Details

sample199.0ms

Algorithm

intervals

Results

61.0ms	511×	pre	80	true
40.0ms	138×	body	160	valid
35.0ms	255×	body	80	nan
24.0ms	57×	body	320	valid
11.0ms	61×	body	80	valid

simplify101.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize44.0ms

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))
37.9b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite67.0ms

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)))
1.0ms	(fma -3 (* c a) (* b b))
45.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
15.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series437.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (fma -3 (* c a) (* b b)))
77.0ms	(fma -3 (* c a) (* b b))
123.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
122.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.1s

Counts

114 → 114

Iterations

Iter	Nodes
3	3402
2	935
1	329
0	152

prune631.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 40.3b

localize62.0ms

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))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite16.0ms

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))
14.0ms	(/ (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:

68.0ms	(fma -3 (* c a) (* b b))
82.0ms	(fma -3 (* c a) (* b b))
659.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
455.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify913.0ms

Counts

69 → 69

Iterations

Iter	Nodes
3	2206
2	614
1	230
0	112

prune698.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 40.3b

localize78.0ms

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 -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (* 3 a))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

rewrite21.0ms

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))
13.0ms	(* -3 (* a c))
6.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (* 3 a))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

90.0ms	(fma -3 (* c a) (* b b))
42.0ms	(* -3 (* a c))
576.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (* 3 a))
430.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
3	3112
2	884
1	313
0	145

prune692.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 40.2b

localize125.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

rewrite3.0ms

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

series1.9s

Counts

4 → 12

Calls

4 calls:

626.0ms	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)))
419.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))
422.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))
386.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

simplify974.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2158
2	603
1	224
0	109

prune653.0ms

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 40.2b

regimes1.1s

Accuracy

0% (3.1b remaining)

Error of 44.0b against oracle of 40.9b and baseline of 44.0b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	29
1	29
0	25

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.4s	16211×	pre	80	true
1.3s	4791×	body	160	valid
1.0s	8211×	body	80	nan
562.0ms	1719×	body	80	valid
539.0ms	1490×	body	320	valid