Details

sample375.0ms

Algorithm

intervals

Results

141.0ms	104×	body	1280	valid
43.0ms	54×	body	640	valid
43.0ms	40×	body	10240	exit
33.0ms	32×	body	1280	nan
25.0ms	201×	body	80	nan
19.0ms	135×	body	80	valid
18.0ms	23×	body	640	nan
15.0ms	28×	body	320	valid
7.0ms	20×	body	160	valid
7.0ms	15×	body	320	nan
2.0ms	7×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	2679
5	667
4	231
3	87
2	35
1	17
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1 n))
1.7b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite121.0ms

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` `insert-posit16` `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 → 152

Calls

3 calls:

6.0ms	(pow x (/ 1 n))
14.0ms	(pow (+ x 1) (/ 1 n))
95.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series439.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(pow x (/ 1 n))
118.0ms	(pow (+ x 1) (/ 1 n))
240.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify6.9s

Counts

161 → 161

Iterations

Iter	Nodes
3	5080
2	1635
1	651
0	257

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize60.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
1.7b	(pow (cbrt (+ x 1)) (/ 1 n))
2.4b	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
3.5b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
13×	`pow1`
11×	`pow-pow`
8×	`unpow-prod-down` `add-exp-log`
7×	`pow1/3`
4×	`cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp`
2×	`pow-to-exp` `pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef` `div-inv` `sqr-pow`
1×	`pow2` `pow-plus` `prod-exp` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

11.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
7.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
0.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
0.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

114.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
140.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
384.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
740.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify9.9s

Counts

106 → 106

Iterations

Iter	Nodes
3	7179
2	1979
1	663
0	245

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.9b

localize130.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
3.5b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
3.5b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
3.5b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

0.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
0.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
0.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
1.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

341.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
739.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
711.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
816.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify2.9s

Counts

56 → 56

Iterations

Iter	Nodes
3	4825
2	1112
1	342
0	139

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.9b

localize80.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (cbrt (+ x 1)) (/ 1 n))
2.1b	(log (exp (fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))))
2.4b	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
3.5b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac`
7×	`unpow-prod-down`
6×	`pow1`
5×	`add-exp-log`
4×	`cbrt-prod` `expm1-log1p-u` `log-prod` `add-cbrt-cube` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `fma-udef`
2×	`pow-pow`
1×	`pow-to-exp` `pow1/3` `rem-log-exp` `exp-sum` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

20.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
2.0ms	(log (exp (fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))))
0.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
0.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
767.0ms	(log (exp (fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))))
785.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
818.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify7.6s

Counts

88 → 88

Iterations

Iter	Nodes
3	6307
2	1727
1	583
0	232

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.9b

regimes402.0ms

Accuracy

84.9% (1.7b remaining)

Error of 19.9b against oracle of 18.2b and baseline of 29.7b

bsearch1.1s

Steps

Iters	Range		Point
6	2.014748274191031e+31	2.2090824881425965e+32	2.054730747417339e+31
11	-2.8059027898901087e-304	2.0906740142923838e-292	2.44541556257196e-310
8	-6.228364059036109e+25	-5.249771667565015e+21	-5.374271620846741e+21

simplify24.0ms

Iterations

Iter	Nodes
3	66
2	66
1	64
0	53

end0.0ms

sample10.9s

Algorithm

intervals

Results

3.3s	3169×	body	1280	valid
1.8s	1586×	body	640	valid
1.7s	1196×	body	10240	exit
826.0ms	4684×	body	80	valid
789.0ms	692×	body	1280	nan
619.0ms	5198×	body	80	nan
582.0ms	666×	body	640	nan
432.0ms	828×	body	320	valid
180.0ms	373×	body	320	nan
153.0ms	487×	body	160	valid
47.0ms	162×	body	160	nan