Details

sample81.0ms

Algorithm

intervals

Results

31.0ms	286×	body	80	valid
10.0ms	98×	body	80	nan

simplify356.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	103
6	103
5	97
4	70
3	53
2	36
1	21
0	12

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize145.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
4.3b	(* (* x y) z)
10.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.9b	(sqrt (- (* z z) (* t a)))

rewrite233.0ms

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` `insert-posit16`
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 → 80

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
70.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
38.0ms	(sqrt (- (* z z) (* t a)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* z z) (* t a))
53.0ms	(* (* x y) z)
246.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
111.0ms	(sqrt (- (* z z) (* t a)))

simplify3.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1462
1	364
0	138

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize115.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
4.1b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.9b	(sqrt (- (* z z) (* t a)))

rewrite232.0ms

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/` `insert-posit16` `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 → 116

Calls

4 calls:

39.0ms	(/ z (sqrt (- (* z z) (* t a))))
21.0ms	(- (* z z) (* t a))
128.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
36.0ms	(sqrt (- (* z z) (* t a)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ z (sqrt (- (* z z) (* t a))))
55.0ms	(- (* z z) (* t a))
247.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
148.0ms	(sqrt (- (* z z) (* t a)))

simplify4.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1736
1	478
0	170

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize138.0ms

Local error

Found 4 expressions with local error:

0.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
0.8b	(- (* z z) (* t a))
2.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
25.9b	(sqrt (- (* z z) (* t a)))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down` `insert-posit16`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 96

Calls

4 calls:

148.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
20.0ms	(- (* z z) (* t a))
124.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
29.0ms	(sqrt (- (* z z) (* t a)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
67.0ms	(- (* z z) (* t a))
164.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
139.0ms	(sqrt (- (* z z) (* t a)))

simplify3.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	1379
1	430
0	165

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

localize150.0ms

Local error

Found 4 expressions with local error:

0.6b	(* x (* (* y z) (/ 1 (sqrt (- (* z z) (* t a))))))
0.8b	(- (* z z) (* t a))
7.1b	(* (* y z) (/ 1 (sqrt (- (* z z) (* t a)))))
25.9b	(sqrt (- (* z z) (* t a)))

rewrite479.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
34×	`add-cbrt-cube`
33×	`prod-exp`
25×	`associate-r`
20×	`add-sqr-sqrt`
19×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
17×	`cbrt-unprod`
12×	`sqrt-prod`
9×	`pow-prod-down`
8×	`div-exp`
6×	`add-log-exp`
4×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `associate-l` `associate-*r/` `insert-posit16`
3×	`flip3--` `flip--`
2×	`associate-/r/` `un-div-inv` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 111

Calls

4 calls:

237.0ms	(* x (* (* y z) (/ 1 (sqrt (- (* z z) (* t a))))))
37.0ms	(- (* z z) (* t a))
176.0ms	(* (* y z) (/ 1 (sqrt (- (* z z) (* t a)))))
20.0ms	(sqrt (- (* z z) (* t a)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* x (* (* y z) (/ 1 (sqrt (- (* z z) (* t a))))))
87.0ms	(- (* z z) (* t a))
147.0ms	(* (* y z) (/ 1 (sqrt (- (* z z) (* t a)))))
115.0ms	(sqrt (- (* z z) (* t a)))

simplify4.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1694
1	535
0	186

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.3b

regimes2.8s

Accuracy

84.6% (3.0b remaining)

Error of 6.4b against oracle of 3.5b and baseline of 22.6b

bsearch171.0ms

Steps

Iters	Range		Point
6	4.976139366752269e+101	2.1828196885728892e+102	1.1757746865835248e+102
10	-1.7445526317241335e+161	-1.6517060916622868e+149	-7.751960138449552e+153

simplify20.0ms

Iterations

Iter	Nodes
done	30
2	30
1	28
0	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

941.0ms	8868×	body	80	valid
659.0ms	2919×	body	80	nan