Details

sample107.0ms

Algorithm

intervals

Results

61.0ms	286×	body	80	valid
16.0ms	98×	body	80	nan

simplify91.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize35.0ms

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)))

rewrite81.0ms

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:

14.0ms	(- (* z z) (* t a))
16.0ms	(* (* x y) z)
35.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms	(sqrt (- (* z z) (* t a)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* z z) (* t a))
42.0ms	(* (* x y) z)
102.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
93.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	2362
1	371
0	138

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

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:

12.0ms	(/ z (sqrt (- (* z z) (* t a))))
8.0ms	(- (* z z) (* t a))
63.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
16.0ms	(sqrt (- (* z z) (* t a)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ z (sqrt (- (* z z) (* t a))))
50.0ms	(- (* z z) (* t a))
118.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
96.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5002
2	2880
1	480
0	171

prune753.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.7b	(* x (/ z (sqrt (- (* z z) (* t a)))))
2.0b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
25.9b	(sqrt (- (* z z) (* t a)))

rewrite119.0ms

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:

8.0ms	(- (* z z) (* t a))
41.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
60.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
7.0ms	(sqrt (- (* z z) (* t a)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* z z) (* t a))
90.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
122.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
75.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1928
1	444
0	166

prune571.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize57.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (* y x) (* (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
25.9b	(sqrt (- (* z z) (* t a)))
25.9b	(sqrt (- (* z z) (* t a)))
25.9b	(sqrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
29×	`add-cbrt-cube`
18×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-l/` `associate-r/` `div-inv` `associate-/l`

Counts

4 → 85

Calls

4 calls:

20.0ms	(/ (* y x) (* (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
10.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (* y x) (* (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
88.0ms	(sqrt (- (* z z) (* t a)))
89.0ms	(sqrt (- (* z z) (* t a)))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify2.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1922
1	409
0	134

prune613.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

regimes698.0ms

Accuracy

83.9% (3.1b remaining)

Error of 6.6b against oracle of 3.4b and baseline of 22.7b

bsearch141.0ms

Steps

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

simplify5.0ms

Iterations

Iter	Nodes
done	30
2	30
1	28
0	21

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	8868×	body	80	valid
409.0ms	2919×	body	80	nan