Details

sample173.0ms

Algorithm

intervals

Results

66.0ms	107×	body	1280	valid
23.0ms	49×	body	640	valid
19.0ms	30×	body	10240	exit
13.0ms	130×	body	80	valid
9.0ms	17×	body	1280	nan
9.0ms	129×	body	80	nan
7.0ms	21×	body	320	valid
4.0ms	13×	body	320	nan
3.0ms	18×	body	160	valid
3.0ms	7×	body	640	nan
0.0ms	3×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite64.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series73.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
45.0ms	(- (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

prune829.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
3.3b	(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)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
10×	`cbrt-prod`
9×	`times-frac`
7×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `fma-udef` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
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)))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt x)
11.0ms	(cbrt x)
32.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
183.0ms	(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)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	573	768
1	2166	709
2	5003	703

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.7b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
3.3b	(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)))))
8.4b	(log (exp (cbrt x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
10×	`cbrt-prod`
9×	`times-frac`
7×	`unpow-prod-down` `log-pow`
6×	`pow1` `exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`pow-pow` `pow1/3`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `fma-udef` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

0.0ms	(cbrt x)
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)))))
2.0ms	(log (exp (cbrt x)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt x)
32.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
179.0ms	(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)))))
10.0ms	(log (exp (cbrt x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	607	793
1	2220	730
2	5003	724

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.8b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (* (pow x 2) n))
1.5b	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
7.9b	(* x (pow n 2))
8.8b	(* (pow x 2) n)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
24×	`add-sqr-sqrt`
15×	`prod-exp`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
8×	`unpow-prod-down` `div-exp` `unswap-sqr`
5×	`pow1` `pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`times-frac` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `*-commutative`
1×	`pow-flip` `frac-2neg` `clear-num` `associate-/r*` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 103

Calls

4 calls:

5.0ms	(/ 1 (* (pow x 2) n))
0.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
7.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series34.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 1 (* (pow x 2) n))
19.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
7.0ms	(* x (pow n 2))
4.0ms	(* (pow x 2) n)

simplify53.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	377	604
1	1714	520
2	5001	513

prune858.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.2b

regimes539.0ms

Accuracy

88.7% (2.2b remaining)

Error of 22.3b against oracle of 20.1b and baseline of 39.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	55
1	65	55
2	65	55

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.9s	3134×	body	1280	valid
737.0ms	1576×	body	640	valid
681.0ms	1104×	body	10240	exit
430.0ms	681×	body	1280	nan
407.0ms	4783×	body	80	valid
333.0ms	5079×	body	80	nan
302.0ms	651×	body	640	nan
266.0ms	841×	body	320	valid
106.0ms	370×	body	320	nan
85.0ms	410×	body	160	valid
33.0ms	184×	body	160	nan