Details

sample309.0ms

Algorithm

intervals

Results

59.0ms	322×	body	80	nan
49.0ms	18×	body	320	valid
16.0ms	156×	body	80	valid
12.0ms	38×	body	640	valid
12.0ms	32×	body	1280	valid
11.0ms	23×	body	1280	nan
7.0ms	22×	body	640	nan
3.0ms	10×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (49.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize39.0ms

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)
13.9b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
19.6b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite167.0ms

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:

54.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
11.0ms	(* (sqrt 2.0) t)
21.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
75.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

665.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
398.0ms	(* (sqrt 2.0) t)
300.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
471.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify3.9s

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

prune527.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.3b

localize36.0ms

Local error

Found 4 expressions with local error:

4.2b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
7.8b	(/ (pow l 2) x)
9.2b	(/ (pow t 2) x)
27.3b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite49.0ms

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

series520.0ms

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)
21.0ms	(/ (pow t 2) x)
368.0ms	(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

prune708.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
4.2b	(fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x)))
9.2b	(/ (pow t 2) x)
27.3b	(sqrt (fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite23.0ms

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 (/ (pow l (/ 2 2)) (/ x l)))
1.0ms	(fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x)))
15.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
102.0ms	(fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x)))
26.0ms	(/ (pow t 2) x)
419.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

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

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize42.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (pow t 2) x)
9.2b	(/ (pow t 2) x)
27.3b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
27.3b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite46.0ms

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:

17.0ms	(/ (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))))
3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (pow t 2) x)
29.0ms	(/ (pow t 2) x)
408.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
414.0ms	(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

prune905.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.1b

regimes505.0ms

Accuracy

75.6% (5.7b remaining)

Error of 9.7b against oracle of 4.0b and baseline of 27.5b

bsearch873.0ms

Steps

Iters	Range		Point
9	1.199445854275694e+37	2.286004827212558e+42	1.49940571128711e+42
8	1.9331730416670513e-145	3.203389628538628e-142	1.96678984226064e-145
7	2.9864185856163577e-279	3.6043515955327495e-277	3.155486028136924e-278
7	-4.881804416771232e-192	-8.553073611070034e-194	-8.36950043765991e-193
8	-2.1756869906241315e-162	-6.361245379467226e-165	-1.899175960211412e-162
9	-1.085661897034274e+121	-2.7815652200329975e+115	-9.558743729877633e+120

simplify20.0ms

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	44	175
1	52	153
2	57	125
3	60	125
done	60	125

end0.0ms

sample3.5s

Algorithm

intervals

Results

776.0ms	10246×	body	80	nan
408.0ms	5071×	body	80	valid
358.0ms	895×	body	1280	valid
322.0ms	1045×	body	640	valid
224.0ms	605×	body	1280	nan
175.0ms	603×	body	640	nan
132.0ms	603×	body	320	valid
72.0ms	320×	body	320	nan
58.0ms	386×	body	160	valid
26.0ms	175×	body	160	nan