Details

sample235.0ms

Algorithm

intervals

Results

64.0ms	341×	body	80	nan
14.0ms	168×	body	80	valid
12.0ms	35×	body	640	valid
9.0ms	24×	body	1280	valid
7.0ms	23×	body	640	nan
6.0ms	23×	body	320	valid
5.0ms	14×	body	1280	nan
1.0ms	5×	body	320	nan
1.0ms	6×	body	160	valid
0.0ms	3×	body	160	nan

simplify5.5s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize97.0ms

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)
11.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite329.0ms

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:

113.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
28.0ms	(* (sqrt 2.0) t)
53.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
128.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series4.0s

Counts

4 → 12

Calls

4 calls:

975.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
70.0ms	(* (sqrt 2.0) t)
557.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.4s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify3.6s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
2	1593
1	449
0	171

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.3b

localize141.0ms

Local error

Found 4 expressions with local error:

3.2b	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
5.9b	(/ (* l l) x)
9.3b	(/ x (* t t))
26.7b	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `flip3-+` `sqrt-div` `div-exp` `frac-add` `associate-r/` `flip-+` `insert-posit16` `associate-/l*`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

45.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
17.0ms	(/ (* l l) x)
22.0ms	(/ x (* t t))
116.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

series750.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
34.0ms	(/ (* l l) x)
59.0ms	(/ x (* t t))
515.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

simplify3.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2001
1	509
0	172

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

localize149.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.2b	(+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t))))
9.3b	(/ x (* t t))
26.7b	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `associate-*r/` `insert-posit16`
3×	`times-frac` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 68

Calls

4 calls:

22.0ms	(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
68.0ms	(+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t))))
23.0ms	(/ x (* t t))
97.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))

series905.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
175.0ms	(+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t))))
54.0ms	(/ x (* t t))
555.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))

simplify3.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1660
1	435
0	155

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize289.0ms

Local error

Found 4 expressions with local error:

9.3b	(/ x (* t t))
9.3b	(/ x (* t t))
26.7b	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))
26.7b	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`pow1` `times-frac` `sqrt-prod` `associate-/l*`
4×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `associate-*r/` `flip-+` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

21.0ms	(/ x (* t t))
19.0ms	(/ x (* t t))
77.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))
75.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ x (* t t))
60.0ms	(/ x (* t t))
534.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))
608.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (/ 4.0 (/ x (* t t)))))

simplify3.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1302
1	345
0	123

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

regimes2.1s

Accuracy

76.8% (5.4b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 27.1b

bsearch436.0ms

Steps

Iters	Range		Point
8	2.0215799830271626e+96	1.863612731888614e+99	1.4235245726759946e+99
7	-8.62882115661326e+99	-1.9133687329772835e+98	-3.6519455046374026e+98

simplify43.0ms

Iterations

Iter	Nodes
done	59
1	59
0	48

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	10091×	body	80	nan
717.0ms	903×	body	1280	valid
711.0ms	5042×	body	80	valid
690.0ms	1038×	body	640	valid
345.0ms	607×	body	1280	nan
317.0ms	627×	body	640	nan
278.0ms	661×	body	320	valid
137.0ms	335×	body	320	nan
105.0ms	356×	body	160	valid
44.0ms	186×	body	160	nan