Details

sample268.0ms

Algorithm

intervals

Results

88.0ms	96×	body	1280	valid
46.0ms	46×	body	640	valid
30.0ms	32×	body	10240	exit
22.0ms	164×	body	80	valid
16.0ms	22×	body	640	nan
15.0ms	152×	body	80	nan
11.0ms	29×	body	320	valid
11.0ms	15×	body	1280	nan
5.0ms	17×	body	160	valid
5.0ms	12×	body	320	nan
1.0ms	5×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1 n))
1.1b	(pow (+ x 1) (/ 1 n))
2.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite80.0ms

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:

5.0ms	(pow x (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))
58.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series440.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(pow x (/ 1 n))
104.0ms	(pow (+ x 1) (/ 1 n))
262.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify6.0s

Counts

158 → 158

Iterations

Iter	Nodes
3	5037
2	1606
1	643
0	254

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (log1p (pow x (/ 1 n))))
0.3b	(pow x (/ 1 n))
1.1b	(pow (+ x 1) (/ 1 n))
32.0b	(- (pow (+ x 1) (/ 1 n)) (expm1 (log1p (pow x (/ 1 n)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`unpow-prod-down` `prod-diff`
18×	`times-frac`
8×	`fma-neg`
7×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `expm1-udef`
1×	`expm1-log1p` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 121

Calls

4 calls:

0.0ms	(expm1 (log1p (pow x (/ 1 n))))
2.0ms	(pow x (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
73.0ms	(- (pow (+ x 1) (/ 1 n)) (expm1 (log1p (pow x (/ 1 n)))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(expm1 (log1p (pow x (/ 1 n))))
76.0ms	(pow x (/ 1 n))
125.0ms	(pow (+ x 1) (/ 1 n))
336.0ms	(- (pow (+ x 1) (/ 1 n)) (expm1 (log1p (pow x (/ 1 n)))))

simplify5.1s

Counts

133 → 133

Iterations

Iter	Nodes
3	4499
2	1402
1	544
0	211

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.9b

localize99.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
1.1b	(pow (cbrt (+ x 1)) (/ 1 n))
3.2b	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
4.8b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

rewrite30.0ms

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` `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 → 90

Calls

4 calls:

15.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
13.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
0.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
1.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

series948.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
149.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
140.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
491.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

simplify9.5s

Counts

102 → 102

Iterations

Iter	Nodes
3	7038
2	1847
1	602
0	222

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.8b

localize79.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
3.2b	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
3.2b	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
4.8b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

rewrite1.0ms

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` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

0.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
0.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
0.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
0.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

series926.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
138.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
140.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
490.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

simplify2.1s

Counts

52 → 52

Iterations

Iter	Nodes
3	4321
2	954
1	285
0	119

prune965.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.8b

regimes389.0ms

Accuracy

88.5% (1.4b remaining)

Error of 19.2b against oracle of 17.8b and baseline of 29.9b

bsearch1.1s

Steps

Iters	Range		Point
8	93375547299409.69	2.3994573669576374e+17	94933831758200.45
12	-2.264957913631552e-298	1.2273583806003095e-259	-1.1373843048178e-311
9	-996945.4648223005	-3.870062084897049	-210118.23628303723

simplify13.0ms

Iterations

Iter	Nodes
2	54
1	54
0	47

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.3s	3152×	body	1280	valid
1.6s	1624×	body	640	valid
1.3s	1161×	body	10240	exit
1.1s	4685×	body	80	valid
676.0ms	626×	body	1280	nan
590.0ms	5001×	body	80	nan
448.0ms	638×	body	640	nan
440.0ms	846×	body	320	valid
198.0ms	390×	body	320	nan
130.0ms	433×	body	160	valid
81.0ms	189×	body	160	nan