Details

sample70.0ms

Algorithm

intervals

Results

30.0ms	69×	body	1280	valid
14.0ms	51×	body	640	valid
7.0ms	20×	body	2560	valid
5.0ms	33×	body	320	valid
3.0ms	71×	body	80	valid
1.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	9
1	9
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize41.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1.0)))
3.1b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.2b	(sqrt (+ (* x x) 1.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 42

Calls

3 calls:

28.0ms	(+ x (sqrt (+ (* x x) 1.0)))
26.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
16.0ms	(sqrt (+ (* x x) 1.0))

series435.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(+ x (sqrt (+ (* x x) 1.0)))
249.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
81.0ms	(sqrt (+ (* x x) 1.0))

simplify1.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
2	1377
1	320
0	134

prune243.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
18×	`pow1`
17×	`prod-exp` `cbrt-unprod`
16×	`times-frac`
14×	`associate-r`
13×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
10×	`cbrt-undiv` `div-exp`
5×	`pow-prod-up`
4×	`pow-prod-down`
3×	`sqrt-prod` `unswap-sqr`
2×	`*-commutative` `div-inv` `add-log-exp`
1×	`pow2` `frac-times` `pow-plus` `cube-unmult` `associate-l/` `associate-r/` `pow-sqr`

Counts

2 → 77

Calls

2 calls:

13.0ms	(* x (* x x))
51.0ms	(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

series154.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(* x (* x x))
98.0ms	(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

simplify2.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	3548
1	453
0	141

prune350.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* x x))
0.2b	(/ 0.125 (* x (* x x)))
9.5b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log`
17×	`add-cbrt-cube`
16×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`log-prod` `prod-exp` `cbrt-unprod`
5×	`pow-prod-up`
4×	`distribute-lft-out`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `pow-prod-down` `associate-/l*` `add-log-exp`
2×	`log-div` `distribute-lft-out--`
1×	`pow2` `clear-num` `associate-/r` `frac-2neg` `flip3-+` `pow-plus` `cube-unmult` `rem-log-exp` `associate-r` `pow-sqr` `log-pow` `-commutative` `flip-+` `div-inv` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

17.0ms	(* x (* x x))
26.0ms	(/ 0.125 (* x (* x x)))
196.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

series276.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* x (* x x))
42.0ms	(/ 0.125 (* x (* x x)))
194.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	2238
1	351
0	138

prune221.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.125 (* x (* x x)))
0.3b	(/ 0.0625 (pow x 5))
11.7b	(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.1b	(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`add-cbrt-cube`
12×	`unpow-prod-down`
9×	`add-log-exp`
8×	`associate-/r*`
6×	`log-prod` `div-exp` `frac-sub` `associate-/l*`
5×	`pow1` `log-div`
4×	`cbrt-undiv` `distribute-lft-out--` `sqr-pow`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `diff-log` `frac-add` `flip-+` `div-inv` `flip--` `distribute-lft-out` `difference-of-squares`
1×	`pow-to-exp` `sum-log` `sub-neg` `rem-log-exp` `pow-exp` `log-pow` `associate--r+`

Counts

4 → 108

Calls

4 calls:

13.0ms	(/ 0.125 (* x (* x x)))
8.0ms	(/ 0.0625 (pow x 5))
91.0ms	(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
110.0ms	(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 0.125 (* x (* x x)))
58.0ms	(/ 0.0625 (pow x 5))
195.0ms	(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
61.0ms	(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify2.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	3946
1	694
0	268

prune591.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.1b

bsearch159.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.8987700841367662
10	-17239113253358.373	-4.96108325192681e-05	-1.0098163723001696

simplify10.0ms

Iterations

Iter	Nodes
done	40
1	40
0	34

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	2408×	body	1280	valid
835.0ms	1473×	body	640	valid
367.0ms	786×	body	2560	valid
238.0ms	808×	body	320	valid
103.0ms	2122×	body	80	valid
84.0ms	403×	body	160	valid