Details

sample145.0ms

Algorithm

intervals

Results

49.0ms	84×	body	2560	valid
40.0ms	95×	body	1280	valid
14.0ms	262×	body	80	nan
11.0ms	36×	body	640	valid
5.0ms	22×	body	320	valid
3.0ms	14×	body	160	valid
0.0ms	5×	body	80	valid

simplify661.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	944
5	254
4	155
3	84
2	43
1	20
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))
0.1b	(* (* v 5.0) v)
0.4b	(acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-l` `*-commutative` `div-inv`

Counts

3 → 68

Calls

3 calls:

19.0ms	(/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))
19.0ms	(* (* v 5.0) v)
1.0ms	(acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))
50.0ms	(* (* v 5.0) v)
4.0ms	(acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))

simplify1.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1976
1	373
0	148

prune382.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0)))
0.0b	(/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0)))
0.0b	(* (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0))) (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0))))
1.4b	(acos (* (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0))) (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0)))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
132×	`times-frac`
128×	`*-un-lft-identity`
85×	`sqrt-prod`
76×	`add-cube-cbrt`
42×	`associate-r`
30×	`associate-l`
26×	`difference-of-squares`
20×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out` `distribute-lft-out--`
12×	`associate-/l*`
10×	`associate-/r*`
9×	`unswap-sqr`
8×	`associate-/r/`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `flip-+` `flip--`
1×	`acos-asin` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 227

Calls

4 calls:

13.0ms	(/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0)))
13.0ms	(/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0)))
118.0ms	(* (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0))) (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0))))
1.0ms	(acos (* (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0))) (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0)))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0)))
210.0ms	(/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0)))
335.0ms	(* (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0))) (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0))))
19.0ms	(acos (* (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (+ v (sqrt 1.0))) (/ (sqrt (fma (- v) (* v 5.0) 1.0)) (- v (sqrt 1.0)))))

simplify2.8s

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
2	4837
1	837
0	298

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b	(acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))
1.0b	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0b	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0b	(* (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))) (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

1.0ms	(acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))
2.0ms	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
2.0ms	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
22.0ms	(* (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))) (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))
26.0ms	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
49.0ms	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
13.0ms	(* (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))) (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))))

simplify2.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	786
1	147
0	82

prune482.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0))))
1.0b	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0b	(sqrt (acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0)))))
1.0b	(* (sqrt (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))) (pow (sqrt (sqrt (acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0)))))) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
63×	`add-sqr-sqrt`
24×	`associate-r` `unswap-sqr`
18×	`unpow-prod-down` `cube-prod`
16×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l` `add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`acos-asin` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

1.0ms	(acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0))))
1.0ms	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0ms	(sqrt (acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0)))))
30.0ms	(* (sqrt (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))) (pow (sqrt (sqrt (acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0)))))) 3))

series554.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0))))
43.0ms	(sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
43.0ms	(sqrt (acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0)))))
454.0ms	(* (sqrt (sqrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))) (pow (sqrt (sqrt (acos (/ (fma (* (- v) 5.0) v 1.0) (fma v v (- 1.0)))))) 3))

simplify1.4s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1424
1	292
0	144

prune586.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes105.0ms

Accuracy

0% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.4s	3026×	body	2560	valid
1.1s	2444×	body	1280	valid
534.0ms	8221×	body	80	nan
404.0ms	1280×	body	640	valid
169.0ms	610×	body	320	valid
109.0ms	442×	body	160	valid
16.0ms	198×	body	80	valid