Details

sample235.0ms

Algorithm

intervals

Results

78.0ms	110×	body	1280	valid
45.0ms	55×	body	640	valid
29.0ms	35×	body	10240	exit
12.0ms	19×	body	1280	nan
12.0ms	141×	body	80	valid
9.0ms	16×	body	640	nan
9.0ms	144×	body	80	nan
7.0ms	19×	body	320	valid
4.0ms	16×	body	160	valid
3.0ms	12×	body	320	nan
2.0ms	8×	body	160	nan

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	543
1	17	543
2	35	543
3	86	543
4	238	543
5	673	543
6	3086	543
done	5000	543

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.8b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite144.0ms

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))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
106.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series725.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(pow x (/ 1.0 n))
250.0ms	(pow (+ x 1.0) (/ 1.0 n))
357.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.5s

Counts

158 → 158

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	270	129390
1	711	115809
2	1895	107003
done	5000	92449

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 n) (log x))
0.8b	(pow (+ 1.0 x) (/ 1.0 n))
2.3b	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))))
2.8b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

191×	`log-prod`
182×	`exp-sum`
154×	`*-un-lft-identity`
145×	`add-sqr-sqrt`
144×	`prod-diff`
110×	`add-cube-cbrt`
86×	`unpow-prod-down`
57×	`distribute-rgt-in` `distribute-lft-in`
26×	`sqr-pow`
20×	`distribute-lft-out`
19×	`times-frac`
18×	`difference-of-squares`
15×	`log-pow`
13×	`pow-unpow` `exp-prod` `associate-l`
10×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`fma-neg`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`pow-to-exp` `cbrt-undiv` `log-div` `pow-pow` `flip3--` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `flip--`

Counts

4 → 277

Calls

4 calls:

22.0ms	(* (/ 1.0 n) (log x))
20.0ms	(pow (+ 1.0 x) (/ 1.0 n))
255.0ms	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))))
105.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ 1.0 n) (log x))
224.0ms	(pow (+ 1.0 x) (/ 1.0 n))
419.0ms	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))))
398.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

simplify3.9s

Counts

289 → 289

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	522	289267
1	1060	235389
2	2712	214326
done	5002	193207

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.8b

localize52.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x)))))))
2.3b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x)))))))
2.8b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
2.8b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

rewrite700.0ms

Algorithm

rewrite-expression-head

Rules

376×	`log-prod`
364×	`exp-sum`
288×	`prod-diff`
266×	`*-un-lft-identity`
242×	`add-sqr-sqrt`
182×	`add-cube-cbrt`
164×	`unpow-prod-down`
154×	`sqrt-prod`
108×	`distribute-rgt-in` `distribute-lft-in`
50×	`sqr-pow`
38×	`distribute-lft-out`
36×	`difference-of-squares`
32×	`log-pow`
28×	`sqrt-pow1`
26×	`exp-prod`
16×	`fma-neg`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 422

Calls

4 calls:

218.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x)))))))
194.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x)))))))
150.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
108.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

series2.4s

Counts

4 → 12

Calls

4 calls:

779.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x)))))))
718.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x)))))))
423.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
448.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

simplify6.1s

Counts

434 → 434

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	513	553832
1	865	492522
2	1744	450084
3	4939	374692
done	5000	374662

prune4.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.8b

localize127.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (exp (* (cbrt (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))) (cbrt (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))))))
2.8b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
2.8b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
2.8b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

216×	`prod-diff`
203×	`*-un-lft-identity`
182×	`add-sqr-sqrt`
165×	`log-prod`
162×	`exp-sum`
137×	`add-cube-cbrt`
129×	`unpow-prod-down`
81×	`distribute-rgt-in` `distribute-lft-in`
39×	`sqr-pow`
30×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
11×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--` `distribute-lft-out--`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 328

Calls

4 calls:

5.0ms	(log (exp (* (cbrt (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))) (cbrt (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))))))
127.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
110.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
123.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

series3.2s

Counts

4 → 12

Calls

4 calls:

2.0s	(log (exp (* (cbrt (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))) (cbrt (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))))))
402.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
426.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))
372.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (/ 1.0 n) (log x))))

simplify3.0s

Counts

340 → 340

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	284	385390
1	665	340562
2	1542	308637
done	5000	273237

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.8b

regimes560.0ms

Accuracy

82.3% (1.5b remaining)

Error of 22.0b against oracle of 20.5b and baseline of 29.0b

bsearch232.0ms

Steps

Iters	Range		Point
8	3.7006020166960794e+27	5.36663774086131e+30	3.751685039024179e+27
7	-632461689.9334153	-25918459.56888027	-152059583.1304194

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	1316
1	36	1316
done	36	1316

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.6s	3158×	body	1280	valid
1.5s	1207×	body	10240	exit
1.1s	1597×	body	640	valid
917.0ms	5012×	body	80	nan
567.0ms	648×	body	1280	nan
499.0ms	4937×	body	80	valid
401.0ms	633×	body	640	nan
303.0ms	809×	body	320	valid
145.0ms	326×	body	320	nan
143.0ms	420×	body	160	valid
36.0ms	179×	body	160	nan