Details

sample79.0ms

Algorithm

intervals

Results

35.0ms	294×	body	80	valid
7.0ms	91×	body	80	nan

simplify121.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
6.7b	(* (* x y) z)
7.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite71.0ms

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:

7.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) z)
35.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms	(sqrt (- (* z z) (* t a)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* z z) (* t a))
30.0ms	(* (* x y) z)
121.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
92.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1403
1	359
0	134

prune599.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
3.6b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite99.0ms

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×	`sqrt-div` `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` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

27.0ms	(/ (sqrt (- (* z z) (* t a))) z)
12.0ms	(- (* z z) (* t a))
33.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
20.0ms	(sqrt (- (* z z) (* t a)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (sqrt (- (* z z) (* t a))) z)
54.0ms	(- (* z z) (* t a))
133.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
73.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1895
1	557
0	210

prune885.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.9b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 227

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
21.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
51.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
7.0ms	(sqrt (- (* z z) (* t a)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* z z) (* t a))
80.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
124.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
96.0ms	(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts

239 → 239

Iterations

Iter	Nodes
done	5001
2	2702
1	920
0	330

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize114.0ms

Local error

Found 4 expressions with local error:

1.9b	(* x (* (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)))))
22.9b	(sqrt (- (* z z) (* t a)))
22.9b	(sqrt (- (* z z) (* t a)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-exp-log`
56×	`add-cbrt-cube`
43×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
12×	`pow1`
11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`associate-*r/` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `pow-prod-down` `flip--`
1×	`frac-times` `associate-r` `associate-l/` `-commutative`

Counts

4 → 94

Calls

4 calls:

371.0ms	(* x (* (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)))))
14.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* x (* (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)))))
105.0ms	(sqrt (- (* z z) (* t a)))
64.0ms	(sqrt (- (* z z) (* t a)))
83.0ms	(sqrt (- (* z z) (* t a)))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2543
1	599
0	185

prune810.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

regimes876.0ms

Accuracy

86.6% (2.5b remaining)

Error of 5.7b against oracle of 3.2b and baseline of 22.0b

bsearch154.0ms

Steps

Iters	Range		Point
9	3.376770166686323e+133	6.368260996247714e+142	1.6462812507916996e+140
9	-1.8254437613711665e+160	-4.7960040549310305e+153	-1.2479983353367598e+154

simplify17.0ms

Iterations

Iter	Nodes
done	36
2	36
1	33
0	27

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8830×	body	80	valid
142.0ms	3000×	body	80	nan