Details

sample30.0ms

Algorithm

intervals

Results

14.0ms

491×

body

valid

simplify999.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	19	13
2	49	13
3	136	13
4	287	13
5	418	13
6	500	13
7	567	13
8	709	13
9	1004	13
done	1004	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.2b	(* (* y 4.0) (- (* z z) t))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `sub-neg`
4×	`distribute-rgt-in` `add-cube-cbrt` `-un-lft-identity` `distribute-lft-in` `associate-r*` `associate--r+`
3×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 54

Calls

3 calls:

3.0ms	(- (* z z) t)
3.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
14.0ms	(* (* y 4.0) (- (* z z) t))

series157.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(- (* z z) t)
75.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
58.0ms	(* (* y 4.0) (- (* z z) t))

simplify810.0ms

Counts

63 → 63

Iterations

Useful iterations: done (807.0ms)

Iter	Nodes	Cost
0	103	843
1	289	802
2	1111	696
done	5001	692

prune145.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
5.2b	(sqrt (- (* z z) t))
5.2b	(sqrt (- (* z z) t))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-r`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 89

Calls

4 calls:

15.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
48.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series233.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
66.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
50.0ms	(sqrt (- (* z z) t))
45.0ms	(sqrt (- (* z z) t))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	136	1685
1	372	1362
2	1385	1120
done	5000	1116

prune245.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
5.2b	(sqrt (- (* z z) t))
5.2b	(sqrt (- (* z z) t))
5.2b	(sqrt (- (* z z) t))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`associate-*r/`
23×	`sqrt-prod`
21×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
14×	`associate-*l/`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-l` `*-commutative`

Counts

4 → 105

Calls

4 calls:

169.0ms	(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series210.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
45.0ms	(sqrt (- (* z z) t))
50.0ms	(sqrt (- (* z z) t))
50.0ms	(sqrt (- (* z z) t))

simplify1.1s

Counts

117 → 117

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	184	3218
1	509	2689
2	1773	1875
done	5001	1872

prune388.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ z (sqrt t))
0.0b	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
0.1b	(* (* y 4.0) (+ z (sqrt t)))
0.1b	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `associate-r/` `associate-r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`
4×	`frac-times` `flip3--` `flip--` `associate--r+`
2×	`associate-l` `associate-l/` `-commutative` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `diff-log` `sum-log` `sqrt-prod` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

3.0ms	(+ z (sqrt t))
3.0ms	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
15.0ms	(* (* y 4.0) (+ z (sqrt t)))
42.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ z (sqrt t))
84.0ms	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
54.0ms	(* (* y 4.0) (+ z (sqrt t)))
93.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

simplify1.0s

Counts

99 → 99

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	170	1672
1	517	1414
2	2492	1206
done	5000	1200

prune228.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 1.9b

regimes357.0ms

Accuracy

83.8% (0.5b remaining)

Error of 3.3b against oracle of 2.8b and baseline of 6.1b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	25	36
done	25	36

end0.0ms

sample874.0ms

Algorithm

intervals

Results

485.0ms

15938×

body

valid