Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	273×	body	80	valid
7.0ms	266×	body	80	nan

simplify24.0ms

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))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify45.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (16.0ms)

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

prune32.0ms

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

rewrite12.0ms

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

series200.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (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))))
38.0ms	(fma (sqrt x) y (- 1.0 x))
43.0ms	(fma (sqrt x) y (- 1.0 x))

simplify158.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (149.0ms)

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

prune180.0ms

Filtered

98 candidates to 62 candidates (63.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	95	5	100

Merged error: 0.0b

Counts

100 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-prod`
46×	`add-sqr-sqrt`
32×	`sqrt-pow1`
27×	`pow1`
16×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

10.0ms	(* (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) (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))
1.0ms	(fma (sqrt x) y (- 1.0 x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))) (sqrt (sqrt (fma (sqrt x) y (- 1.0 x)))))
42.0ms	(fma (sqrt x) y (- 1.0 x))
38.0ms	(fma (sqrt x) y (- 1.0 x))
43.0ms	(fma (sqrt x) y (- 1.0 x))

simplify43.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	230	836
1	865	709
2	5002	670

prune214.0ms

Filtered

119 candidates to 64 candidates (53.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	118	6	124

Merged error: 0.0b

Counts

124 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (sqrt x) y (- 1.0 x))) (cbrt (fma (sqrt x) y (- 1.0 x))))
0.4b	(cbrt (fma (sqrt x) y (- 1.0 x)))
0.4b	(cbrt (fma (sqrt x) y (- 1.0 x)))
0.4b	(cbrt (fma (sqrt x) y (- 1.0 x)))

rewrite11.0ms

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:

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

series552.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (cbrt (fma (sqrt x) y (- 1.0 x))) (cbrt (fma (sqrt x) y (- 1.0 x))))
138.0ms	(cbrt (fma (sqrt x) y (- 1.0 x)))
143.0ms	(cbrt (fma (sqrt x) y (- 1.0 x)))
141.0ms	(cbrt (fma (sqrt x) y (- 1.0 x)))

simplify117.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	238	888
1	755	823
2	3353	765
3	5001	747

prune260.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	93	6	99

Merged error: 0.0b

Counts

99 → 6

regimes52.0ms

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

sample720.0ms

Algorithm

intervals

Results

237.0ms	8518×	body	80	valid
220.0ms	8559×	body	80	nan