Details

sample67.0ms

Algorithm

intervals

Results

22.0ms	291×	body	80	valid
6.0ms	96×	body	80	nan

simplify81.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
5	114
4	93
3	68
2	45
1	21
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
4.4b	(* (* x y) z)
11.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
18.0ms	(* (* x y) z)
26.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms	(sqrt (- (* z z) (* t a)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) z)
166.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
110.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2365
1	368
0	134

prune656.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
2.7b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite500.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
24×	`associate-r` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `associate-r/` `-commutative`

Counts

4 → 112

Calls

4 calls:

15.0ms	(/ z (sqrt (- (* z z) (* t a))))
406.0ms	(- (* z z) (* t a))
68.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
8.0ms	(sqrt (- (* z z) (* t a)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ z (sqrt (- (* z z) (* t a))))
70.0ms	(- (* z z) (* t a))
140.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
122.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	2925
1	474
0	167

prune888.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize60.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* y x) (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
23.1b	(sqrt (- (* z z) (* t a)))
23.1b	(sqrt (- (* z z) (* t a)))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
29×	`add-cbrt-cube`
23×	`prod-exp` `cbrt-unprod`
19×	`pow1`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`cbrt-undiv` `div-exp` `pow-prod-down`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`associate-*r/` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`frac-times` `associate-r` `associate-l` `associate-l/` `-commutative`

Counts

4 → 82

Calls

4 calls:

125.0ms	(* (* y x) (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
14.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
8.0ms	(sqrt (- (* z z) (* t a)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(* (* y x) (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
112.0ms	(sqrt (- (* z z) (* t a)))
89.0ms	(sqrt (- (* z z) (* t a)))
103.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1642
1	368
0	127

prune909.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
2.7b	(* (/ z (sqrt (- (* z z) (* t a)))) (* y x))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
24×	`associate-l` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r` `associate-l/` `-commutative`

Counts

4 → 112

Calls

4 calls:

13.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
74.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (* y x))
15.0ms	(sqrt (- (* z z) (* t a)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ z (sqrt (- (* z z) (* t a))))
59.0ms	(- (* z z) (* t a))
167.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (* y x))
105.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1940
1	438
0	163

prune813.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.4b

regimes1.4s

Accuracy

85.2% (2.8b remaining)

Error of 6.4b against oracle of 3.6b and baseline of 22.8b

bsearch132.0ms

Steps

Iters	Range		Point
6	1.617693491755188e+79	1.7073293593355337e+80	4.846268586746066e+79
9	-9.685109581380507e+154	-6.858309052333425e+145	-1.3165060744056039e+150

simplify7.0ms

Iterations

Iter	Nodes
done	34
2	34
1	30
0	25

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	8830×	body	80	valid
255.0ms	2961×	body	80	nan