Details

sample91.0ms

Algorithm

intervals

Results

26.0ms	49×	body	1280	valid
13.0ms	250×	body	80	nan
13.0ms	142×	body	80	valid
12.0ms	36×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize8.0ms

Local error

Found 2 expressions with local error:

2.4b	(log (+ N 1.0))
3.1b	(- (log (+ N 1.0)) (log N))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

5.0ms	(log (+ N 1.0))
15.0ms	(- (log (+ N 1.0)) (log N))

series190.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(log (+ N 1.0))
137.0ms	(- (log (+ N 1.0)) (log N))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	127	1052
1	288	863
2	1098	705
done	5001	614

prune180.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.2b	(log (/ (+ N 1.0) N))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

34.0ms	(/ (+ N 1.0) N)
7.0ms	(log (/ (+ N 1.0) N))

series202.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (+ N 1.0) N)
142.0ms	(log (/ (+ N 1.0) N))

simplify724.0ms

Counts

70 → 70

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	112	749
1	253	708
2	1053	660
done	5000	647

prune205.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.3b	(/ 0.3333333333333333 (pow N 3))
0.3b	(/ 0.5 (* N N))
13.6b	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

260×	`times-frac`
209×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
189×	`add-cube-cbrt`
182×	`prod-diff`
93×	`associate-+l+`
43×	`div-inv`
14×	`add-exp-log`
13×	`fma-neg` `associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
8×	`fma-def` `difference-of-squares`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `frac-add` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `associate-+l-` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 335

Calls

4 calls:

38.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
10.0ms	(/ 0.3333333333333333 (pow N 3))
9.0ms	(/ 0.5 (* N N))
257.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
52.0ms	(/ 0.3333333333333333 (pow N 3))
37.0ms	(/ 0.5 (* N N))
47.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

simplify553.0ms

Counts

347 → 347

Iterations

Useful iterations: done (532.0ms)

Iter	Nodes	Cost
0	361	8661
1	877	7037
done	5000	5859

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 N))
0.6b	(cbrt (/ 1.0 N))
0.6b	(cbrt (/ 1.0 N))
13.6b	(+ (fma (* (cbrt (/ 1.0 N)) (cbrt (/ 1.0 N))) (cbrt (/ 1.0 N)) (/ (- 0.5) (* N N))) (/ 0.3333333333333333 (pow N 3)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
28×	`*-un-lft-identity`
27×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `fma-def` `pow1/3` `div-inv`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

4.0ms	(cbrt (/ 1.0 N))
4.0ms	(cbrt (/ 1.0 N))
4.0ms	(cbrt (/ 1.0 N))
39.0ms	(+ (fma (* (cbrt (/ 1.0 N)) (cbrt (/ 1.0 N))) (cbrt (/ 1.0 N)) (/ (- 0.5) (* N N))) (/ 0.3333333333333333 (pow N 3)))

series1.5s

Counts

4 → 12

Calls

4 calls:

303.0ms	(cbrt (/ 1.0 N))
324.0ms	(cbrt (/ 1.0 N))
704.0ms	(cbrt (/ 1.0 N))
191.0ms	(+ (fma (* (cbrt (/ 1.0 N)) (cbrt (/ 1.0 N))) (cbrt (/ 1.0 N)) (/ (- 0.5) (* N N))) (/ 0.3333333333333333 (pow N 3)))

simplify686.0ms

Counts

102 → 102

Iterations

Useful iterations: done (681.0ms)

Iter	Nodes	Cost
0	111	1359
1	218	1315
2	741	1071
done	5000	1002

prune406.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.2b

bsearch39.0ms

Steps

Iters	Range		Point
9	0.02325869037085268	28918.939680702064	9187.863337025456

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	20	25
done	20	25

end0.0ms

sample2.5s

Algorithm

intervals

Results

729.0ms	1784×	body	1280	valid
539.0ms	7835×	body	80	nan
369.0ms	1229×	body	640	valid
284.0ms	4095×	body	80	valid
184.0ms	618×	body	320	valid
29.0ms	274×	body	160	valid