Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	275×	body	80	valid
5.0ms	275×	body	80	nan

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	13	4
1	25	3
2	44	3
3	69	3
4	102	3
5	171	3
6	192	3
7	225	3
8	316	3
9	351	3
10	351	3

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.1b

Counts

2 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (sqrt x) y (- 1.0 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (sqrt x) y (- 1.0 x))

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

(fma (sqrt x) y (- 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	64	71
1	162	57
2	476	55
3	1755	54
4	5001	54

prune30.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	12	3	15

Merged error: 0.0b

Counts

15 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (- 1.0 x) (* y (sqrt x)))
0.2b	(* y (sqrt x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`prod-diff`
7×	`add-log-exp`
6×	`associate-r`
5×	`fma-def`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`associate-l`
2×	`expm1-log1p-u` `sum-log` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 55

Calls

2 calls:

7.0ms	(+ (- 1.0 x) (* y (sqrt x)))
5.0ms	(* y (sqrt x))

series77.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (- 1.0 x) (* y (sqrt x)))
42.0ms	(* y (sqrt x))

simplify40.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	339
1	1115	252
2	5002	244

prune118.0ms

Filtered

61 candidates to 46 candidates (75.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 0.0b

Counts

64 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.3b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`*-commutative`

Counts

4 → 96

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
12.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (sqrt x))
137.0ms	(sqrt (sqrt x))
79.0ms	(* y (sqrt (sqrt x)))
40.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	351	549
1	1519	488
2	5001	461

prune186.0ms

Filtered

108 candidates to 68 candidates (63.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	108	7	115

Merged error: 0b

Counts

115 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- 1.0 x) (* (* y (sqrt (sqrt x))) (pow x 1/4)))
0.1b	(sqrt (sqrt x))
0.3b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (pow x 1/4))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
21×	`*-un-lft-identity`
19×	`add-exp-log` `add-cube-cbrt`
16×	`associate-r`
11×	`associate-+l+` `add-cbrt-cube`
10×	`prod-exp`
9×	`prod-diff` `add-log-exp`
8×	`pow1`
5×	`fma-def`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `cbrt-unprod` `log1p-expm1-u`
3×	`unpow-prod-down` `unswap-sqr`
2×	`pow-to-exp` `rem-sqrt-square` `pow1/2` `pow-exp` `sum-log` `*-commutative`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

8.0ms	(+ (- 1.0 x) (* (* y (sqrt (sqrt x))) (pow x 1/4)))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
8.0ms	(* (* y (sqrt (sqrt x))) (pow x 1/4))

series360.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (- 1.0 x) (* (* y (sqrt (sqrt x))) (pow x 1/4)))
137.0ms	(sqrt (sqrt x))
78.0ms	(* y (sqrt (sqrt x)))
81.0ms	(* (* y (sqrt (sqrt x))) (pow x 1/4))

simplify80.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	586	817
1	2765	696
2	5002	690

prune232.0ms

Filtered

118 candidates to 84 candidates (71.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	118	7	125

Merged error: 0b

Counts

125 → 7

regimes83.0ms

Accuracy

0% (0.1b 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	9	4
1	9	4

end0.0ms

sample592.0ms

Algorithm

intervals

Results

176.0ms	8497×	body	80	valid
157.0ms	8410×	body	80	nan