Details

sample16.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize7.0ms

Local error

Found 1 expressions with local error:

12.2b

(/ x (+ (* x x) 1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

20.0ms

(/ x (+ (* x x) 1))

series78.0ms

Counts

1 → 3

Calls

1 calls:

78.0ms

(/ x (+ (* x x) 1))

simplify1.8s

Counts

33 → 33

Iterations

Iter	Nodes
done	5003
3	2410
2	562
1	163
0	69

prune102.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

6.8b	(/ (* (cbrt x) (cbrt x)) (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))))
12.6b	(cbrt (+ (* x x) 1))
12.6b	(cbrt (+ (* x x) 1))
12.6b	(cbrt (+ (* x x) 1))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
16×	`add-exp-log`
9×	`cbrt-prod` `flip3-+` `flip-+`
8×	`add-cbrt-cube` `associate-/r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`associate-l/` `associate-r/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

26.0ms	(/ (* (cbrt x) (cbrt x)) (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))))
4.0ms	(cbrt (+ (* x x) 1))
4.0ms	(cbrt (+ (* x x) 1))
4.0ms	(cbrt (+ (* x x) 1))

series562.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (* (cbrt x) (cbrt x)) (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))))
126.0ms	(cbrt (+ (* x x) 1))
126.0ms	(cbrt (+ (* x x) 1))
121.0ms	(cbrt (+ (* x x) 1))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1384
1	393
0	145

prune388.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (* x (* x x)))
0.1b	(* x (* x x))
15.9b	(+ (pow x 5) (- x (* x (* x x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
10×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `pow-prod-up`
4×	`add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`associate-+r+` `sum-log` `sub-neg` `diff-log`
1×	`pow2` `+-commutative` `associate-+r-` `flip3-+` `pow-plus` `flip3--` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `flip-+` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

5.0ms	(- x (* x (* x x)))
13.0ms	(* x (* x x))
13.0ms	(+ (pow x 5) (- x (* x (* x x))))

series229.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(- x (* x (* x x)))
63.0ms	(* x (* x x))
84.0ms	(+ (pow x 5) (- x (* x (* x x))))

simplify3.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	3894
2	729
1	194
0	82

prune179.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.3b	(/ 1 (pow x 5))
0.6b	(/ 1 (* x (* x x)))
20.2b	(+ (- (/ 1 x) (/ 1 (* x (* x x)))) (/ 1 (pow x 5)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
38×	`*-un-lft-identity`
33×	`pow1`
24×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-inv`
12×	`unpow-prod-down` `div-exp` `prod-exp`
10×	`pow-prod-up` `distribute-lft-out`
9×	`pow-flip` `add-log-exp`
8×	`associate-/r*` `distribute-lft-out--`
6×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod` `associate-/l*`
4×	`cbrt-undiv` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `associate-l` `frac-add` `pow-exp`
2×	`pow2` `associate-+l+` `clear-num` `sum-log` `frac-2neg` `pow-plus` `cube-unmult` `pow-sqr` `inv-pow`
1×	`+-commutative` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-r` `*-commutative` `frac-sub` `associate-+l-` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 147

Calls

4 calls:

23.0ms	(* x (* x x))
11.0ms	(/ 1 (pow x 5))
22.0ms	(/ 1 (* x (* x x)))
202.0ms	(+ (- (/ 1 x) (/ 1 (* x (* x x)))) (/ 1 (pow x 5)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* x (* x x))
69.0ms	(/ 1 (pow x 5))
44.0ms	(/ 1 (* x (* x x)))
50.0ms	(+ (- (/ 1 x) (/ 1 (* x (* x x)))) (/ 1 (pow x 5)))

simplify1.5s

Counts

159 → 159

Iterations

Iter	Nodes
done	5051
2	1928
1	520
0	203

prune447.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 15.8b

bsearch83.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	68.55102067575892	1.0197885553055124
9	-17438.246738609338	-0.0018335887134067947	-1.0028494934768706

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

1.1s

8000×

body

valid