Details

sample692.0ms

Algorithm

intervals

Results

181.0ms	288×	body	80	nan
53.0ms	155×	body	80	valid
20.0ms	31×	body	1280	valid
14.0ms	28×	body	640	valid
11.0ms	26×	body	640	nan
10.0ms	30×	body	320	valid
9.0ms	20×	body	1280	nan
3.0ms	12×	body	160	valid
3.0ms	8×	body	320	nan
0.0ms	2×	body	160	nan

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	100	26
3	234	26
4	531	26
5	1051	26
6	1929	26
7	4593	26
done	5000	26

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 48.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
16.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite226.0ms

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--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

93.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
21.0ms	(* (sqrt 2.0) t)
42.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
63.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

629.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
61.0ms	(* (sqrt 2.0) t)
313.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.5s

Counts

102 → 102

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	179	2660
1	484	2380
2	2740	2183
done	5001	2176

prune719.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.6b

localize28.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
8.3b	(/ (pow l 2) x)
9.8b	(/ (pow t 2) x)
29.7b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite32.0ms

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:

1.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
12.0ms	(/ (pow l 2) x)
9.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
41.0ms	(/ (pow l 2) x)
36.0ms	(/ (pow t 2) x)
250.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify960.0ms

Counts

139 → 139

Iterations

Useful iterations: done (954.0ms)

Iter	Nodes	Cost
0	216	1767
1	398	1621
2	1576	1429
done	5000	1426

prune733.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma t t (* l (/ l x)))
3.8b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x)))))
9.8b	(/ (pow t 2) x)
29.7b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x))))))

rewrite25.0ms

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:

1.0ms	(fma t t (* l (/ l x)))
1.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x)))))
16.0ms	(/ (pow t 2) x)
4.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma t t (* l (/ l x)))
78.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x)))))
32.0ms	(/ (pow t 2) x)
316.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x))))))

simplify659.0ms

Counts

98 → 98

Iterations

Useful iterations: done (656.0ms)

Iter	Nodes	Cost
0	158	1364
1	292	1263
2	1169	1121
done	5001	1119

prune904.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize43.0ms

Local error

Found 4 expressions with local error:

9.8b	(/ (pow t 2) x)
29.7b	(sqrt (fma t t (* l (/ l x))))
29.7b	(sqrt (fma t t (* l (/ l x))))
29.7b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

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

series492.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (pow t 2) x)
103.0ms	(sqrt (fma t t (* l (/ l x))))
134.0ms	(sqrt (fma t t (* l (/ l x))))
231.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))))))

simplify739.0ms

Counts

108 → 108

Iterations

Useful iterations: done (734.0ms)

Iter	Nodes	Cost
0	155	1536
1	291	1194
2	1002	1090
done	5000	1088

prune578.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

regimes697.0ms

Accuracy

77.8% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 27.9b

bsearch886.0ms

Steps

Iters	Range		Point
6	5.7073382686318015e+118	6.873052400883988e+119	1.2779874262281365e+119
8	-1.2189785736955123e-260	-1.0581386398353699e-263	-1.323606909102099e-261
9	-2.2413056698092415e-178	-9.02348106815201e-184	-6.111047820265304e-179
9	-5.293841536497144e+53	-1.3313326719732008e+47	-2.6156735074350363e+50

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	201
1	59	201
done	59	201

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.8s	9975×	body	80	nan
1.2s	5071×	body	80	valid
557.0ms	886×	body	1280	valid
553.0ms	1002×	body	640	valid
326.0ms	564×	body	1280	nan
266.0ms	576×	body	640	nan
203.0ms	667×	body	320	valid
165.0ms	319×	body	320	nan
157.0ms	374×	body	160	valid
31.0ms	175×	body	160	nan