Details

sample84.0ms

Algorithm

intervals

Results

15.0ms	323×	body	80	nan
14.0ms	32×	body	1280	valid
8.0ms	164×	body	80	valid
7.0ms	40×	body	640	valid
4.0ms	20×	body	1280	nan
2.0ms	13×	body	640	nan
2.0ms	16×	body	320	valid
2.0ms	13×	body	320	nan
0.0ms	4×	body	160	valid
0.0ms	4×	body	160	nan

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	100	26
3	224	26
4	497	26
5	941	26
6	1555	26
7	3305	26
done	5001	26

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize20.0ms

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))))
0.4b	(* (sqrt 2.0) t)
12.4b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
18.1b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite117.0ms

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:

43.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
10.0ms	(* (sqrt 2.0) t)
26.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
34.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.1s

Counts

4 → 12

Calls

4 calls:

478.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
42.0ms	(* (sqrt 2.0) t)
202.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
332.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify2.4s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	155	2445
1	345	2250
2	1195	2062
3	4993	2025
done	5000	2025

prune379.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.4b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
7.1b	(/ (pow l 2) x)
7.6b	(/ (pow t 2) x)
24.8b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite24.0ms

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 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
9.0ms	(/ (pow l 2) x)
9.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
23.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
269.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts

139 → 139

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	217	1761
1	376	1614
2	912	1411
3	3182	1411
done	5000	1410

prune480.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.4b	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
7.6b	(/ (pow t 2) x)
24.8b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite27.0ms

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:

10.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
12.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
75.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
19.0ms	(/ (pow t 2) x)
270.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	176	1385
1	317	1274
2	808	1134
3	2651	1134
done	5000	1133

prune382.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.4b	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
7.6b	(/ (pow t 2) x)
24.8b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite61.0ms

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:

44.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
12.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
76.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
19.0ms	(/ (pow t 2) x)
274.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	184	1646
1	361	1526
2	1018	1199
3	3077	1124
done	5000	1123

prune342.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

regimes368.0ms

Accuracy

77.9% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.4b

bsearch430.0ms

Steps

Iters	Range		Point
8	4.675023421196728e+36	4.923303098506139e+39	4.8698681991528654e+39
9	3.742612203784258e-160	2.9120561417431717e-154	5.832383717323897e-160
10	9.221801955237562e-239	2.899958115691549e-221	4.894745026611551e-226
8	-2.0068295615508747e+75	-1.897864979438576e+72	-1.6066236751871663e+75

simplify10.0ms

Iterations

Useful iterations: done (9.0ms)

Iter	Nodes	Cost
0	40	132
1	49	116
2	52	85
3	55	85
done	55	84

end0.0ms

sample2.2s

Algorithm

intervals

Results

483.0ms	10130×	body	80	nan
263.0ms	5168×	body	80	valid
214.0ms	861×	body	1280	valid
186.0ms	999×	body	640	valid
137.0ms	589×	body	1280	nan
107.0ms	600×	body	640	nan
86.0ms	602×	body	320	valid
49.0ms	340×	body	320	nan
37.0ms	370×	body	160	valid
18.0ms	195×	body	160	nan