Details

sample139.0ms

Algorithm

intervals

Results

59.0ms	256×	body	80	valid
52.0ms	239×	body	80	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	849
2	162
1	46
0	19

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* v v) -5 1)
0.0b	(fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))
0.4b	(/ (/ (fma (* v v) -5 1) PI) t)
0.4b	(/ (/ (/ (fma (* v v) -5 1) PI) t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac`
230×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
56×	`associate-/l*`
22×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
9×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef` `associate-/l/`

Counts

4 → 290

Calls

4 calls:

0.0ms	(fma (* v v) -5 1)
0.0ms	(fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))
12.0ms	(/ (/ (fma (* v v) -5 1) PI) t)
11.0ms	(/ (/ (/ (fma (* v v) -5 1) PI) t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (* v v) -5 1)
221.0ms	(fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))
89.0ms	(/ (/ (fma (* v v) -5 1) PI) t)
668.0ms	(/ (/ (/ (fma (* v v) -5 1) PI) t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))

simplify2.6s

Counts

302 → 302

Iterations

Iter	Nodes
done	5006
2	3620
1	1294
0	563

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma -5 (* v v) 1)
0.0b	(fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))
0.4b	(* (/ (fma -5 (* v v) 1) PI) (/ (/ 1 t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
0.5b	(/ (/ 1 t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
116×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
88×	`add-cube-cbrt`
48×	`add-exp-log`
43×	`associate-r`
30×	`add-cbrt-cube`
23×	`div-exp`
13×	`associate-l` `associate-/l*`
12×	`cbrt-undiv`
10×	`prod-exp` `div-inv`
8×	`unswap-sqr`
6×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `associate-/r*` `1-exp`
2×	`fma-udef`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 192

Calls

4 calls:

0.0ms	(fma -5 (* v v) 1)
0.0ms	(fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))
17.0ms	(* (/ (fma -5 (* v v) 1) PI) (/ (/ 1 t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
14.0ms	(/ (/ 1 t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma -5 (* v v) 1)
241.0ms	(fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))
679.0ms	(* (/ (fma -5 (* v v) 1) PI) (/ (/ 1 t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
367.0ms	(/ (/ 1 t) (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))

simplify2.5s

Counts

204 → 204

Iterations

Iter	Nodes
done	5017
2	3540
1	1105
0	384

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (* v v))
0.2b	(* PI t)
0.3b	(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))
0.4b	(* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-cbrt-cube` `add-exp-log`
18×	`associate-*r/`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`flip3--` `sqrt-div` `associate-r` `associate-/r/` `flip--`
7×	`associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `frac-times` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `unswap-sqr` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-sub` `sqrt-prod` `div-inv`

Counts

4 → 106

Calls

4 calls:

14.0ms	(* 3 (* v v))
6.0ms	(* PI t)
111.0ms	(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))
35.0ms	(* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))

series905.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 3 (* v v))
34.0ms	(* PI t)
570.0ms	(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))
255.0ms	(* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))

simplify2.4s

Counts

118 → 118

Iterations

Iter	Nodes
done	5007
2	3493
1	730
0	241

prune709.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
0.4b	(/ (/ (sqrt (fma (* v v) -5 1)) PI) t)
0.4b	(* (/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))) (/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))
1.0b	(/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

3515×	`times-frac`
1868×	`add-sqr-sqrt`
1436×	`*-un-lft-identity`
1355×	`add-cube-cbrt`
528×	`sqrt-prod`
471×	`cbrt-prod`
424×	`associate-r`
397×	`add-exp-log`
269×	`div-exp`
162×	`associate-/l*`
143×	`add-cbrt-cube`
111×	`cbrt-undiv`
108×	`unswap-sqr`
95×	`prod-exp`
74×	`associate-l`
73×	`div-inv`
50×	`1-exp`
43×	`cbrt-unprod`
10×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1509

Calls

4 calls:

23.0ms	(/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
8.0ms	(/ (/ (sqrt (fma (* v v) -5 1)) PI) t)
87.0ms	(* (/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))) (/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))
19.0ms	(/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))

series4.5s

Counts

4 → 12

Calls

4 calls:

1.8s	(/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
189.0ms	(/ (/ (sqrt (fma (* v v) -5 1)) PI) t)
680.0ms	(* (/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))) (/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))
1.8s	(/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))

simplify6.7s

Counts

1521 → 1521

Iterations

Iter	Nodes
done	5000
0	1995

prune14.3s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes459.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
1.6s	8098×	body	80	nan