Details

sample317.0ms

Algorithm

intervals

Results

113.0ms	104×	body	1280	valid
44.0ms	68×	body	640	valid
35.0ms	34×	body	10240	exit
26.0ms	27×	body	1280	nan
25.0ms	147×	body	80	valid
18.0ms	29×	body	640	nan
15.0ms	155×	body	80	nan
11.0ms	22×	body	320	valid
5.0ms	13×	body	320	nan
3.0ms	11×	body	160	valid
1.0ms	3×	body	160	nan

simplify1.4s

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize15.0ms

Local error

Found 3 expressions with local error:

1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))
0.5b	(pow x (/ 1 n))

rewrite117.0ms

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:

Slowest

101.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))

series807.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

621.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
125.0ms	(pow (+ x 1) (/ 1 n))
61.0ms	(pow x (/ 1 n))

simplify864.0ms

Counts: 161 → 161

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.3b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))
0.5b	(pow x (/ 1 n))

rewrite277.0ms

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` `insert-posit16` `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 → 241

Calls

4 calls:

Slowest

185.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
65.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
12.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))

series724.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

284.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
258.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
101.0ms	(pow (+ x 1) (/ 1 n))
81.0ms	(pow x (/ 1 n))

simplify1.1s

Counts: 253 → 253

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

localize50.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.6b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.6b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite619.0ms

Algorithm

rewrite-expression-head

Rules

252×	`unpow-prod-down`
224×	`prod-diff`
218×	`*-un-lft-identity`
183×	`log-prod`
180×	`add-sqr-sqrt`
174×	`exp-sum`
132×	`add-cube-cbrt`
85×	`sqr-pow`
48×	`log-pow`
45×	`exp-prod`
36×	`difference-of-squares`
33×	`distribute-lft-out`
12×	`distribute-lft-out--`
8×	`fma-neg`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`log-div` `exp-diff` `rem-log-exp`
1×	`flip3--` `diff-log` `flip--`

Counts

4 → 358

Calls

4 calls:

Slowest

202.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
165.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
155.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
80.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

274.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
273.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
255.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
242.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.7s

Counts: 370 → 370

prune6.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.3b

localize87.0ms

Local error

Found 4 expressions with local error:

3.5b	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
3.3b	(log (exp (fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
1.6b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.6b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

126×	`log-prod`
124×	`unpow-prod-down`
117×	`exp-sum`
112×	`*-un-lft-identity` `prod-diff`
94×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
42×	`sqr-pow`
36×	`log-pow`
33×	`exp-prod`
18×	`difference-of-squares`
16×	`distribute-lft-out`
7×	`pow1`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`log-div` `sub-neg` `exp-diff` `fma-udef`

Counts

4 → 208

Calls

4 calls:

Slowest

156.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
156.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
2.0ms	(log (exp (fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
0.0ms	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))

series2.1s

Counts

4 → 12

Calls

4 calls:

Slowest

838.0ms	(log (exp (fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
808.0ms	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
258.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
246.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

simplify1.9s

Counts: 220 → 220

prune4.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.3b

regimes514.0ms

Accuracy

89.7% (1.2b remaining)

Error of 18.8b against oracle of 17.6b and baseline of 29.2b

bsearch1.2s

end0.0ms

sample11.0s

Algorithm

intervals

Results

3.8s	3124×	body	1280	valid
1.4s	1186×	body	10240	exit
1.3s	1650×	body	640	valid
1.0s	5122×	body	80	nan
810.0ms	4766×	body	80	valid
743.0ms	618×	body	1280	nan
538.0ms	798×	body	320	valid
520.0ms	674×	body	640	nan
225.0ms	383×	body	320	nan
141.0ms	439×	body	160	valid
63.0ms	215×	body	160	nan