Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	274×	body	80	valid
6.0ms	302×	body	80	nan

simplify20.0ms

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

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

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))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(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

prune26.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	2	14

Merged error: 0.1b

Counts

14 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt x) y (- 1.0 x)))
0.1b	(fma (sqrt x) y (- 1.0 x))
0.1b	(fma (sqrt x) y (- 1.0 x))
0.1b	(* (sqrt (fma (sqrt x) y (- 1.0 x))) (sqrt (fma (sqrt x) y (- 1.0 x))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (fma (sqrt x) y (- 1.0 x)))
1.0ms	(fma (sqrt x) y (- 1.0 x))
1.0ms	(fma (sqrt x) y (- 1.0 x))
6.0ms	(* (sqrt (fma (sqrt x) y (- 1.0 x))) (sqrt (fma (sqrt x) y (- 1.0 x))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (fma (sqrt x) y (- 1.0 x)))
40.0ms	(fma (sqrt x) y (- 1.0 x))
37.0ms	(fma (sqrt x) y (- 1.0 x))
38.0ms	(* (sqrt (fma (sqrt x) y (- 1.0 x))) (sqrt (fma (sqrt x) y (- 1.0 x))))

simplify168.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (160.0ms)

Iter	Nodes	Cost
0	202	579
1	700	493
2	3972	465
3	5001	462

prune165.0ms

Filtered

98 candidates to 62 candidates (63.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	96	4	100

Merged error: 0.1b

Counts

100 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3) (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
0.1b	(fma (sqrt x) y (- 1.0 x))
0.1b	(fma (sqrt x) y (- 1.0 x))
0.1b	(pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

87×	`sqrt-prod`
66×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`associate-l` `unswap-sqr`
21×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`associate-r`
8×	`pow1`
7×	`add-cbrt-cube`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `pow1/2` `unpow3` `pow-exp` `fma-udef`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 135

Calls

4 calls:

12.0ms	(* (pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3) (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
1.0ms	(fma (sqrt x) y (- 1.0 x))
1.0ms	(fma (sqrt x) y (- 1.0 x))
4.0ms	(pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3)

series355.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3) (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
40.0ms	(fma (sqrt x) y (- 1.0 x))
37.0ms	(fma (sqrt x) y (- 1.0 x))
240.0ms	(pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3)

simplify64.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	394	1505
1	1624	1249
2	5002	1033

prune244.0ms

Filtered

147 candidates to 74 candidates (50.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	147	4	151

Merged error: 0.0b

Counts

151 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
0.1b	(cbrt (sqrt (fma (sqrt x) y (- 1.0 x))))
0.1b	(* (pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3) (cbrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
0.1b	(pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

77×	`sqrt-prod`
71×	`add-sqr-sqrt`
37×	`cbrt-prod`
27×	`unpow-prod-down` `cube-prod`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l` `unswap-sqr`
10×	`add-exp-log`
9×	`associate-r`
7×	`pow1`
6×	`add-cbrt-cube`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `pow1/2` `pow1/3` `unpow3` `pow-exp`
1×	`*-commutative` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 148

Calls

4 calls:

2.0ms	(cbrt (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
2.0ms	(cbrt (sqrt (fma (sqrt x) y (- 1.0 x))))
14.0ms	(* (pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3) (cbrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
4.0ms	(pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3)

series686.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
139.0ms	(cbrt (sqrt (fma (sqrt x) y (- 1.0 x))))
161.0ms	(* (pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3) (cbrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
247.0ms	(pow (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) 3)

simplify76.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	608	2173
1	2104	2079
2	5002	2019

prune352.0ms

Filtered

160 candidates to 86 candidates (53.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	160	4	164

Merged error: 0.0b

Counts

164 → 4

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	3

end0.0ms

sample625.0ms

Algorithm

intervals

Results

186.0ms	8529×	body	80	valid
164.0ms	8642×	body	80	nan
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid