Details

sample160.0ms

Algorithm

intervals

Results

52.0ms	154×	body	160	valid
33.0ms	277×	body	80	nan
30.0ms	533×	pre	80	true
17.0ms	46×	body	320	valid
7.0ms	56×	body	80	valid

simplify118.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.2b	(fma -3 (* c a) (* b b))
0.3b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
38.9b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite62.0ms

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))
20.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series414.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (fma -3 (* c a) (* b b)))
55.0ms	(fma -3 (* c a) (* b b))
117.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
137.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
3	3402
2	935
1	329
0	152

prune1.4s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 40.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma -3 (* c a) (* b b))
0.2b	(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))

rewrite14.0ms

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))
12.0ms	(/ (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:

84.0ms	(fma -3 (* c a) (* b b))
70.0ms	(fma -3 (* c a) (* b b))
621.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
430.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify899.0ms

Counts

69 → 69

Iterations

Iter	Nodes
3	2206
2	614
1	230
0	112

prune1.0s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 40.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma -3 (* c a) (* b b))
0.3b	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (* 3 a))
0.3b	(* -3 (* a c))
43.7b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

rewrite36.0ms

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))
12.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (* 3 a))
23.0ms	(* -3 (* a c))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

series1.2s

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma -3 (* c a) (* b b))
673.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (* 3 a))
31.0ms	(* -3 (* a c))
409.0ms	(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	3029
2	879
1	316
0	145

prune1.2s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 40.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (/ 1/3 a))
0.3b	(* -3 (* a c))
0.3b	(/ 1/3 a)
43.7b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

9.0ms	(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (/ 1/3 a))
14.0ms	(* -3 (* a c))
4.0ms	(/ 1/3 a)
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

series979.0ms

Counts

4 → 12

Calls

4 calls:

609.0ms	(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b)) (/ 1/3 a))
21.0ms	(* -3 (* a c))
17.0ms	(/ 1/3 a)
331.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma b b (* -3 (* a c))))) (- b))

simplify3.2s

Counts

109 → 109

Iterations

Iter	Nodes
3	4101
2	1198
1	373
0	171

prune1.3s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 40.5b

regimes1.0s

Accuracy

0% (3.0b remaining)

Error of 43.3b against oracle of 40.3b and baseline of 43.3b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	25
1	25
0	22

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.6s	4838×	body	160	valid
1.0s	8306×	body	80	nan
978.0ms	16306×	pre	80	true
964.0ms	1373×	body	320	valid
227.0ms	1789×	body	80	valid