Details

sample237.0ms

Algorithm

intervals

Results

78.0ms	295×	body	80	nan
18.0ms	39×	body	1280	valid
16.0ms	151×	body	80	valid
13.0ms	32×	body	640	valid
13.0ms	28×	body	1280	nan
9.0ms	18×	body	640	nan
6.0ms	21×	body	320	valid
3.0ms	7×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4703
6	1985
5	1092
4	526
3	232
2	100
1	41
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
14.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `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` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

46.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
8.0ms	(* (sqrt 2.0) t)
37.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
40.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts

4 → 12

Calls

4 calls:

660.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
82.0ms	(* (sqrt 2.0) t)
323.0ms	(- (* (/ (+ 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)))

simplify2.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	2749
1	482
0	178

prune636.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.5b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
28.5b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`fma-udef` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 59

Calls

4 calls:

16.0ms	(* (sqrt 2.0) t)
0.0ms	(fma t t (/ l (/ x l)))
0.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
3.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sqrt 2.0) t)
75.0ms	(fma t t (/ l (/ x l)))
102.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
254.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify879.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	786
1	204
0	102

prune605.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t)) (sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))))
1.5b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
28.5b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
6×	`associate-/r*` `times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
2×	`fma-udef`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l*`

Counts

4 → 66

Calls

4 calls:

49.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t)) (sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))))
0.0ms	(fma t t (/ l (/ x l)))
0.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
2.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

395.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t)) (sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))))
69.0ms	(fma t t (/ l (/ x l)))
99.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
208.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify1.8s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1786
1	316
0	127

prune713.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))) (* (sqrt (sqrt 2.0)) t))
1.5b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
28.5b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
6×	`times-frac` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `fma-udef`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 64

Calls

4 calls:

11.0ms	(/ (sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))) (* (sqrt (sqrt 2.0)) t))
0.0ms	(fma t t (/ l (/ x l)))
0.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
1.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

612.0ms	(/ (sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))) (* (sqrt (sqrt 2.0)) t))
82.0ms	(fma t t (/ l (/ x l)))
113.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
282.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1021
1	257
0	122

prune694.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

regimes826.0ms

Accuracy

77.5% (5.3b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 27.3b

bsearch238.0ms

Steps

Iters	Range		Point
3	4.1523530552241535e+92	5.424691173039659e+92	4.225315466536892e+92
7	-1.3589006648119579e+99	-3.650405087160364e+97	-6.758930516841978e+97

simplify18.0ms

Iterations

Iter	Nodes
done	51
1	51
0	44

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.3s	9914×	body	80	nan
1.1s	5072×	body	80	valid
684.0ms	580×	body	640	nan
538.0ms	870×	body	1280	valid
528.0ms	1037×	body	640	valid
322.0ms	633×	body	1280	nan
227.0ms	674×	body	320	valid
86.0ms	341×	body	320	nan
69.0ms	194×	body	160	nan
68.0ms	347×	body	160	valid