Details

sample64.0ms

Algorithm

intervals

Results

25.0ms	288×	body	80	valid
6.0ms	78×	body	80	nan

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	118
5	118
4	97
3	72
2	46
1	22
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
5.1b	(* (* x y) z)
9.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite83.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
15.0ms	(* (* x y) z)
39.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms	(sqrt (- (* z z) (* t a)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* z z) (* t a))
30.0ms	(* (* x y) z)
124.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
107.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2299
1	385
0	146

prune736.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
2.7b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `div-inv`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 142

Calls

4 calls:

14.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
28.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
17.0ms	(sqrt (- (* z z) (* t a)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (sqrt (- (* z z) (* t a))) z)
44.0ms	(- (* z z) (* t a))
112.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
88.0ms	(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	3689
1	591
0	222

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
2.0b	(/ (* x y) (sqrt (- (* z z) (* t a))))
7.8b	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
23.7b	(sqrt (- (* z z) (* t a)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `associate-l` `sqrt-prod`
7×	`pow1`
6×	`associate-/r*` `sqrt-div` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `flip3--` `div-exp` `associate-/r/` `log1p-expm1-u` `flip--`
3×	`associate-r`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `-commutative` `associate-/l*` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
30.0ms	(/ (* x y) (sqrt (- (* z z) (* t a))))
78.0ms	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
17.0ms	(sqrt (- (* z z) (* t a)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* z z) (* t a))
108.0ms	(/ (* x y) (sqrt (- (* z z) (* t a))))
121.0ms	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
93.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

110 → 110

Iterations

Iter	Nodes
done	5002
2	2236
1	411
0	156

prune706.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
1.2b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
3.0b	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

828×	`times-frac`
400×	`add-sqr-sqrt`
399×	`*-un-lft-identity` `add-cube-cbrt`
147×	`sqrt-prod`
73×	`associate-/r*`
25×	`associate-/l*`
22×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `flip3--` `sqrt-div` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `associate-/l/`

Counts

4 → 443

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
32.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
53.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
17.0ms	(sqrt (- (* z z) (* t a)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* z z) (* t a))
120.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
139.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
76.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

455 → 455

Iterations

Iter	Nodes
done	5001
1	1954
0	667

prune3.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.0b

regimes1.3s

Accuracy

79.5% (4.2b remaining)

Error of 7.3b against oracle of 3.2b and baseline of 23.5b

bsearch144.0ms

Steps

Iters	Range		Point
8	2.102189781311534e-06	0.007353525239946609	0.007263648305243834
9	-2.0853333964574043e+66	-6.594765004499323e+58	-2.1069764153509517e+65

simplify4.0ms

Iterations

Iter	Nodes
done	33
1	33
0	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

778.0ms	8822×	body	80	valid
632.0ms	2998×	body	80	nan