Details

sample132.0ms

Algorithm

intervals

Results

40.0ms	90×	body	1280	valid
21.0ms	62×	body	640	valid
16.0ms	26×	body	10240	exit
8.0ms	162×	body	80	valid
7.0ms	31×	body	320	valid
6.0ms	15×	body	1280	nan
6.0ms	22×	body	640	nan
5.0ms	143×	body	80	nan
2.0ms	13×	body	320	nan
1.0ms	10×	body	160	valid
1.0ms	8×	body	160	nan

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite67.0ms

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:

53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))

series472.0ms

Counts

3 → 9

Calls

3 calls:

272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
54.0ms	(pow x (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	654	2164
1	2162	1642
2	5002	1637

prune327.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 19.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (cbrt x) (/ 1.0 n))
1.3b	(pow (cbrt x) (/ 1.0 n))
1.8b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.9b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
33×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
19×	`unpow-prod-down`
10×	`cbrt-prod`
7×	`pow1` `add-exp-log`
6×	`pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow1/3` `pow-exp` `div-inv` `sqr-pow`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 110

Calls

4 calls:

3.0ms	(pow (cbrt x) (/ 1.0 n))
3.0ms	(pow (cbrt x) (/ 1.0 n))
6.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
0.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow (cbrt x) (/ 1.0 n))
95.0ms	(pow (cbrt x) (/ 1.0 n))
308.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.2s	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	664	1094
1	2459	1033
2	5003	1028

prune665.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 19.9b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (cbrt x) (/ 1.0 n))
1.3b	(pow (cbrt x) (/ 1.0 n))
1.8b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
4.0b	(pow (/ 1 x) -1/3)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`pow-unpow`
27×	`times-frac`
25×	`unpow-prod-down`
11×	`add-exp-log`
8×	`pow1`
7×	`pow-pow`
6×	`cbrt-prod` `pow-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `div-inv` `sqr-pow`
2×	`pow1/3` `div-exp`
1×	`rec-exp` `pow-flip` `1-exp` `fma-udef` `inv-pow`

Counts

4 → 110

Calls

4 calls:

3.0ms	(pow (cbrt x) (/ 1.0 n))
3.0ms	(pow (cbrt x) (/ 1.0 n))
0.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
4.0ms	(pow (/ 1 x) -1/3)

series1.2s

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow (cbrt x) (/ 1.0 n))
95.0ms	(pow (cbrt x) (/ 1.0 n))
783.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
179.0ms	(pow (/ 1 x) -1/3)

simplify63.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	654	1042
1	2589	963
2	5001	955

prune808.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.8b

localize47.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (cbrt x) (/ 1.0 n))
1.8b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
3.2b	(log1p (fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))))
4.0b	(pow (/ 1 x) -1/3)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`unpow-prod-down`
18×	`times-frac`
16×	`pow-unpow`
10×	`add-exp-log`
7×	`pow1`
5×	`expm1-log1p-u` `pow-pow` `pow-exp`
4×	`add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`pow-to-exp` `div-exp` `div-inv` `sqr-pow`
1×	`rec-exp` `log1p-udef` `pow-flip` `pow1/3` `1-exp` `log1p-expm1` `fma-udef` `inv-pow`

Counts

4 → 88

Calls

4 calls:

3.0ms	(pow (cbrt x) (/ 1.0 n))
0.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
0.0ms	(log1p (fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))))
4.0ms	(pow (/ 1 x) -1/3)

series3.0s

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow (cbrt x) (/ 1.0 n))
795.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
2.0s	(log1p (fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 0.3333333333333333 (/ 1 (* x n)) (fma 1.0 (/ (log (pow (/ 1 x) -1/3)) n) 1)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))))
173.0ms	(pow (/ 1 x) -1/3)

simplify84.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	927	1416
1	3791	1282
2	5001	1278

prune705.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.8b

regimes256.0ms

Accuracy

79.1% (1.7b remaining)

Error of 22.6b against oracle of 20.9b and baseline of 29.2b

bsearch297.0ms

Steps

Iters	Range		Point
8	0.00010735495496369802	0.23449948331106904	0.2317853494525819
9	-238.82950093874626	-3.0083479578817887e-06	-235.54342409600352

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	87
1	78	87
2	78	87

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3112×	body	1280	valid
560.0ms	1611×	body	640	valid
526.0ms	1146×	body	10240	exit
303.0ms	647×	body	1280	nan
247.0ms	4800×	body	80	valid
210.0ms	650×	body	640	nan
185.0ms	849×	body	320	valid
185.0ms	5126×	body	80	nan
69.0ms	369×	body	320	nan
59.0ms	422×	body	160	valid
19.0ms	179×	body	160	nan