Details

sample231.0ms

Algorithm

intervals

Results

55.0ms	113×	body	1280	valid
45.0ms	42×	body	1280	nan
28.0ms	54×	body	640	valid
22.0ms	33×	body	640	nan
19.0ms	132×	body	80	overflowed
12.0ms	125×	body	80	valid
9.0ms	194×	body	80	nan
8.0ms	20×	body	320	nan
7.0ms	24×	body	320	valid
4.0ms	21×	body	160	valid
1.0ms	7×	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

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: 33.5b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

66×	`unpow-prod-down`
56×	`*-un-lft-identity` `prod-diff`
45×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
22×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 90

Calls

1 calls:

11.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series278.0ms

Counts

1 → 3

Calls

1 calls:

278.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	413	1840
1	1182	1320
2	5002	1316

prune134.0ms

Filtered

93 candidates to 44 candidates (47.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 22.2b

Counts

94 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
4.7b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
9.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ x 1.0))
87.0ms	(cbrt (+ x 1.0))
106.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
845.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify59.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	596	1015
1	2175	941
2	5001	893

prune341.0ms

Filtered

109 candidates to 80 candidates (73.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Merged error: 21.9b

Counts

112 → 5

localize38.0ms

Local error

Found 4 expressions with local error:

4.9b	(pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (pow (/ 1 (pow x 4)) 1/3)))) (/ 1.0 n))
5.1b	(pow (/ 1 x) 1/3)
6.1b	(pow (/ 1 x) -2/3)
33.6b	(pow (/ 1 (pow x 4)) 1/3)

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

63×	`unpow-prod-down`
48×	`times-frac`
43×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
22×	`pow-unpow` `pow-exp`
10×	`pow1` `pow-pow` `div-exp`
7×	`pow-to-exp` `sqr-pow`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `inv-pow`
2×	`unpow1/3`

Counts

4 → 151

Calls

4 calls:

3.0ms	(pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (pow (/ 1 (pow x 4)) 1/3)))) (/ 1.0 n))
141.0ms	(pow (/ 1 x) 1/3)
5.0ms	(pow (/ 1 x) -2/3)
7.0ms	(pow (/ 1 (pow x 4)) 1/3)

series771.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (pow (/ 1 (pow x 4)) 1/3)))) (/ 1.0 n))
167.0ms	(pow (/ 1 x) 1/3)
165.0ms	(pow (/ 1 x) -2/3)
180.0ms	(pow (/ 1 (pow x 4)) 1/3)

simplify70.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	824	1136
1	2930	1026
2	5001	1011

prune531.0ms

Filtered

163 candidates to 84 candidates (51.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	164	4	168

Merged error: 21.9b

Counts

168 → 4

localize41.0ms

Local error

Found 4 expressions with local error:

1.4b	(fma (pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (log1p (expm1 (pow (/ 1 (pow x 4)) 1/3)))))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
5.1b	(pow (/ 1 x) 1/3)
6.1b	(pow (/ 1 x) -2/3)
33.6b	(pow (/ 1 (pow x 4)) 1/3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

60×	`unpow-prod-down`
39×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log`
21×	`pow-exp`
10×	`div-exp`
9×	`pow1` `pow-unpow` `pow-pow`
6×	`pow-to-exp` `sqr-pow`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `div-inv` `inv-pow`
2×	`unpow1/3`
1×	`fma-udef`

Counts

4 → 132

Calls

4 calls:

1.0ms	(fma (pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (log1p (expm1 (pow (/ 1 (pow x 4)) 1/3)))))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
5.0ms	(pow (/ 1 x) 1/3)
5.0ms	(pow (/ 1 x) -2/3)
7.0ms	(pow (/ 1 (pow x 4)) 1/3)

series1.5s

Counts

4 → 12

Calls

4 calls:

934.0ms	(fma (pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (log1p (expm1 (pow (/ 1 (pow x 4)) 1/3)))))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
180.0ms	(pow (/ 1 x) 1/3)
172.0ms	(pow (/ 1 x) -2/3)
183.0ms	(pow (/ 1 (pow x 4)) 1/3)

simplify77.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	929	1116
1	3243	972
2	5002	957

prune481.0ms

Filtered

144 candidates to 71 candidates (49.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	144	4	148

Merged error: 21.9b

Counts

148 → 4

regimes171.0ms

bsearch151.0ms

Steps

Iters	Range		Point
9	-35960.30255326699	-0.0014566459989916651	-393.5929326446645