Details

sample39.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	10	25
1	32	25
2	169	23
3	1029	19
done	5001	15

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ 1.0 (* i i))
0.7b	(/ (/ 1 (* 2.0 2.0)) (- (* 2.0 2.0) (/ 1.0 (* i i))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
40×	`add-sqr-sqrt`
26×	`add-exp-log`
24×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube` `difference-of-squares`
13×	`div-exp`
10×	`associate-/l*`
8×	`div-inv`
7×	`cbrt-undiv`
6×	`associate-/r*`
4×	`prod-exp`
2×	`pow1` `expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`flip3--` `flip--` `associate-/l/`

Counts

2 → 95

Calls

2 calls:

9.0ms	(/ 1.0 (* i i))
48.0ms	(/ (/ 1 (* 2.0 2.0)) (- (* 2.0 2.0) (/ 1.0 (* i i))))

series132.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ 1.0 (* i i))
80.0ms	(/ (/ 1 (* 2.0 2.0)) (- (* 2.0 2.0) (/ 1.0 (* i i))))

simplify1.3s

Counts

101 → 101

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	209	2015
1	527	1914
2	2453	1764
done	5000	1762

prune246.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ (/ 1 (* 2.0 2.0)) (+ 2.0 (/ (sqrt 1.0) i))) (- 2.0 (/ (sqrt 1.0) i)))
0.1b	(/ (/ 1 (* 2.0 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

671×	`times-frac`
463×	`add-sqr-sqrt`
381×	`*-un-lft-identity`
183×	`add-cube-cbrt`
105×	`difference-of-squares`
64×	`distribute-lft-out`
49×	`add-exp-log`
47×	`div-inv`
41×	`associate-/l*`
35×	`sqrt-prod` `distribute-lft-out--`
30×	`div-exp`
25×	`add-cbrt-cube`
20×	`associate-/r/`
14×	`cbrt-undiv`
11×	`associate-/r*`
9×	`flip3-+` `flip-+`
6×	`prod-exp`
4×	`rec-exp` `1-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `flip--`

Counts

2 → 370

Calls

2 calls:

108.0ms	(/ (/ (/ 1 (* 2.0 2.0)) (+ 2.0 (/ (sqrt 1.0) i))) (- 2.0 (/ (sqrt 1.0) i)))
69.0ms	(/ (/ 1 (* 2.0 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))

series282.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(/ (/ (/ 1 (* 2.0 2.0)) (+ 2.0 (/ (sqrt 1.0) i))) (- 2.0 (/ (sqrt 1.0) i)))
73.0ms	(/ (/ 1 (* 2.0 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))

simplify672.0ms

Counts

376 → 376

Iterations

Useful iterations: done (632.0ms)

Iter	Nodes	Cost
0	466	12719
1	1270	11963
done	5000	11675

prune729.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ 1.0 (* i i))
0.7b	(/ 1 (- (* 2.0 2.0) (/ 1.0 (* i i))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`difference-of-squares`
6×	`associate-/r` `associate-/l`
4×	`div-exp`
3×	`pow1` `cbrt-undiv`
2×	`expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `prod-exp` `flip--` `cbrt-unprod` `inv-pow`

Counts

2 → 66

Calls

2 calls:

13.0ms	(/ 1.0 (* i i))
31.0ms	(/ 1 (- (* 2.0 2.0) (/ 1.0 (* i i))))

series122.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ 1.0 (* i i))
67.0ms	(/ 1 (- (* 2.0 2.0) (/ 1.0 (* i i))))

simplify887.0ms

Counts

72 → 72

Iterations

Useful iterations: done (883.0ms)

Iter	Nodes	Cost
0	140	989
1	319	909
2	1423	839
done	5001	835

prune177.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 16.0 (pow i 6))
0.0b	(fma 4.0 (pow i 4) (* 16.0 (pow i 6)))
0.2b	(* (/ 1 (* 2.0 2.0)) (- (fma 1.0 (* i i) (fma 4.0 (pow i 4) (* 16.0 (pow i 6))))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
21×	`add-sqr-sqrt`
17×	`associate-r`
14×	`add-cbrt-cube`
13×	`prod-exp`
12×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`associate-l`
6×	`unswap-sqr`
5×	`pow1` `times-frac` `cbrt-unprod`
4×	`unpow-prod-down` `div-exp`
3×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `distribute-neg-in` `1-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `neg-mul-1` `distribute-lft-in` `pow-prod-down` `associate-*l/` `pow-exp` `distribute-rgt-neg-out` `div-inv`

Counts

3 → 82

Calls

3 calls:

26.0ms	(* 16.0 (pow i 6))
1.0ms	(fma 4.0 (pow i 4) (* 16.0 (pow i 6)))
71.0ms	(* (/ 1 (* 2.0 2.0)) (- (fma 1.0 (* i i) (fma 4.0 (pow i 4) (* 16.0 (pow i 6))))))

series347.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* 16.0 (pow i 6))
175.0ms	(fma 4.0 (pow i 4) (* 16.0 (pow i 6)))
114.0ms	(* (/ 1 (* 2.0 2.0)) (- (fma 1.0 (* i i) (fma 4.0 (pow i 4) (* 16.0 (pow i 6))))))

simplify2.2s

Counts

91 → 91

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	170	1730
1	456	1659
2	2560	1393
done	5001	1383

prune421.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	15	19
done	15	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

964.0ms	8000×	body	80	valid
156.0ms	8000×	pre	80	true