Details

sample238.0ms

Algorithm

intervals

Results

26.0ms	311×	body	80	nan
15.0ms	165×	body	80	valid
12.0ms	34×	body	640	valid
12.0ms	28×	body	1280	valid
6.0ms	20×	body	640	nan
5.0ms	14×	body	1280	nan
5.0ms	18×	body	320	valid
2.0ms	11×	body	160	valid
2.0ms	7×	body	320	nan
1.0ms	7×	body	160	nan

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	2276
6	1138
5	616
4	361
3	179
2	90
1	39
0	18

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.7b

localize64.0ms

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)
11.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite205.0ms

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×	`sqrt-div`
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` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

68.0ms	(/ (* (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)
49.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
67.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.1s

Counts

4 → 12

Calls

4 calls:

635.0ms	(/ (* (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)
297.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1572
1	445
0	167

prune836.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize70.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
4.5b	(/ (* l l) x)
9.9b	(/ (* t t) x)
29.8b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-*r/`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`associate-+r+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 74

Calls

4 calls:

39.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
16.0ms	(/ (* l l) x)
16.0ms	(/ (* t t) x)
44.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
25.0ms	(/ (* l l) x)
24.0ms	(/ (* t t) x)
229.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5012
2	2531
1	547
0	167

prune657.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (/ l (/ x l)) (* t t))
4.0b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ l (/ x l)) (* t t))))
9.9b	(/ (* t t) x)
29.8b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ l (/ x l)) (* t t)))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

61.0ms	(+ (/ l (/ x l)) (* t t))
54.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ l (/ x l)) (* t t))))
16.0ms	(/ (* t t) x)
40.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ l (/ x l)) (* t t)))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (/ l (/ x l)) (* t t))
79.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ l (/ x l)) (* t t))))
34.0ms	(/ (* t t) x)
230.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ l (/ x l)) (* t t)))))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	2114
1	472
0	150

prune616.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* l (/ l x)) (* t t))
4.0b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
9.9b	(/ (* t t) x)
29.8b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

10.0ms	(+ (* l (/ l x)) (* t t))
20.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
9.0ms	(/ (* t t) x)
30.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* l (/ l x)) (* t t))
83.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
26.0ms	(/ (* t t) x)
253.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5004
2	2151
1	475
0	150

prune519.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

regimes1.0s

Accuracy

75.4% (5.9b remaining)

Error of 9.5b against oracle of 3.6b and baseline of 27.6b

bsearch690.0ms

Steps

Iters	Range		Point
8	1.5006603296515914e+61	3.0732393759999008e+65	2.4462062203769888e+64
7	-5.065066611154205e-207	-2.784466189462717e-208	-1.7671121844270954e-207
6	-1.7922940879838889e-177	-1.4018148741289176e-178	-5.242249805913046e-178
7	-59079395044398.75	-894857869810.5616	-58247696904127.21

simplify46.0ms

Iterations

Iter	Nodes
done	71
1	71
0	56

end0.0ms

sample6.0s

Algorithm

intervals

Results

1.2s	967×	body	640	valid
1.2s	9831×	body	80	nan
819.0ms	5150×	body	80	valid
682.0ms	867×	body	1280	valid
336.0ms	590×	body	1280	nan
327.0ms	617×	body	640	nan
290.0ms	673×	body	320	valid
157.0ms	343×	body	160	valid
123.0ms	322×	body	320	nan
73.0ms	203×	body	160	nan