Details

sample246.0ms

Algorithm

intervals

Results

68.0ms	65×	body	1280	valid
54.0ms	42×	body	640	valid
49.0ms	47×	body	10240	exit
42.0ms	288×	body	80	valid
11.0ms	21×	body	320	valid
1.0ms	3×	body	160	valid

simplify677.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	1521
3	381
2	122
1	48
0	19

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (+ -1 eps)))
0.0b	(exp (* x (- -1 eps)))
0.0b	(exp (* x (- -1 eps)))
1.0b	(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-log-exp`
16×	`*-un-lft-identity`
10×	`exp-sum`
6×	`add-sqr-sqrt` `sub-neg` `diff-log` `distribute-lft-out--`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt` `insert-posit16`
3×	`exp-prod` `flip3--` `exp-to-pow` `flip--` `rem-exp-log`
2×	`sum-log` `flip3-+` `flip-+` `distribute-lft-out` `associate--r+`
1×	`associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

5.0ms	(exp (* x (+ -1 eps)))
7.0ms	(exp (* x (- -1 eps)))
6.0ms	(exp (* x (- -1 eps)))
179.0ms	(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* x (+ -1 eps)))
25.0ms	(exp (* x (- -1 eps)))
19.0ms	(exp (* x (- -1 eps)))
142.0ms	(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	2001
2	1509
1	398
0	146

prune409.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* 2/3 x) (* x x))
0.3b	(* 2/3 x)
5.6b	(+ (* (* 2/3 x) (* x x)) (- 2 (* x x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`associate-+r+` `sum-log` `*-commutative`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

28.0ms	(* (* 2/3 x) (* x x))
5.0ms	(* 2/3 x)
27.0ms	(+ (* (* 2/3 x) (* x x)) (- 2 (* x x)))

series106.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (* 2/3 x) (* x x))
24.0ms	(* 2/3 x)
39.0ms	(+ (* (* 2/3 x) (* x x)) (- 2 (* x x)))

simplify640.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2003
2	869
1	232
0	88

prune226.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (* 2/3 x))
0.3b	(* 2/3 x)
5.6b	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`associate-+r+` `sum-log` `*-commutative`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

23.0ms	(* (* x x) (* 2/3 x))
5.0ms	(* 2/3 x)
32.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (* x x) (* 2/3 x))
21.0ms	(* 2/3 x)
45.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))

simplify816.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2001
2	924
1	256
0	88

prune268.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize55.0ms

Local error

Found 4 expressions with local error:

1.5b	(cbrt (* (* (+ (* (* x x) (* 2/3 x)) (- 2 (* x x))) (+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))) (+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))))
5.6b	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))
5.6b	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))
5.6b	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`cbrt-div`
19×	`add-log-exp`
14×	`associate-*l/`
8×	`associate-*r/`
6×	`associate-+r+` `sum-log`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`+-commutative` `associate-+r-` `sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 85

Calls

4 calls:

354.0ms	(cbrt (* (* (+ (* (* x x) (* 2/3 x)) (- 2 (* x x))) (+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))) (+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))))
28.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))
26.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))
50.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* (* (+ (* (* x x) (* 2/3 x)) (- 2 (* x x))) (+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))) (+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))))
53.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))
46.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))
39.0ms	(+ (* (* x x) (* 2/3 x)) (- 2 (* x x)))

simplify718.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2001
1	425
0	136

prune489.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.6b

regimes152.0ms

Accuracy

96.6% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.3b

bsearch283.0ms

Steps

Iters	Range		Point
9	0.5242927222148749	19453700.538560145	41.6575809018513

simplify13.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample10.9s

Algorithm

intervals

Results

3.7s	1899×	body	10240	exit
2.6s	9973×	body	80	valid
2.3s	1743×	body	1280	valid
1.5s	1295×	body	640	valid
352.0ms	620×	body	320	valid
104.0ms	307×	body	160	valid