Details

sample42.0ms

Algorithm

intervals

Results

15.0ms	282×	body	80	valid
5.0ms	102×	body	80	nan

simplify104.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
6.1b	(* (* x y) z)
11.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite76.0ms

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:

6.0ms	(- (* z z) (* t a))
13.0ms	(* (* x y) z)
40.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms	(sqrt (- (* z z) (* t a)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* z z) (* t a))
45.0ms	(* (* x y) z)
125.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1403
1	359
0	134

prune563.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
3.8b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite83.0ms

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:

17.0ms	(/ z (sqrt (- (* z z) (* t a))))
6.0ms	(- (* z z) (* t a))
47.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(sqrt (- (* z z) (* t a)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ z (sqrt (- (* z z) (* t a))))
57.0ms	(- (* z z) (* t a))
144.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
105.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1762
1	472
0	166

prune846.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.2b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite113.0ms

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`
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 → 92

Calls

4 calls:

11.0ms	(- (* z z) (* t a))
51.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
41.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
7.0ms	(sqrt (- (* z z) (* t a)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* z z) (* t a))
82.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
120.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
88.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1364
1	425
0	161

prune671.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.3b

localize41.0ms

Local error

Found 4 expressions with local error:

2.2b	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
7.1b	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
23.8b	(cbrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-cbrt-cube` `associate-r` `add-exp-log`
33×	`*-un-lft-identity` `add-cube-cbrt`
22×	`sqrt-prod`
17×	`cbrt-prod`
16×	`associate-l`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`cbrt-div`
5×	`associate-*r/`
4×	`pow-prod-down` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow1/3` `sqrt-div` `associate-l/` `associate-/r/` `-commutative` `div-inv`

Counts

4 → 127

Calls

4 calls:

50.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
52.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
12.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))

series818.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
234.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
136.0ms	(cbrt (- (* z z) (* t a)))
123.0ms	(cbrt (- (* z z) (* t a)))

simplify2.5s

Counts

139 → 139

Iterations

Iter	Nodes
done	5003
2	2797
1	777
0	264

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.3b

regimes1.4s

Accuracy

84.9% (2.9b remaining)

Error of 6.3b against oracle of 3.3b and baseline of 22.7b

bsearch131.0ms

Steps

Iters	Range		Point
8	4.271611683557293e+96	5.363233345281319e+99	2.466136078144351e+99
10	-5.3731394571269196e+157	-1.8419256827959713e+147	-7.806488284801272e+152

simplify5.0ms

Iterations

Iter	Nodes
done	30
2	30
1	27
0	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

845.0ms	8855×	body	80	valid
242.0ms	2804×	body	80	nan