Details

sample191.0ms

Algorithm

intervals

Results

106.0ms

513×

body

valid

simplify11.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4982
4	2301
3	721
2	217
1	67
0	28

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize108.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 4.0) i)
0.2b	(* (* x 18.0) y)
4.5b	(* (* (* x 18.0) y) z)
6.4b	(* (* (* (* x 18.0) y) z) t)

rewrite654.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1` `add-exp-log` `add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-r`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-l` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

4 → 89

Calls

4 calls:

54.0ms	(* (* x 4.0) i)
40.0ms	(* (* x 18.0) y)
126.0ms	(* (* (* x 18.0) y) z)
403.0ms	(* (* (* (* x 18.0) y) z) t)

series530.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* x 4.0) i)
117.0ms	(* (* x 18.0) y)
104.0ms	(* (* (* x 18.0) y) z)
271.0ms	(* (* (* (* x 18.0) y) z) t)

simplify5.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	1347
1	371
0	141

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* j 27.0) k)
0.2b	(* (* x 4.0) i)
4.5b	(* (* 18.0 (* x y)) z)
6.4b	(* (* (* 18.0 (* x y)) z) t)

rewrite737.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1` `add-exp-log` `add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-r`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-l` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

4 → 89

Calls

4 calls:

87.0ms	(* (* j 27.0) k)
90.0ms	(* (* x 4.0) i)
185.0ms	(* (* 18.0 (* x y)) z)
299.0ms	(* (* (* 18.0 (* x y)) z) t)

series236.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* j 27.0) k)
36.0ms	(* (* x 4.0) i)
79.0ms	(* (* 18.0 (* x y)) z)
89.0ms	(* (* (* 18.0 (* x y)) z) t)

simplify5.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1678
1	445
0	167

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize199.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* y x) 18.0)
0.3b	(* 27.0 (* k j))
3.4b	(fma (* (* (* y x) 18.0) t) z (- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j)))))
3.8b	(* (* (* y x) 18.0) t)

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef`

Counts

4 → 73

Calls

4 calls:

39.0ms	(* (* y x) 18.0)
34.0ms	(* 27.0 (* k j))
1.0ms	(fma (* (* (* y x) 18.0) t) z (- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j)))))
149.0ms	(* (* (* y x) 18.0) t)

series5.1s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* y x) 18.0)
37.0ms	(* 27.0 (* k j))
5.0s	(fma (* (* (* y x) 18.0) t) z (- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j)))))
51.0ms	(* (* (* y x) 18.0) t)

simplify7.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4588
2	1119
1	319
0	135

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.6b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j))))
0.3b	(* 27.0 (* k j))
3.4b	(fma (* (* y x) (* 18.0 t)) z (- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j)))))
3.8b	(* (* y x) (* 18.0 t))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-r` `*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `associate--r+`

Counts

4 → 73

Calls

4 calls:

18.0ms	(- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j))))
32.0ms	(* 27.0 (* k j))
1.0ms	(fma (* (* y x) (* 18.0 t)) z (- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j)))))
70.0ms	(* (* y x) (* 18.0 t))

series4.7s

Counts

4 → 12

Calls

4 calls:

629.0ms	(- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j))))
39.0ms	(* 27.0 (* k j))
4.0s	(fma (* (* y x) (* 18.0 t)) z (- (* b c) (fma 4.0 (fma t a (* i x)) (* 27.0 (* k j)))))
48.0ms	(* (* y x) (* 18.0 t))

simplify3.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	1345
1	397
0	166

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes5.9s

Accuracy

44.4% (2.6b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 4.8b

bsearch613.0ms

Steps

Iters	Range		Point
9	1.311814387936794e-169	1.835842643712574e-164	1.8068831272582442e-164
8	-1.5133775762134652e+24	-2.2897742511483079e+21	-7.702228306921126e+21

simplify26.0ms

Iterations

Iter	Nodes
done	79
1	79
0	54

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.4s

16178×

body

valid