Details

sample302.0ms

Algorithm

intervals

Results

83.0ms	94×	body	1280	valid
44.0ms	71×	body	640	valid
39.0ms	39×	body	10240	exit
33.0ms	22×	body	1280	nan
19.0ms	151×	body	80	valid
19.0ms	178×	body	80	nan
16.0ms	22×	body	640	nan
14.0ms	31×	body	320	valid
6.0ms	17×	body	320	nan
3.0ms	14×	body	160	valid
3.0ms	11×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	2654
5	661
4	233
3	89
2	37
1	19
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite92.0ms

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:

3.0ms	(pow x (/ 1 n))
8.0ms	(pow (+ x 1) (/ 1 n))
75.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series407.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(pow x (/ 1 n))
123.0ms	(pow (+ x 1) (/ 1 n))
213.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.0s

Counts

161 → 161

Iterations

Iter	Nodes
3	5158
2	1593
1	651
0	257

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
3.7b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
32×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
11×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
2×	`distribute-lft-out`
1×	`fma-udef`

Counts

4 → 103

Calls

4 calls:

3.0ms	(pow x (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
0.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow x (/ 1 n))
125.0ms	(pow (+ x 1) (/ 1 n))
115.0ms	(pow (+ x 1) (/ 1 n))
367.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

simplify1.2s

Counts

115 → 115

Iterations

Iter	Nodes
3	3250
2	1070
1	416
0	156

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.0b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
3.2b	(log (exp (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
3.7b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

13.0ms	(pow (+ x 1) (/ 1 n))
13.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(log (exp (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
1.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

118.0ms	(pow (+ x 1) (/ 1 n))
127.0ms	(pow (+ x 1) (/ 1 n))
386.0ms	(log (exp (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
419.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

simplify2.4s

Counts

104 → 104

Iterations

Iter	Nodes
4	4902
3	1801
2	729
1	318
0	136

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.0b

localize74.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (exp (* (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))) (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))))
3.7b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
3.7b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
3.7b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow` `fma-udef`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 50

Calls

4 calls:

3.0ms	(log (exp (* (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))) (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))))
0.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
0.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
0.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

series2.1s

Counts

4 → 12

Calls

4 calls:

797.0ms	(log (exp (* (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))) (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))))
461.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
440.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
388.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

simplify2.8s

Counts

62 → 62

Iterations

Iter	Nodes
4	5708
3	1621
2	566
1	247
0	106

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.0b

regimes408.0ms

Accuracy

88.5% (1.3b remaining)

Error of 18.9b against oracle of 17.6b and baseline of 29.3b

bsearch1.4s

Steps

Iters	Range		Point
8	2.9153003979912226e+20	1.105297713965197e+23	2.9397635619222146e+20
10	-1.9740548581083487e-307	1.900685292670916e-295	-6.7690117056222e-311
8	-113870195.14890273	-253714.50464925767	-30729818.785387494

simplify24.0ms

Iterations

Iter	Nodes
4	79
3	79
2	77
1	69
0	55

end0.0ms

sample10.2s

Algorithm

intervals

Results

3.1s	3102×	body	1280	valid
1.4s	1139×	body	10240	exit
1.2s	616×	body	1280	nan
1.1s	1629×	body	640	valid
691.0ms	4813×	body	80	valid
630.0ms	5080×	body	80	nan
542.0ms	355×	body	320	nan
456.0ms	609×	body	640	nan
449.0ms	865×	body	320	valid
136.0ms	436×	body	160	valid
53.0ms	199×	body	160	nan