Details

sample882.0ms

Algorithm

intervals

Results

235.0ms	277×	body	80	nan
69.0ms	175×	body	80	valid
33.0ms	34×	body	640	valid
31.0ms	19×	body	1280	nan
23.0ms	10×	body	320	nan
22.0ms	16×	body	1280	valid
16.0ms	22×	body	640	nan
9.0ms	21×	body	320	valid
3.0ms	10×	body	160	valid
2.0ms	8×	body	160	nan

simplify9.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2949
6	1613
5	897
4	444
3	209
2	98
1	41
0	18

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(* t (/ (sqrt 2.0) (sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
0.4b	(/ (sqrt 2.0) (sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
12.5b	(- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
21.8b	(sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite423.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
76×	`times-frac`
74×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
42×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`sqrt-div` `associate-/r` `associate-/l` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 164

Calls

4 calls:

191.0ms	(* t (/ (sqrt 2.0) (sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
74.0ms	(/ (sqrt 2.0) (sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
42.0ms	(- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
100.0ms	(sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series3.1s

Counts

4 → 12

Calls

4 calls:

978.0ms	(* t (/ (sqrt 2.0) (sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
1.1s	(/ (sqrt 2.0) (sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
388.0ms	(- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
660.0ms	(sqrt (- (* (fma (* t t) 2.0 (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify3.0s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	1441
1	501
0	217

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.7b

localize70.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma t t (/ l (/ x l)))
3.6b	(fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t)))
9.6b	(* (/ 4.0 x) (* t t))
25.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
13×	`associate-l`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `times-frac`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `div-exp` `fma-udef` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `associate-l/` `-commutative` `div-inv`

Counts

4 → 72

Calls

4 calls:

1.0ms	(fma t t (/ l (/ x l)))
1.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t)))
62.0ms	(* (/ 4.0 x) (* t t))
3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

series857.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma t t (/ l (/ x l)))
142.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t)))
65.0ms	(* (/ 4.0 x) (* t t))
558.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

simplify5.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5042
3	3958
2	944
1	334
0	139

prune890.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.7b

localize104.0ms

Local error

Found 4 expressions with local error:

9.6b	(* (/ 4.0 x) (* t t))
9.6b	(* (/ 4.0 x) (* t t))
25.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
25.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
26×	`associate-l`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
16×	`pow1`
12×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `sqrt-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `associate-l/` `-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

50.0ms	(* (/ 4.0 x) (* t t))
61.0ms	(* (/ 4.0 x) (* t t))
3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

series1.2s

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (/ 4.0 x) (* t t))
71.0ms	(* (/ 4.0 x) (* t t))
503.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
523.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

simplify4.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5009
3	3452
2	849
1	290
0	114

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.7b

localize258.0ms

Local error

Found 4 expressions with local error:

25.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
26.3b	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
26.3b	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
26.3b	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
2.0ms	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
2.0ms	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
2.0ms	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

series1.9s

Counts

4 → 12

Calls

4 calls:

541.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
449.0ms	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
447.0ms	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))
435.0ms	(cbrt (fma 2.0 (fma t t (/ l (/ x l))) (* (/ 4.0 x) (* t t))))

simplify3.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
3	1813
2	567
1	221
0	101

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.7b

regimes940.0ms

Accuracy

77.1% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.0b

bsearch331.0ms

Steps

Iters	Range		Point
7	6.127523386061855e+92	6.524677852657816e+94	1.9700005358929724e+94
5	-6.434131299274751e+123	-3.143476380631542e+123	-6.009472995498685e+123

simplify21.0ms

Iterations

Iter	Nodes
done	42
1	42
0	35

end1.0ms

sample8.8s

Algorithm

intervals

Results

2.9s	10108×	body	80	nan
1.2s	5094×	body	80	valid
985.0ms	877×	body	1280	valid
723.0ms	334×	body	320	nan
655.0ms	951×	body	640	valid
509.0ms	583×	body	1280	nan
410.0ms	648×	body	640	nan
329.0ms	690×	body	320	valid
115.0ms	388×	body	160	valid
49.0ms	195×	body	160	nan