Details

sample438.0ms

Algorithm

intervals

Results

67.0ms	321×	body	80	nan
61.0ms	27×	body	320	valid
34.0ms	162×	body	80	valid
33.0ms	42×	body	640	valid
20.0ms	18×	body	1280	nan
19.0ms	24×	body	640	nan
17.0ms	17×	body	1280	valid
6.0ms	9×	body	320	nan
3.0ms	8×	body	160	valid
3.0ms	7×	body	160	nan

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
7	3164
6	1632
5	695
4	400
3	180
2	91
1	40
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
12.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.5b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite150.0ms

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` `insert-posit16`
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 → 84

Calls

4 calls:

55.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
39.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
45.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

473.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
56.0ms	(* (sqrt 2) t)
244.0ms	(- (* (/ (+ 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)))

simplify7.4s

Counts

96 → 96

Iterations

Iter	Nodes
3	7219
2	1568
1	440
0	170

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (/ l (/ x l)) (* t t))
4.2b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
13.5b	(* (/ 4 x) (* t t))
27.5b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
13×	`associate-l`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `times-frac`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`sqrt-div` `frac-add` `associate-*r/` `insert-posit16`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

24.0ms	(+ (/ l (/ x l)) (* t t))
28.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
29.0ms	(* (/ 4 x) (* t t))
48.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (/ l (/ x l)) (* t t))
105.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
35.0ms	(* (/ 4 x) (* t t))
492.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify640.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2070
1	527
0	176

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize67.0ms

Local error

Found 4 expressions with local error:

13.5b	(* (/ 4 x) (* t t))
27.5b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (sqrt (+ (/ l (/ x l)) (* t t))) (sqrt (+ (/ l (/ x l)) (* t t)))))))
27.7b	(sqrt (+ (/ l (/ x l)) (* t t)))
27.7b	(sqrt (+ (/ l (/ x l)) (* t t)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
20×	`add-sqr-sqrt`
16×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
12×	`pow1`
11×	`associate-*l/`
10×	`times-frac` `associate-*r/`
9×	`flip3-+` `sqrt-prod` `flip-+`
8×	`frac-add`
6×	`prod-exp` `cbrt-unprod`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`cbrt-undiv` `div-exp` `unswap-sqr`
1×	`associate-r` `*-commutative` `div-inv`

Counts

4 → 92

Calls

4 calls:

35.0ms	(* (/ 4 x) (* t t))
65.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (sqrt (+ (/ l (/ x l)) (* t t))) (sqrt (+ (/ l (/ x l)) (* t t)))))))
14.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))
26.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))

series959.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ 4 x) (* t t))
455.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (sqrt (+ (/ l (/ x l)) (* t t))) (sqrt (+ (/ l (/ x l)) (* t t)))))))
225.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))
233.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))

simplify8.0s

Counts

104 → 104

Iterations

Iter	Nodes
3	8555
2	1880
1	567
0	220

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* (/ l x) l) (* t t))
4.2b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
13.5b	(* (/ 4 x) (* t t))
27.5b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
13×	`associate-l`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `times-frac`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`sqrt-div` `frac-add` `associate-*r/` `insert-posit16`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

14.0ms	(+ (* (/ l x) l) (* t t))
49.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
37.0ms	(* (/ 4 x) (* t t))
57.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* (/ l x) l) (* t t))
74.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
30.0ms	(* (/ 4 x) (* t t))
390.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

simplify556.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2106
1	529
0	176

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

regimes659.0ms

Accuracy

77.7% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.1b

bsearch512.0ms

Steps

Iters	Range		Point
8	3.497382872215968e+81	1.6000133661041192e+84	4.8064993713964147e+83
8	-9.097297478766575e+61	-4.797907393882946e+57	-8.954275544416124e+61

simplify12.0ms

Iterations

Iter	Nodes
2	51
1	51
0	39

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.2s	9928×	body	80	nan
1.3s	1013×	body	640	valid
1.3s	835×	body	1280	valid
1.1s	5169×	body	80	valid
772.0ms	621×	body	320	valid
636.0ms	605×	body	1280	nan
491.0ms	629×	body	640	nan
268.0ms	335×	body	320	nan
209.0ms	362×	body	160	valid
61.0ms	174×	body	160	nan