Details

sample169.0ms

Algorithm

intervals

Results

68.0ms	90×	body	2560	valid
42.0ms	81×	body	1280	valid
17.0ms	239×	body	80	nan
12.0ms	32×	body	640	valid
8.0ms	30×	body	320	valid
3.0ms	15×	body	160	valid
1.0ms	8×	body	80	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2053
4	491
3	180
2	67
1	26
0	9

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (fma (* -5 v) v 1) (fma v v -1))
0.7b	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 41

Calls

2 calls:

9.0ms	(/ (fma (* -5 v) v 1) (fma v v -1))
2.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (fma (* -5 v) v 1) (fma v v -1))
5.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

simplify1.9s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	1188
2	395
1	154
0	86

prune231.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
0.0b	(/ (fma (* -5 v) v 1) (fma v v -1))
0.0b	(expm1 (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))
0.7b	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u`
4×	`pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
1×	`acos-asin` `cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `log1p-expm1` `div-inv` `expm1-udef`

Counts

4 → 65

Calls

4 calls:

0.0ms	(log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
5.0ms	(/ (fma (* -5 v) v 1) (fma v v -1))
0.0ms	(expm1 (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))
2.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
97.0ms	(/ (fma (* -5 v) v 1) (fma v v -1))
186.0ms	(expm1 (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))
3.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

simplify1.9s

Counts

77 → 77

Iterations

Iter	Nodes
done	5002
3	1263
2	437
1	184
0	108

prune486.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))) (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))))
0.0b	(expm1 (* (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))) (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))))
0.7b	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
0.7b	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`acos-asin`
1×	`pow2` `expm1-log1p` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `expm1-udef`

Counts

4 → 86

Calls

4 calls:

9.0ms	(* (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))) (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))))
0.0ms	(expm1 (* (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))) (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))))
1.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
1.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))) (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))))
158.0ms	(expm1 (* (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1))))) (sqrt (log1p (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))))
4.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
2.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

simplify3.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5007
4	3462
3	688
2	265
1	145
0	84

prune408.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (* v -5) v 1) (fma v v -1))
0.0b	(* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1)))
0.0b	(cbrt (* (* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1))) (/ (fma (* v -5) v 1) (fma v v -1))))
0.7b	(acos (cbrt (* (* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1))) (/ (fma (* v -5) v 1) (fma v v -1)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`times-frac`
40×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
7×	`cbrt-div`
6×	`frac-times` `associate-*l/`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `associate-*r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
1×	`cbrt-prod` `pow2` `acos-asin` `clear-num` `frac-2neg` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 131

Calls

4 calls:

7.0ms	(/ (fma (* v -5) v 1) (fma v v -1))
14.0ms	(* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1)))
28.0ms	(cbrt (* (* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1))) (/ (fma (* v -5) v 1) (fma v v -1))))
1.0ms	(acos (cbrt (* (* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1))) (/ (fma (* v -5) v 1) (fma v v -1)))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (fma (* v -5) v 1) (fma v v -1))
135.0ms	(* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1)))
105.0ms	(cbrt (* (* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1))) (/ (fma (* v -5) v 1) (fma v v -1))))
6.0ms	(acos (cbrt (* (* (/ (fma (* v -5) v 1) (fma v v -1)) (/ (fma (* v -5) v 1) (fma v v -1))) (/ (fma (* v -5) v 1) (fma v v -1)))))

simplify1.7s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	1580
1	528
0	195

prune739.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

regimes124.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	2978×	body	2560	valid
1.3s	2495×	body	1280	valid
623.0ms	8125×	body	80	nan
512.0ms	630×	body	320	valid
428.0ms	1260×	body	640	valid
67.0ms	411×	body	160	valid
19.0ms	226×	body	80	valid