Details

sample376.0ms

Algorithm

intervals

Results

144.0ms	72×	body	1280	valid
107.0ms	195×	body	80	valid
66.0ms	45×	body	640	valid
22.0ms	23×	body	320	valid
14.0ms	16×	body	160	valid

simplify753.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
3	1174
2	189
1	54
0	19

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.0b

localize55.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ t (* (/ l t) (/ l t)))
2.7b	(* (/ t (* (/ l t) (/ l t))) (sin k))
3.9b	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
14.1b	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite684.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-cbrt-cube` `add-exp-log`
56×	`prod-exp` `cbrt-unprod`
36×	`cbrt-undiv` `div-exp`
20×	`pow1`
15×	`add-sqr-sqrt`
12×	`associate-l` `associate-*l/`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow-prod-down`
9×	`associate-r`
7×	`times-frac`
6×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `tan-quot` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`fma-udef` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`

Counts

4 → 146

Calls

4 calls:

11.0ms	(/ t (* (/ l t) (/ l t)))
42.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
157.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
471.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

series844.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ t (* (/ l t) (/ l t)))
104.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
235.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
458.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

simplify659.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
1	672
0	235

prune929.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* t (sin k)) (sin k))
0.4b	(/ 2 (/ (* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2)) (* (* (/ l t) (/ l t)) (cos k))))
3.2b	(* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2))
15.6b	(/ (* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2)) (* (* (/ l t) (/ l t)) (cos k)))

rewrite410.0ms

Algorithm

rewrite-expression-head

Rules

316×	`add-cbrt-cube` `add-exp-log`
153×	`prod-exp` `cbrt-unprod`
105×	`cbrt-undiv` `div-exp`
29×	`times-frac`
20×	`associate-*l/`
19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
16×	`associate-/r/`
9×	`associate-/r*` `pow-prod-down`
6×	`associate-r` `div-inv`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 213

Calls

4 calls:

43.0ms	(* (* t (sin k)) (sin k))
142.0ms	(/ 2 (/ (* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2)) (* (* (/ l t) (/ l t)) (cos k))))
110.0ms	(* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2))
102.0ms	(/ (* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2)) (* (* (/ l t) (/ l t)) (cos k)))

series1.0s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (* t (sin k)) (sin k))
503.0ms	(/ 2 (/ (* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2)) (* (* (/ l t) (/ l t)) (cos k))))
134.0ms	(* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2))
330.0ms	(/ (* (* (* t (sin k)) (sin k)) (fma (/ k t) (/ k t) 2)) (* (* (/ l t) (/ l t)) (cos k)))

simplify866.0ms

Counts

225 → 225

Iterations

Iter	Nodes
done	2006
1	1074
0	355

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (/ (* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (* (/ l t) (/ l t)) (cos k))))
0.5b	(* (sin k) (fma (/ k t) (/ k t) 2))
2.8b	(* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2)))
15.6b	(/ (* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (* (/ l t) (/ l t)) (cos k)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

396×	`add-cbrt-cube` `add-exp-log`
195×	`prod-exp` `cbrt-unprod`
131×	`cbrt-undiv` `div-exp`
29×	`times-frac`
21×	`add-sqr-sqrt`
20×	`associate-*l/`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
16×	`associate-/r/`
9×	`associate-/r*` `pow-prod-down`
6×	`fma-udef` `div-inv`
5×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 242

Calls

4 calls:

92.0ms	(/ 2 (/ (* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (* (/ l t) (/ l t)) (cos k))))
18.0ms	(* (sin k) (fma (/ k t) (/ k t) 2))
57.0ms	(* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2)))
82.0ms	(/ (* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (* (/ l t) (/ l t)) (cos k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

554.0ms	(/ 2 (/ (* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (* (/ l t) (/ l t)) (cos k))))
78.0ms	(* (sin k) (fma (/ k t) (/ k t) 2))
141.0ms	(* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2)))
326.0ms	(/ (* (* t (sin k)) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (* (/ l t) (/ l t)) (cos k)))

simplify960.0ms

Counts

254 → 254

Iterations

Iter	Nodes
done	2005
1	1220
0	401

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.9b

localize76.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (* t (sin k)) (* (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))))
10.8b	(sqrt (fma (/ k t) (/ k t) 2))
10.8b	(sqrt (fma (/ k t) (/ k t) 2))
15.6b	(/ (* (* t (sin k)) (* (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2)))) (* (* (/ l t) (/ l t)) (cos k)))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

290×	`add-cbrt-cube` `add-exp-log`
168×	`prod-exp` `cbrt-unprod`
70×	`cbrt-undiv` `div-exp`
27×	`pow1`
15×	`pow-prod-down`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-r` `associate-l` `associate-r/` `-commutative` `div-inv` `associate-/l`

Counts

4 → 166

Calls

4 calls:

117.0ms	(* (* t (sin k)) (* (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))))
1.0ms	(sqrt (fma (/ k t) (/ k t) 2))
1.0ms	(sqrt (fma (/ k t) (/ k t) 2))
173.0ms	(/ (* (* t (sin k)) (* (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2)))) (* (* (/ l t) (/ l t)) (cos k)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* t (sin k)) (* (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))))
73.0ms	(sqrt (fma (/ k t) (/ k t) 2))
71.0ms	(sqrt (fma (/ k t) (/ k t) 2))
286.0ms	(/ (* (* t (sin k)) (* (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2)))) (* (* (/ l t) (/ l t)) (cos k)))

simplify897.0ms

Counts

178 → 178

Iterations

Iter	Nodes
done	2007
1	849
0	260

prune991.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.5b

regimes836.0ms

Accuracy

9.7% (8.4b remaining)

Error of 15.3b against oracle of 6.8b and baseline of 16.2b

bsearch1.9s

Steps

Iters	Range		Point
9	3.6742441519344763e+99	1.7558875369180712e+105	9.600966579055477e+99
8	2.97651747423293e-85	3.595421908753787e-82	3.438337439326428e-85
10	-1.409330416317469e-135	-1.507459994972452e-149	-1.7515234209579402e-149
9	-1.189678541977112e+69	-1.1481465705136179e+64	-1.1912096216701534e+67

simplify40.0ms

Iterations

Iter	Nodes
done	71
3	71
2	68
1	65
0	47

end0.0ms

sample14.0s

Algorithm

intervals

Results

5.2s	2037×	body	1280	valid
3.4s	5882×	body	80	valid
3.2s	1754×	body	640	valid
1.5s	846×	body	320	valid
358.0ms	452×	body	160	valid