Details

sample209.0ms

Algorithm

intervals

Results

67.0ms	138×	body	1280	valid
39.0ms	66×	body	1280	nan
20.0ms	39×	body	10240	exit
20.0ms	57×	body	640	nan
17.0ms	51×	body	640	valid
8.0ms	198×	body	80	nan
5.0ms	26×	body	320	valid
5.0ms	21×	body	320	nan
4.0ms	91×	body	80	valid
3.0ms	19×	body	160	nan
2.0ms	15×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.9b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

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:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series549.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
143.0ms	(pow (+ x 1.0) (/ 1.0 n))
346.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify68.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune291.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	152	6	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	6	159

Merged error: 18.3b

Counts

159 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite54.0ms

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` `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 → 237

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
16.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
279.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify88.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune441.0ms

Filtered

249 candidates to 133 candidates (53.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	247	8	255

Merged error: 18.3b

Counts

255 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
3.9b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

112×	`unpow-prod-down`
93×	`*-un-lft-identity`
84×	`add-sqr-sqrt`
80×	`prod-diff`
67×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac`
12×	`distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sqrt-pow2` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

4.0ms	(pow (sqrt x) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series1.9s

Counts

4 → 12

Calls

4 calls:

213.0ms	(pow (sqrt x) (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
452.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify97.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	836	4182
1	2867	3044
2	5001	3025

prune498.0ms

Filtered

202 candidates to 112 candidates (55.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	6	6
Picked	1	0	1
Done	1	0	1
Total	203	7	210

Merged error: 18.3b

Counts

210 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
3.9b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

204×	`unpow-prod-down`
160×	`prod-diff`
152×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
85×	`log-prod`
82×	`exp-sum`
54×	`sqrt-prod`
52×	`sqr-pow`
24×	`difference-of-squares`
22×	`distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`pow-unpow`
9×	`times-frac`
8×	`fma-neg`
6×	`pow1` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `distribute-lft-out--`
1×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `flip--` `fma-udef` `div-inv`

Counts

4 → 268

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
20.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))
17.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.2s

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
449.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))
442.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify121.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	954	7474
1	2868	5251
2	5001	5222

prune625.0ms

Filtered

280 candidates to 129 candidates (46.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	279	1	280
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	279	8	287

Merged error: 18.2b

Counts

287 → 8

regimes246.0ms

Accuracy

83.7% (1.7b remaining)

Error of 24.5b against oracle of 22.8b and baseline of 33.2b

bsearch243.0ms

Steps

Iters	Range		Point
11	3.935433936840197e-20	28487.23375504778	28170.08653940645
8	-45386.90934105675	-58.70303594915981	-44775.669105648325

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	37
1	51	37

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.8s	3890×	body	1280	valid
1.4s	2237×	body	1280	nan
725.0ms	1810×	body	640	nan
635.0ms	1455×	body	10240	exit
628.0ms	1871×	body	640	valid
271.0ms	6267×	body	80	nan
216.0ms	912×	body	320	nan
195.0ms	898×	body	320	valid
161.0ms	3123×	body	80	valid
62.0ms	444×	body	160	nan
59.0ms	436×	body	160	valid