Details

sample127.0ms

Algorithm

intervals

Results

51.0ms	868×	body	80	nan
18.0ms	288×	body	80	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	10
1	111	8
2	464	8
3	1654	8
4	5001	8

prune9.0ms

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

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma i y (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.1b	(fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))
0.2b	(fma x (log y) z)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`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

3 → 30

Calls

3 calls:

1.0ms	(fma i y (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))
1.0ms	(fma x (log y) z)

series1.1s

Counts

3 → 9

Calls

3 calls:

662.0ms	(fma i y (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
353.0ms	(fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))
53.0ms	(fma x (log y) z)

simplify33.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	117	283
1	268	241
2	1047	236
3	5002	233

prune172.0ms

Filtered

39 candidates to 34 candidates (87.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Merged error: 0.1b

Counts

40 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))) (cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

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:

5.0ms	(* (cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))) (cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))) (cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a)))))
545.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
541.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
531.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

simplify48.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	380	1678
1	1357	1552
2	5002	1427

prune490.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	87	9	96

Merged error: 0.1b

Counts

96 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

series2.2s

Counts

4 → 12

Calls

4 calls:

543.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
541.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
539.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
541.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

simplify50.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	181	1004
1	465	932
2	1739	904
3	5002	896

prune563.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	64	9	73

Merged error: 0.1b

Counts

73 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
0.5b	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
1.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

series2.1s

Counts

4 → 12

Calls

4 calls:

526.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
520.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
525.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))
525.0ms	(cbrt (fma (log c) (- b 0.5) (+ (fma x (log y) z) (+ t a))))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	181	1004
1	465	932
2	1739	904
3	5002	896

prune406.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	64	9	73

Merged error: 0.1b

Counts

73 → 9

regimes672.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	27710×	body	80	nan
596.0ms	9106×	body	80	valid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	640	valid