Details

sample544.0ms

Algorithm

intervals

Results

168.0ms	26×	body	1280	valid
54.0ms	34×	body	640	valid
38.0ms	355×	body	80	nan
20.0ms	163×	body	80	valid
11.0ms	20×	body	1280	nan
9.0ms	24×	body	640	nan
8.0ms	20×	body	320	valid
3.0ms	13×	body	320	nan
3.0ms	13×	body	160	valid
2.0ms	10×	body	160	nan

simplify3.3s

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: 40.8b

localize34.0ms

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)))

rewrite199.0ms

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:

73.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
17.0ms	(* (sqrt 2.0) t)
47.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
57.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

667.0ms	(/ (* (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)
326.0ms	(- (* (/ (+ 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)))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1672
1	471
0	178

prune808.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.4b

localize46.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
5.5b	(/ (* l l) x)
7.6b	(/ (* t t) x)
25.5b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite22.0ms

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))))
10.0ms	(/ (* l l) x)
7.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
23.0ms	(/ (* l l) x)
24.0ms	(/ (* t t) x)
224.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
2	1490
1	354
0	131

prune575.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* l (/ l x)) (* t t))
4.4b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t))))
7.6b	(/ (* t t) x)
25.5b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t)))))

rewrite37.0ms

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:

17.0ms	(+ (* 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)
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t)))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* l (/ l x)) (* t t))
98.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* l (/ l x)) (* t t))))
36.0ms	(/ (* t t) x)
275.0ms	(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

prune584.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize90.0ms

Local error

Found 4 expressions with local error:

7.6b	(/ (* t t) x)
25.4b	(sqrt (+ (* l (/ l x)) (* t t)))
25.4b	(sqrt (+ (* l (/ l x)) (* t t)))
25.5b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (* (sqrt (+ (* l (/ l x)) (* t t))) (sqrt (+ (* l (/ l x)) (* t t)))))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

15.0ms	(/ (* t t) x)
21.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
27.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (* (sqrt (+ (* l (/ l x)) (* t t))) (sqrt (+ (* l (/ l x)) (* t t)))))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (* t t) x)
245.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
230.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
289.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (* (sqrt (+ (* l (/ l x)) (* t t))) (sqrt (+ (* l (/ l x)) (* t t)))))))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1201
1	316
0	120

prune642.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

regimes1.0s

Accuracy

76.4% (5.6b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 27.6b

bsearch299.0ms

Steps

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

simplify64.0ms

Iterations

Iter	Nodes
done	55
1	55
0	46

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.2s	10040×	body	80	nan
1.2s	5162×	body	80	valid
607.0ms	981×	body	640	valid
509.0ms	827×	body	1280	valid
352.0ms	603×	body	1280	nan
255.0ms	646×	body	640	nan
198.0ms	657×	body	320	valid
90.0ms	327×	body	320	nan
76.0ms	373×	body	160	valid
32.0ms	166×	body	160	nan