Details

sample442.0ms

Algorithm

intervals

Results

114.0ms	347×	body	80	nan
69.0ms	161×	body	80	valid
31.0ms	38×	body	640	valid
31.0ms	31×	body	1280	valid
20.0ms	22×	body	640	nan
18.0ms	18×	body	1280	nan
9.0ms	17×	body	320	valid
6.0ms	10×	body	320	nan
6.0ms	9×	body	160	valid
2.0ms	5×	body	160	nan

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2040
6	2040
5	1370
4	472
3	215
2	101
1	44
0	18

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
15.2b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite169.0ms

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` `insert-posit16` `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 → 94

Calls

4 calls:

79.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
36.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
42.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

456.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
57.0ms	(* (sqrt 2) t)
260.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	2000
3	2000
2	1605
1	483
0	181

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.9b

localize39.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
8.3b	(/ (* 4 (* t t)) x)
8.8b	(/ (* l l) x)
25.2b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 77

Calls

4 calls:

0.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
43.0ms	(/ (* 4 (* t t)) x)
18.0ms	(/ (* l l) x)
2.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
26.0ms	(/ (* 4 (* t t)) x)
20.0ms	(/ (* l l) x)
377.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	2000
3	2000
2	1482
1	398
0	148

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.6b

localize45.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma t t (* l (/ l x)))
5.2b	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
8.3b	(/ (* 4 (* t t)) x)
25.2b	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`fma-udef`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

0.0ms	(fma t t (* l (/ l x)))
0.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
35.0ms	(/ (* 4 (* t t)) x)
3.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma t t (* l (/ l x)))
91.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
26.0ms	(/ (* 4 (* t t)) x)
374.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	2001
3	2001
2	949
1	298
0	127

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.6b

localize47.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ (* 4 (* t t)) x)
25.2b	(sqrt (fma t t (* l (/ l x))))
25.2b	(sqrt (fma t t (* l (/ l x))))
25.2b	(sqrt (fma 2 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (/ (* 4 (* t t)) x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
7×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

23.0ms	(/ (* 4 (* t t)) x)
1.0ms	(sqrt (fma t t (* l (/ l x))))
2.0ms	(sqrt (fma t t (* l (/ l x))))
3.0ms	(sqrt (fma 2 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (/ (* 4 (* t t)) x)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* 4 (* t t)) x)
97.0ms	(sqrt (fma t t (* l (/ l x))))
98.0ms	(sqrt (fma t t (* l (/ l x))))
349.0ms	(sqrt (fma 2 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (/ (* 4 (* t t)) x)))

simplify970.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	2003
3	2003
2	897
1	296
0	124

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.6b

regimes611.0ms

Accuracy

78.3% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.8b

bsearch362.0ms

Steps

Iters	Range		Point
6	1.1534490798277808e+139	5.896067947804245e+139	4.088323180304518e+139
8	-2.771602622336687e+93	-5.381658407530287e+90	-2.661507795721962e+93

simplify24.0ms

Iterations

Iter	Nodes
done	51
1	51
0	45

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.2s	10466×	body	80	nan
1.2s	5143×	body	80	valid
1.1s	1004×	body	640	valid
928.0ms	865×	body	1280	valid
797.0ms	640×	body	320	valid
656.0ms	606×	body	1280	nan
544.0ms	624×	body	640	nan
176.0ms	338×	body	320	nan
117.0ms	348×	body	160	valid
69.0ms	197×	body	160	nan