Details

sample694.0ms

Algorithm

intervals

Results

460.0ms	295×	body	80	nan
23.0ms	39×	body	1280	valid
17.0ms	32×	body	640	valid
16.0ms	151×	body	80	valid
16.0ms	28×	body	1280	nan
9.0ms	21×	body	320	valid
7.0ms	18×	body	640	nan
3.0ms	13×	body	160	valid
2.0ms	7×	body	320	nan
1.0ms	6×	body	160	nan

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5010
7	2894
6	1606
5	890
4	445
3	209
2	98
1	41
0	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize72.0ms

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)))

rewrite250.0ms

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:

90.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
16.0ms	(* (sqrt 2.0) t)
57.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
77.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

698.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
58.0ms	(* (sqrt 2.0) t)
341.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1672
1	471
0	178

prune804.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.5b

localize48.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
5.9b	(/ (* l l) x)
8.8b	(/ (* t t) x)
28.5b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

1.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
16.0ms	(/ (* l l) x)
12.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
38.0ms	(/ (* l l) x)
37.0ms	(/ (* t t) x)
233.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
2	1490
1	354
0	131

prune568.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize70.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* l (/ l x)) (* t t))
4.4b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t))))
8.8b	(/ (* t t) x)
28.5b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `fma-def` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

18.0ms	(+ (* l (/ l x)) (* t t))
1.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t))))
15.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t)))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* l (/ l x)) (* t t))
120.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t))))
23.0ms	(/ (* t t) x)
240.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t)))))

simplify1.4s

Counts

74 → 74

Iterations

Iter	Nodes
done	5010
2	1398
1	340
0	122

prune720.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.3b

localize73.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
4.4b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.8b	(/ (* t t) x)
28.5b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `fma-def` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

26.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
0.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
103.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
36.0ms	(/ (* t t) x)
260.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

simplify1.5s

Counts

74 → 74

Iterations

Iter	Nodes
done	5011
2	1416
1	348
0	123

prune570.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.3b

regimes1.0s

Accuracy

77.7% (5.3b remaining)

Error of 9.0b against oracle of 3.7b and baseline of 27.3b

bsearch220.0ms

Steps

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

simplify24.0ms

Iterations

Iter	Nodes
done	53
1	53
0	44

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.6s	9914×	body	80	nan
781.0ms	5072×	body	80	valid
729.0ms	674×	body	320	valid
616.0ms	1037×	body	640	valid
540.0ms	341×	body	320	nan
514.0ms	870×	body	1280	valid
500.0ms	633×	body	1280	nan
264.0ms	580×	body	640	nan
126.0ms	194×	body	160	nan
73.0ms	347×	body	160	valid