Details

sample304.0ms

Algorithm

intervals

Results

84.0ms	333×	body	80	valid
83.0ms	65×	body	10240	exit
66.0ms	53×	body	1280	valid
29.0ms	35×	body	640	valid
9.0ms	16×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2743
3	459
2	122
1	48
0	19

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 eps) x)
0.0b	(exp (- (* (+ 1 eps) x)))
0.0b	(exp (- (* (- 1 eps) x)))
2.1b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3-+` `flip3--` `flip-+` `flip--`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`associate-l` `insert-posit16` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 152

Calls

4 calls:

15.0ms	(* (+ 1 eps) x)
5.0ms	(exp (- (* (+ 1 eps) x)))
7.0ms	(exp (- (* (- 1 eps) x)))
43.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (+ 1 eps) x)
18.0ms	(exp (- (* (+ 1 eps) x)))
23.0ms	(exp (- (* (- 1 eps) x)))
141.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.4s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
1	1227
0	364

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2 (* x x))
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 2/3)
6.0b	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
11×	`add-log-exp`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `pow-plus` `associate-r*` `pow-prod-up` `add-cube-cbrt`
4×	`insert-posit16`
2×	`pow2` `associate-+r+` `sum-log` `sub-neg` `diff-log` `associate-l` `pow-sqr` `*-commutative`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `pow3` `flip-+` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

7.0ms	(- 2 (* x x))
15.0ms	(* (* x x) x)
50.0ms	(* (* (* x x) x) 2/3)
56.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- 2 (* x x))
50.0ms	(* (* x x) x)
71.0ms	(* (* (* x x) x) 2/3)
59.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))

simplify2.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	2584
1	331
0	110

prune382.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

2.6b	(cbrt (* (* (+ (* (* (* x x) x) 2/3) (- 2 (* x x))) (+ (* (* (* x x) x) 2/3) (- 2 (* x x)))) (+ (* (* (* x x) x) 2/3) (- 2 (* x x)))))
6.0b	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))
6.0b	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))
6.0b	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))

rewrite875.0ms

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:

670.0ms	(cbrt (* (* (+ (* (* (* x x) x) 2/3) (- 2 (* x x))) (+ (* (* (* x x) x) 2/3) (- 2 (* x x)))) (+ (* (* (* x x) x) 2/3) (- 2 (* x x)))))
78.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))
60.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))
65.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (* (* (+ (* (* (* x x) x) 2/3) (- 2 (* x x))) (+ (* (* (* x x) x) 2/3) (- 2 (* x x)))) (+ (* (* (* x x) x) 2/3) (- 2 (* x x)))))
41.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))
64.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))
43.0ms	(+ (* (* (* x x) x) 2/3) (- 2 (* x x)))

simplify2.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2443
1	429
0	136

prune493.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2/3 x) (* x x))
0.3b	(* 2/3 x)
4.5b	(posit16->real (real->posit16 (- (+ 2 (* (* 2/3 x) (* x x))) (* x x))))
6.0b	(- (+ 2 (* (* 2/3 x) (* x x))) (* x x))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l` `insert-posit16`
2×	`diff-log` `*-commutative`
1×	`sum-log` `sub-neg` `flip3--` `associate--l+` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

48.0ms	(* (* 2/3 x) (* x x))
11.0ms	(* 2/3 x)
0.0ms	(posit16->real (real->posit16 (- (+ 2 (* (* 2/3 x) (* x x))) (* x x))))
39.0ms	(- (+ 2 (* (* 2/3 x) (* x x))) (* x x))

series181.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* 2/3 x) (* x x))
21.0ms	(* 2/3 x)
46.0ms	(posit16->real (real->posit16 (- (+ 2 (* (* 2/3 x) (* x x))) (* x x))))
61.0ms	(- (+ 2 (* (* 2/3 x) (* x x))) (* x x))

simplify1.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1605
1	277
0	101

prune567.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.3b

regimes179.0ms

Accuracy

96.4% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.0b

bsearch207.0ms

Steps

Iters	Range		Point
7	1.5150962181605006	32.81305289360078	30.43326508471591

simplify11.0ms

Iterations

Iter	Nodes
done	60
3	60
2	58
1	49
0	30

end0.0ms

sample11.6s

Algorithm

intervals

Results

4.0s	1905×	body	10240	exit
2.6s	10231×	body	80	valid
2.4s	1648×	body	1280	valid
1.7s	1245×	body	640	valid
392.0ms	650×	body	320	valid
211.0ms	314×	body	160	valid