Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

459×

body

valid

simplify94.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (18.0ms)

Iter	Nodes	Cost
0	24	9
1	61	9
2	168	8
3	483	6
4	1418	5
5	3857	5
6	5001	5

prune7.0ms

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: 7.4b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 3 (* x.re (- (* x.im x.im))) (pow x.re 3))
8.1b	(* x.re (- (* x.im x.im)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `associate-r`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 34

Calls

2 calls:

1.0ms	(fma 3 (* x.re (- (* x.im x.im))) (pow x.re 3))
5.0ms	(* x.re (- (* x.im x.im)))

series86.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma 3 (* x.re (- (* x.im x.im))) (pow x.re 3))
29.0ms	(* x.re (- (* x.im x.im)))

simplify140.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	129	200
1	707	179
2	4464	174
3	5001	173

prune103.0ms

Filtered

40 candidates to 33 candidates (82.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	35	7	42

Merged error: 0.1b

Counts

42 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x.re (- x.im)) x.im)
0.1b	(fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-out` `associate-l` `*-commutative` `distribute-rgt-neg-out` `fma-udef`

Counts

2 → 31

Calls

2 calls:

6.0ms	(* (* x.re (- x.im)) x.im)
1.0ms	(fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))

series85.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(* (* x.re (- x.im)) x.im)
56.0ms	(fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))

simplify31.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	151	193
1	780	168
2	5001	168

prune88.0ms

Filtered

37 candidates to 27 candidates (73.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	35	9	44

Merged error: 0.1b

Counts

44 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))) (cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))))
13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))

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 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))) (cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))))
1.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
1.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
1.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))) (cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3))))
144.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
140.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
145.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))

simplify83.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	161	1053
1	518	960
2	2570	873
3	5001	862

prune260.0ms

Filtered

93 candidates to 71 candidates (76.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	89	13	102

Merged error: 0.0b

Counts

102 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
13.0b	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))

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 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
1.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
1.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
1.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
140.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
144.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))
143.0ms	(cbrt (fma 3 (* (* x.re (- x.im)) x.im) (pow x.re 3)))

simplify48.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (41.0ms)

Iter	Nodes	Cost
0	79	564
1	164	512
2	443	500
3	1255	488
4	5001	480

prune233.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	64	13	77

Merged error: 0.0b

Counts

77 → 13

regimes151.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	20	5
2	23	5
3	23	5

end0.0ms

sample885.0ms

Algorithm

intervals

Results

667.0ms

14305×

body

valid