Details

sample591.0ms

Algorithm

intervals

Results

218.0ms	157×	body	80	valid
112.0ms	358×	body	80	nan
74.0ms	32×	body	1280	valid
18.0ms	34×	body	640	valid
12.0ms	18×	body	1280	nan
12.0ms	21×	body	640	nan
9.0ms	20×	body	320	valid
4.0ms	11×	body	320	nan
4.0ms	13×	body	160	valid
2.0ms	6×	body	160	nan

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	18	525
1	41	525
2	100	525
3	232	525
4	526	525
5	1092	525
6	1985	525
7	4703	525
done	5000	525

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize43.0ms

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)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite193.0ms

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:

57.0ms	(/ (* (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)
41.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
74.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.5s

Counts

4 → 12

Calls

4 calls:

571.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms	(* (sqrt 2.0) t)
296.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.7s

Counts

102 → 102

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	178	45814
1	482	41801
2	2749	41626
done	5002	41531

prune718.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

localize62.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ (* l l) x))))
6.4b	(/ (* l l) x)
8.3b	(/ (* t t) x)
25.2b	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ (* l l) x)))))

rewrite36.0ms

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 (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ (* l l) x))))
17.0ms	(/ (* l l) x)
15.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ (* l l) x)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ (* l l) x))))
22.0ms	(/ (* l l) x)
21.0ms	(/ (* t t) x)
244.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ (* l l) x)))))

simplify2.1s

Counts

83 → 83

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	131	21657
1	357	18159
2	2814	17759
done	5002	17719

prune627.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* t t) (/ l (/ x l)))
4.4b	(fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.3b	(/ (* t t) x)
25.2b	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite44.0ms

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:

33.0ms	(+ (* t t) (/ l (/ x l)))
0.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ l (/ x l))))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* t t) (/ l (/ x l)))
86.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ l (/ x l)))))
35.0ms	(/ (* t t) x)
239.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	122	22601
1	339	18234
2	2280	17869
done	5000	17094

prune493.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.3b

localize51.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ (* t t) x)
25.2b	(sqrt (+ (* t t) (/ l (/ x l))))
25.2b	(sqrt (+ (* t t) (/ l (/ x l))))
25.2b	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (* (sqrt (+ (* t t) (/ l (/ x l)))) (sqrt (+ (* t t) (/ l (/ x l))))))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

15.0ms	(/ (* t t) x)
45.0ms	(sqrt (+ (* t t) (/ l (/ x l))))
63.0ms	(sqrt (+ (* t t) (/ l (/ x l))))
7.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (* (sqrt (+ (* t t) (/ l (/ x l)))) (sqrt (+ (* t t) (/ l (/ x l))))))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* t t) x)
124.0ms	(sqrt (+ (* t t) (/ l (/ x l))))
118.0ms	(sqrt (+ (* t t) (/ l (/ x l))))
255.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (* (sqrt (+ (* t t) (/ l (/ x l)))) (sqrt (+ (* t t) (/ l (/ x l))))))))

simplify1.6s

Counts

90 → 90

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	122	24113
1	317	19857
2	1988	19487
done	5001	18927

prune679.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

regimes796.0ms

Accuracy

77.6% (5.4b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 28.0b

bsearch1.0s

Steps

Iters	Range		Point
9	8.029604051112713e+47	4.771574953324125e+55	4.214549585149478e+55
10	3.1913228427846884e-157	3.080469255526081e-145	3.2479806443803153e-157
10	7.396249846299801e-250	6.414192999540213e-240	1.8396588411989053e-241
9	-2.2008797770019196e+94	-2.884593901536308e+87	-1.940005881918409e+94

simplify61.0ms

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	46	1734
1	59	1734
2	62	1734
3	65	1734
done	65	1734

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.7s	9922×	body	80	nan
827.0ms	5112×	body	80	valid
691.0ms	644×	body	320	valid
635.0ms	819×	body	1280	valid
518.0ms	365×	body	160	valid
504.0ms	599×	body	1280	nan
452.0ms	1060×	body	640	valid
415.0ms	625×	body	640	nan
99.0ms	335×	body	320	nan
37.0ms	191×	body	160	nan