Details

sample443.0ms

Algorithm

intervals

Results

92.0ms	158×	body	80	valid
51.0ms	349×	body	80	nan
18.0ms	25×	body	1280	valid
17.0ms	32×	body	640	valid
11.0ms	14×	body	1280	nan
10.0ms	20×	body	640	nan
9.0ms	25×	body	320	valid
5.0ms	16×	body	160	valid
3.0ms	10×	body	320	nan
2.0ms	8×	body	160	nan

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (11.0ms)

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize24.0ms

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)
13.3b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
19.9b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite220.0ms

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:

81.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
21.0ms	(* (sqrt 2.0) t)
53.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
63.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.6s

Counts

4 → 12

Calls

4 calls:

734.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
68.0ms	(* (sqrt 2.0) t)
323.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
445.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify4.0s

Counts

100 → 100

Iterations

Useful iterations: 3 (2.1s)

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

prune535.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 28.5b

localize33.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
5.4b	(/ (pow l 2) x)
9.8b	(/ (pow t 2) x)
27.5b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite45.0ms

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)))
18.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
4.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
20.0ms	(/ (pow l 2) x)
36.0ms	(/ (pow t 2) x)
447.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.3s

Counts

139 → 139

Iterations

Useful iterations: done (2.3s)

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

prune840.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
4.0b	(fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x)))
9.8b	(/ (pow t 2) x)
27.5b	(sqrt (fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
0.0ms	(fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x)))
9.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
112.0ms	(fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x)))
27.0ms	(/ (pow t 2) x)
394.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify2.4s

Counts

98 → 98

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	160	1530
1	279	1341
2	670	1108
3	2323	1108
done	5001	1107

prune608.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.9b

localize29.0ms

Local error

Found 4 expressions with local error:

9.8b	(/ (pow t 2) x)
9.8b	(/ (pow t 2) x)
27.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
27.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`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×	`pow1` `div-exp` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

15.0ms	(/ (pow t 2) x)
18.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
14.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (pow t 2) x)
22.0ms	(/ (pow t 2) x)
400.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
383.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify1.4s

Counts

144 → 144

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	133	1862
1	233	1676
2	559	1492
3	1789	1492
done	5000	1490

prune929.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

regimes577.0ms

Accuracy

77.7% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.8b

bsearch830.0ms

Steps

Iters	Range		Point
10	8.394896216821908e+49	9.623627385293308e+64	5.564919863052779e+60
10	1.5758220318623351e-174	8.046018310283969e-162	3.39285568249297e-169
7	1.04743012393885e-255	1.698545711080697e-253	1.2791561736442862e-253
7	-6.210081772932775e+49	-4.6782824394543606e+47	-1.670018113804049e+49

simplify12.0ms

Iterations

Useful iterations: done (12.0ms)

Iter	Nodes	Cost
0	38	122
1	46	102
2	51	76
3	54	76
done	54	75

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.3s	10136×	body	80	nan
1.2s	805×	body	1280	valid
1.1s	5205×	body	80	valid
546.0ms	1006×	body	640	valid
423.0ms	558×	body	1280	nan
326.0ms	609×	body	640	nan
320.0ms	614×	body	320	valid
119.0ms	370×	body	160	valid
109.0ms	362×	body	320	nan
35.0ms	190×	body	160	nan