Details

sample325.0ms

Algorithm

intervals

Results

121.0ms	358×	body	80	nan
26.0ms	30×	body	1280	valid
21.0ms	154×	body	80	valid
17.0ms	32×	body	640	valid
16.0ms	24×	body	1280	nan
11.0ms	24×	body	320	valid
8.0ms	16×	body	640	nan
5.0ms	14×	body	320	nan
4.0ms	16×	body	160	valid
3.0ms	11×	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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.5b

localize86.0ms

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)
15.3b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite173.0ms

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:

74.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
37.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
51.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

509.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
56.0ms	(* (sqrt 2) t)
231.0ms	(- (* (/ (+ 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)))

simplify1.2s

Counts

106 → 106

Iterations

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

prune684.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize67.0ms

Local error

Found 4 expressions with local error:

3.0b	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
6.6b	(/ (* l l) x)
9.9b	(/ (* 4 (* t t)) x)
26.5b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

rewrite42.0ms

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))
17.0ms	(/ (* l l) x)
22.0ms	(/ (* 4 (* t t)) x)
1.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
32.0ms	(/ (* l l) x)
27.0ms	(/ (* 4 (* t t)) x)
326.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

simplify967.0ms

Counts

89 → 89

Iterations

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

prune697.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x))))
3.0b	(fma (* t t) 2 (* 4 (/ (* t t) x)))
9.9b	(/ (* t t) x)
26.5b	(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)
3.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x))))
73.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
22.0ms	(/ (* t t) x)
484.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

simplify951.0ms

Counts

74 → 74

Iterations

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

prune550.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (* l (/ l x)))
3.0b	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
9.9b	(/ (* 4 (* t t)) x)
26.5b	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

rewrite32.0ms

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))
29.0ms	(/ (* 4 (* t t)) x)
2.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma t t (* l (/ l x)))
109.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
37.0ms	(/ (* 4 (* t t)) x)
349.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

simplify969.0ms

Counts

76 → 76

Iterations

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

prune502.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.9b

regimes790.0ms

Accuracy

77.6% (5.2b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 26.8b

bsearch1.1s

Steps

Iters	Range		Point
9	3.418485680637394e+69	2.5394452178869736e+75	1.190119698582846e+73
5	3.7309912156633627e-165	7.625611042088009e-165	3.9773559035809034e-165
8	1.5881823628500624e-279	7.641349737140096e-275	7.466234522592741e-275
9	-3.571300126685226e+102	-1.3399686220244182e+97	-1.3258761248569655e+101

simplify15.0ms

Iterations

Iter	Nodes
done	56
1	56
0	50

end0.0ms

sample9.3s

Algorithm

intervals

Results

2.6s	10227×	body	80	nan
1.4s	835×	body	1280	valid
1.3s	5158×	body	80	valid
1.1s	614×	body	1280	nan
864.0ms	1024×	body	640	valid
536.0ms	594×	body	640	nan
407.0ms	628×	body	320	valid
216.0ms	307×	body	320	nan
152.0ms	355×	body	160	valid
65.0ms	184×	body	160	nan