Details

sample555.0ms

Algorithm

intervals

Results

262.0ms	163×	body	80	valid
40.0ms	355×	body	80	nan
14.0ms	34×	body	640	valid
13.0ms	26×	body	1280	valid
9.0ms	20×	body	1280	nan
8.0ms	24×	body	640	nan
6.0ms	20×	body	320	valid
4.0ms	13×	body	320	nan
2.0ms	13×	body	160	valid
2.0ms	10×	body	160	nan

simplify4.2s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize79.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
12.2b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite236.0ms

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:

88.0ms	(/ (* (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)
52.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
73.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts

4 → 12

Calls

4 calls:

687.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
72.0ms	(* (sqrt 2.0) t)
334.0ms	(- (* (/ (+ 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)))

simplify2.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	2749
1	482
0	178

prune843.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
0.8b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
25.5b	(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))))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sqrt 2.0) t)
53.0ms	(fma t t (/ l (/ x l)))
113.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
278.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify852.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	786
1	204
0	102

prune685.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize57.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l)))))))
25.4b	(sqrt (fma t t (/ l (/ x l))))
25.4b	(sqrt (fma t t (/ l (/ x l))))
25.5b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

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

series637.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l)))))))
121.0ms	(sqrt (fma t t (/ l (/ x l))))
105.0ms	(sqrt (fma t t (/ l (/ x l))))
302.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))

simplify2.2s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	3436
2	560
1	175
0	84

prune681.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.4b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.8b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
25.5b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

57.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.0ms	(fma t t (/ l (/ x l)))
1.0ms	(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))))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
75.0ms	(fma t t (/ l (/ x l)))
86.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
262.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify1.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	895
1	233
0	109

prune537.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.4b

regimes1.2s

Accuracy

76.2% (5.7b remaining)

Error of 9.4b against oracle of 3.7b and baseline of 27.4b

bsearch306.0ms

Steps

Iters	Range		Point
8	4.426853282634998e+56	1.661076069045296e+60	1.6237106520617296e+60
6	-5.111701595882843e+60	-4.544149282436552e+59	-6.172764092322424e+59

simplify28.0ms

Iterations

Iter	Nodes
done	44
1	44
0	41

end0.0ms

sample6.1s

Algorithm

intervals

Results

1.3s	827×	body	1280	valid
1.2s	10040×	body	80	nan
841.0ms	5162×	body	80	valid
593.0ms	981×	body	640	valid
398.0ms	646×	body	640	nan
381.0ms	603×	body	1280	nan
310.0ms	657×	body	320	valid
162.0ms	373×	body	160	valid
93.0ms	327×	body	320	nan
31.0ms	166×	body	160	nan