Details

sample194.0ms

Algorithm

intervals

Results

61.0ms	94×	body	1280	valid
29.0ms	65×	body	640	valid
20.0ms	47×	body	10240	exit
11.0ms	16×	body	1280	nan
11.0ms	23×	body	640	nan
11.0ms	144×	body	80	valid
9.0ms	178×	body	80	nan
7.0ms	25×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	7×	body	320	nan
1.0ms	8×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	252	13
5	1266	13
done	5000	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

6.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
141.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series625.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(pow x (/ 1.0 n))
171.0ms	(pow (+ x 1.0) (/ 1.0 n))
380.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.9s

Counts

158 → 158

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	271	4785
1	740	3759
2	2874	3021
done	5002	2906

prune585.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

7.0ms	(pow x (/ 1.0 n))
15.0ms	(pow (+ x 1.0) (/ 1.0 n))
279.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
181.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.2s

Counts

4 → 12

Calls

4 calls:

100.0ms	(pow x (/ 1.0 n))
238.0ms	(pow (+ x 1.0) (/ 1.0 n))
425.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
452.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.0s

Counts

249 → 249

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	430	9019
1	929	6757
2	3250	5271
done	5000	5268

prune816.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`pow-unpow`
19×	`unpow-prod-down`
18×	`times-frac`
16×	`prod-diff`
13×	`log-prod`
10×	`exp-sum`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
3×	`exp-prod`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 117

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
263.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))))
139.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

89.0ms	(pow x (/ 1.0 n))
228.0ms	(pow (+ x 1.0) (/ 1.0 n))
425.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))

simplify1.7s

Counts

129 → 129

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	235	3731
1	640	2320
2	2544	1850
done	5004	1811

prune726.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.8b

localize29.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite621.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
224×	`prod-diff`
206×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
128×	`log-prod`
122×	`cbrt-prod`
116×	`exp-sum`
74×	`sqr-pow`
32×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 334

Calls

4 calls:

121.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
147.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
148.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
168.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.2s

Counts

4 → 12

Calls

4 calls:

726.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
713.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
431.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
366.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.0s

Counts

346 → 346

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	401	16714
1	682	12230
2	1961	9942
done	5004	8294

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

regimes355.0ms

Accuracy

78.9% (1.8b remaining)

Error of 22.3b against oracle of 20.5b and baseline of 29.0b

bsearch226.0ms

Steps

Iters	Range		Point
6	1.1789255115985561e+27	1.641399239422506e+28	1.197072613876769e+27
7	-517858925.4294923	-8119328.430348501	-54631167.29094556

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	33	86
1	43	63
done	43	63

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.1s	3179×	body	1280	valid
985.0ms	1549×	body	640	valid
920.0ms	1149×	body	10240	exit
529.0ms	4725×	body	80	valid
509.0ms	297×	body	320	nan
503.0ms	627×	body	1280	nan
457.0ms	620×	body	640	nan
441.0ms	4983×	body	80	nan
353.0ms	846×	body	320	valid
100.0ms	452×	body	160	valid
35.0ms	182×	body	160	nan