Details

sample12.0ms

Algorithm

intervals

Results

5.0ms	251×	body	80	valid
0.0ms	2×	body	640	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	4
1	11	4
2	11	4

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: 0.0b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

6.0ms

(+ x (/ (fabs (- y x)) 2.0))

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(+ x (/ (fabs (- y x)) 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	110
1	226	97
2	540	97
3	1522	97
4	5001	97

prune74.0ms

Filtered

20 candidates to 16 candidates (80.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	4	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Merged error: 0.0b

Counts

21 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series724.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (cbrt x) (cbrt x))
186.0ms	(cbrt x)
172.0ms	(cbrt x)
171.0ms	(cbrt x)

simplify88.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune237.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Merged error: 0b

Counts

98 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.5b	(expm1 (log1p (* (cbrt x) (cbrt x))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(expm1 (log1p (* (cbrt x) (cbrt x))))

series854.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt x)
172.0ms	(cbrt x)
177.0ms	(cbrt x)
333.0ms	(expm1 (log1p (* (cbrt x) (cbrt x))))

simplify97.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 4 (93.0ms)

Iter	Nodes	Cost
0	81	208
1	201	168
2	657	161
3	2989	160
4	5001	157

prune205.0ms

Filtered

62 candidates to 54 candidates (87.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	62	6	68

Merged error: 0b

Counts

68 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.3b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `hypot-def` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `times-frac` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

6.0ms	(+ x (/ (fabs (- y x)) 2.0))
9.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
6.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
15.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ x (/ (fabs (- y x)) 2.0))
50.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
46.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	287	1107
1	1125	1001
2	5002	967

prune249.0ms

Filtered

133 candidates to 79 candidates (59.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	133	6	139

Merged error: 0b

Counts

139 → 6

regimes70.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample299.0ms

Algorithm

intervals

Results

150.0ms	7700×	body	80	valid
10.0ms	110×	body	1280	valid
8.0ms	75×	body	640	valid
5.0ms	49×	body	2560	valid
2.0ms	43×	body	320	valid
1.0ms	24×	body	160	valid