s

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma -3 (* c a) (* b b))
80.0ms	(fma -3 (* c a) (* b b))
592.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
445.0ms	(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	2206
2	614
1	230
0	112

prune998.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 40.7b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.3b	(* -3 (* a c))
0.3b	(/ (fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
43.7b	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

0.0ms	(fma -3 (* c a) (* b b))
15.0ms	(* -3 (* a c))
14.0ms	(/ (fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
1.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series476.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma -3 (* c a) (* b b))
34.0ms	(* -3 (* a c))
222.0ms	(/ (fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
133.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
3	2978
2	803
1	287
0	131

prune951.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 40.7b

localize87.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
43.7b	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.7b	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.7b	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite5.0ms

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:

3.0ms	(cbrt (/ (fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
0.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series800.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(cbrt (/ (fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
164.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
158.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
147.0ms	(fma (sqrt (sqrt (fma b b (* -3 (* a c))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.4s

Counts

64 → 64

Iterations

Iter	Nodes
4	3322
3	1128
2	463
1	230
0	124

prune1.2s

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 40.6b

regimes1.1s

Accuracy

0% (3.1b remaining)

Error of 43.4b against oracle of 40.3b and baseline of 43.4b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.1s	4814×	body	160	valid
1.1s	16245×	pre	80	true
1.1s	1395×	body	320	valid
930.0ms	8245×	body	80	nan
241.0ms	1791×	body	80	valid