Details

sample72.0ms

Algorithm

intervals

Results

15.0ms	306×	body	80	nan
8.0ms	159×	body	80	valid
6.0ms	24×	body	1280	valid
5.0ms	26×	body	640	valid
4.0ms	27×	body	320	valid
4.0ms	16×	body	1280	nan
3.0ms	17×	body	640	nan
2.0ms	20×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	11×	body	160	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	94	26
3	214	26
4	433	26
5	834	26
6	1339	26
7	2242	26
8	4931	26
done	5000	26

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.5b	(* (sqrt 2.0) t)
12.4b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
19.7b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

19.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
14.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
18.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.0s

Counts

4 → 12

Calls

4 calls:

463.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
40.0ms	(* (sqrt 2.0) t)
202.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
313.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify548.0ms

Counts

100 → 100

Iterations

Useful iterations: done (545.0ms)

Iter	Nodes	Cost
0	155	2445
1	348	2250
2	1221	2067
done	5001	2034

prune360.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 30.7b

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.9b	(/ (pow l 2) x)
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
21.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
258.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify556.0ms

Counts

139 → 139

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	216	1816
1	373	1665
2	1156	1490
done	5001	1490

prune535.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
3.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
66.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
265.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	175	1440
1	319	1325
2	917	1203
3	3834	1147
done	5001	1146

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
17×	`pow1`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

21.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
63.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
23.0ms	(/ (pow t 2) x)
257.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	183	1701
1	369	1577
2	1124	1264
3	4573	1133
done	5000	1132

prune389.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.9b

regimes287.0ms

Accuracy

76.2% (5.5b remaining)

Error of 9.4b against oracle of 3.9b and baseline of 27.0b

bsearch422.0ms

Steps

Iters	Range		Point
8	2.856659494861968e+113	8.814288912248196e+117	2.527401613686204e+114
6	-1.183890802660123e-282	-2.1055594324771466e-283	-3.3196210034371617e-283
10	-2.4994760714008124e-200	-2.1048616109453496e-212	-4.738432652811407e-208
8	-3.6441438461771793e+143	-1.8976906426182426e+140	-4.097588426365747e+140

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	137
1	46	137
done	46	137

end0.0ms

sample2.2s

Algorithm

intervals

Results

625.0ms	10109×	body	80	nan
269.0ms	5145×	body	80	valid
202.0ms	1012×	body	640	valid
200.0ms	801×	body	1280	valid
145.0ms	591×	body	1280	nan
109.0ms	587×	body	640	nan
100.0ms	654×	body	320	valid
47.0ms	337×	body	320	nan
38.0ms	388×	body	160	valid
21.0ms	215×	body	160	nan