Details

sample140.0ms

Algorithm

intervals

Results

37.0ms	148×	body	160	valid
37.0ms	523×	pre	80	true
30.0ms	267×	body	80	nan
14.0ms	108×	body	80	valid

simplify116.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	126
5	126
4	118
3	87
2	43
1	22
0	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma (* -3 a) c (* b b)))
0.2b	(fma (* -3 a) c (* b b))
0.4b	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
29.5b	(- (sqrt (fma (* -3 a) c (* b b))) b)

rewrite43.0ms

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 a) c (* b b)))
0.0ms	(fma (* -3 a) c (* b b))
24.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
16.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)

series461.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (fma (* -3 a) c (* b b)))
86.0ms	(fma (* -3 a) c (* b b))
159.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
110.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1256
1	349
0	152

prune623.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 27.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))))
0.4b	(/ (- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b)))
0.4b	(/ (/ (- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b))) (* 3 a))
28.2b	(- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
48×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
12×	`pow3`
11×	`difference-cubes` `cube-unmult`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `div-sub` `associate-l` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-up` `flip--` `unswap-sqr`
1×	`sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative`

Counts

4 → 145

Calls

4 calls:

8.0ms	(* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))))
46.0ms	(/ (- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b)))
61.0ms	(/ (/ (- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b))) (* 3 a))
32.0ms	(- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b)))

series3.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))))
449.0ms	(/ (- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b)))
511.0ms	(/ (/ (- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b))) (* 3 a))
1.3s	(- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b)))

simplify2.5s

Counts

157 → 157

Iterations

Iter	Nodes
done	5001
2	3647
1	682
0	248

prune1.3s

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 25.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(* b (* b b))
0.4b	(/ (fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b)))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b)))
0.4b	(/ (/ (fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b)))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b))) (* 3 a))
28.1b	(fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1` `associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `associate-l` `pow-prod-down` `flip-+`
2×	`clear-num` `frac-2neg`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 123

Calls

4 calls:

29.0ms	(* b (* b b))
15.0ms	(/ (fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b)))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b)))
20.0ms	(/ (/ (fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b)))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b))) (* 3 a))
0.0ms	(fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b))))

series1.1s

Counts

4 → 12

Calls

4 calls:

65.0ms	(* b (* b b))
348.0ms	(/ (fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b)))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b)))
401.0ms	(/ (/ (fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b)))) (+ (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) (* b b))) (* 3 a))
270.0ms	(fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b))))

simplify2.4s

Counts

135 → 135

Iterations

Iter	Nodes
done	5002
2	2719
1	536
0	206

prune1.2s

Pruning

51 alts after pruning (51 fresh and 0 done)

Merged error: 25.5b

localize115.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (* b b))
0.7b	(pow (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) 3)
0.7b	(pow (* b b) 3)
28.1b	(fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

124×	`pow1`
37×	`pow-prod-up`
24×	`pow-prod-down`
23×	`pow-sqr`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-plus`
14×	`pow2`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`pow-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3` `sqr-pow`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

51.0ms	(* (* b b) (* b b))
4.0ms	(pow (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) 3)
10.0ms	(pow (* b b) 3)
1.0ms	(fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b))))

series1.1s

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* b b) (* b b))
745.0ms	(pow (fma (sqrt (fma (* c -3) a (* b b))) b (fma (* c -3) a (* b b))) 3)
52.0ms	(pow (* b b) 3)
270.0ms	(fma (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))) (- (* b (* b b))))

simplify2.9s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	3356
1	490
0	154

prune791.0ms

Pruning

52 alts after pruning (52 fresh and 0 done)

Merged error: 25.4b

regimes1.5s

Accuracy

0% (2.9b remaining)

Error of 27.3b against oracle of 24.4b and baseline of 27.3b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	41
2	41
1	37
0	28

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.3s	3529×	body	80	valid
1.2s	4471×	body	160	valid
1.1s	8595×	body	80	nan
995.0ms	16595×	pre	80	true