Details

sample268.0ms

Algorithm

intervals

Results

47.0ms	33×	body	640	valid
45.0ms	347×	body	80	nan
21.0ms	171×	body	80	valid
14.0ms	24×	body	1280	nan
13.0ms	21×	body	1280	valid
10.0ms	18×	body	640	nan
9.0ms	22×	body	320	valid
6.0ms	18×	body	320	nan
2.0ms	9×	body	160	valid
2.0ms	7×	body	160	nan

simplify1.5s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.5b

localize55.0ms

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))))
0.5b	(* (sqrt 2) t)
13.0b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite211.0ms

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:

92.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
17.0ms	(* (sqrt 2) t)
53.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
46.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

494.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
56.0ms	(* (sqrt 2) t)
249.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.7s

Counts

106 → 106

Iterations

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

prune667.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.0b

localize36.0ms

Local error

Found 4 expressions with local error:

4.2b	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
4.5b	(/ (* l l) x)
8.4b	(/ (* 4 (* t t)) x)
29.4b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

rewrite30.0ms

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))
9.0ms	(/ (* l l) x)
18.0ms	(/ (* 4 (* t t)) x)
1.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
38.0ms	(/ (* l l) x)
45.0ms	(/ (* 4 (* t t)) x)
390.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

simplify1.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	2031
3	2031
2	1450
1	393
0	148

prune544.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2) t)
4.2b	(fma (* t t) 2 (* 4 (/ (* t t) x)))
8.4b	(/ (* t t) x)
29.4b	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

15.0ms	(* (sqrt 2) t)
0.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
18.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

series651.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sqrt 2) t)
80.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
21.0ms	(/ (* t t) x)
475.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	2011
3	2011
2	930
1	314
0	136

prune612.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x))))
4.2b	(fma (* t t) 2 (* 4 (/ (* t t) x)))
8.4b	(/ (* t t) x)
29.4b	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`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×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp` `fma-udef`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x))))
0.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
19.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

series662.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x))))
75.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
20.0ms	(/ (* t t) x)
488.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

simplify943.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	2105
3	2105
2	946
1	270
0	118

prune526.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

regimes682.0ms

Accuracy

77.2% (5.4b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 27.5b

bsearch833.0ms

Steps

Iters	Range		Point
5	6.262036766516395e+134	1.782199942337008e+135	1.0888219445242733e+135
8	3.907881210716465e-189	1.576407217143116e-185	9.831366213789788e-187
8	4.056079679036218e-287	4.597436613380927e-284	3.4759257316157413e-284
4	-5.516853907540803e+62	-3.19405123701085e+62	-5.415525381702613e+62

simplify49.0ms

Iterations

Iter	Nodes
done	71
3	71
2	68
1	65
0	55

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.3s	10386×	body	80	nan
1.6s	5227×	body	80	valid
1.4s	608×	body	1280	nan
941.0ms	804×	body	1280	valid
855.0ms	982×	body	640	valid
475.0ms	641×	body	320	valid
474.0ms	587×	body	640	nan
198.0ms	346×	body	160	valid
185.0ms	352×	body	320	nan
59.0ms	168×	body	160	nan