Details

sample55.0ms

Algorithm

intervals

Results

22.0ms

514×

body

valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (100.0ms)

Iter	Nodes	Cost
0	11	13
1	21	13
2	52	13
3	171	13
4	346	12
5	586	12
6	698	12
7	805	12
8	1042	12
9	1225	12
10	1228	12
done	1228	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.2b	(* (* y 4.0) (- (* z z) t))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

16×	`prod-diff`
11×	`add-sqr-sqrt`
10×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`sub-neg`
4×	`associate-r`
3×	`expm1-log1p-u` `flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u`
2×	`fma-neg` `diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 78

Calls

3 calls:

10.0ms	(- (* z z) t)
17.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
42.0ms	(* (* y 4.0) (- (* z z) t))

series270.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(- (* z z) t)
135.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
103.0ms	(* (* y 4.0) (- (* z z) t))

simplify1.6s

Counts

87 → 87

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	148	1288
1	390	1137
2	1270	994
done	5001	966

prune355.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- t (pow z 2))
6.2b	(* (* y 4.0) (- t (pow z 2)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
58×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
29×	`unpow-prod-down`
26×	`distribute-rgt-in` `distribute-lft-in`
11×	`unpow2` `sqr-pow`
8×	`associate-r` `difference-of-squares`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 125

Calls

2 calls:

29.0ms	(- t (pow z 2))
80.0ms	(* (* y 4.0) (- t (pow z 2)))

series191.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- t (pow z 2))
149.0ms	(* (* y 4.0) (- t (pow z 2)))

simplify1.8s

Counts

131 → 131

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	218	3431
1	510	2500
2	1367	1887
done	5001	1538

prune279.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.8b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x x (* t (* y 4.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma x x (* t (* y 4.0)))

series63.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

(fma x x (* t (* y 4.0)))

simplify4.9s

Counts

13 → 13

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	22	138
1	35	135
2	73	135
3	221	119
4	803	119
5	4362	119
done	5000	119

prune62.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize12.0ms

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)))
6.2b	(sqrt (- (* z z) t))
6.2b	(sqrt (- (* z z) t))

rewrite297.0ms

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×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 97

Calls

4 calls:

49.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
213.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
16.0ms	(sqrt (- (* z z) t))
16.0ms	(sqrt (- (* z z) t))

series338.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
104.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
72.0ms	(sqrt (- (* z z) t))
74.0ms	(sqrt (- (* z z) t))

simplify2.5s

Counts

109 → 109

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	142	1771
1	385	1408
2	1343	1175
done	5000	1169

prune464.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

regimes916.0ms

Accuracy

75.5% (0.8b remaining)

Error of 3.6b against oracle of 2.7b and baseline of 6.1b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	34
1	26	34
done	26	34

end0.0ms

sample1.6s

Algorithm

intervals

Results

702.0ms

15750×

body

valid