Details

sample129.0ms

Algorithm

intervals

Results

66.0ms	151×	body	1280	valid
28.0ms	125×	body	640	valid
9.0ms	59×	body	320	valid
7.0ms	146×	body	80	valid
3.0ms	30×	body	160	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	40	7
2	92	7
3	163	7
4	405	7
5	865	7
6	1189	7
7	2769	7
8	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 45.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
6.3b	(- (exp (- im)) (exp im))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
15×	`associate-l`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-r`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-r/` `-commutative` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

2 → 87

Calls

2 calls:

14.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
11.0ms	(- (exp (- im)) (exp im))

series124.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
37.0ms	(- (exp (- im)) (exp im))

simplify55.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	404	1220
1	1634	892
2	5001	840

prune167.0ms

Filtered

93 candidates to 55 candidates (59.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	2	94

Merged error: 0.1b

Counts

94 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow im 5) (* 2 im))
0.0b	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
0.1b	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
0.1b	(* 1/3 (pow im 3))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

378×	`prod-diff`
343×	`add-sqr-sqrt`
239×	`*-un-lft-identity`
227×	`add-cube-cbrt`
194×	`distribute-rgt-neg-in`
190×	`distribute-lft-neg-in`
178×	`associate-r`
128×	`distribute-rgt-in` `distribute-lft-in`
84×	`unpow-prod-down`
80×	`associate-l`
67×	`unswap-sqr`
42×	`fma-neg` `sqr-pow`
23×	`*-commutative`
21×	`unpow3`
14×	`add-exp-log`
11×	`pow1` `add-cbrt-cube`
10×	`neg-mul-1`
8×	`add-log-exp`
6×	`prod-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `associate-*r/` `flip--` `fma-udef` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `neg-log` `pow-exp` `associate--r+`

Counts

4 → 523

Calls

4 calls:

1.0ms	(fma 1/60 (pow im 5) (* 2 im))
19.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
35.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
6.0ms	(* 1/3 (pow im 3))

series433.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(fma 1/60 (pow im 5) (* 2 im))
66.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
187.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
46.0ms	(* 1/3 (pow im 3))

simplify349.0ms

Algorithm

egg-herbie

Counts

535 → 535

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1504	14072
1	5001	8282

prune553.0ms

Filtered

535 candidates to 139 candidates (26.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	525	10	535
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	526	11	537

Merged error: 0.0b

Counts

537 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* (sin re) (* -1/3 (pow im 3))))
0.1b	(* (sin re) (* -1/3 (pow im 3)))
0.1b	(* (* 0.5 (sin re)) (- (fma 1/60 (pow im 5) (* 2 im))))
0.1b	(* -1/3 (pow im 3))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

106×	`associate-r`
83×	`add-sqr-sqrt`
40×	`add-exp-log`
39×	`unswap-sqr`
33×	`associate-l`
25×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `prod-exp` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
9×	`sqr-pow`
8×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `pow-to-exp` `distribute-rgt-neg-in` `unpow3` `pow-exp`
2×	`distribute-neg-in` `fma-udef`
1×	`distribute-rgt-in` `neg-mul-1` `distribute-lft-in` `distribute-rgt-neg-out`

Counts

4 → 176

Calls

4 calls:

20.0ms	(* 0.5 (* (sin re) (* -1/3 (pow im 3))))
15.0ms	(* (sin re) (* -1/3 (pow im 3)))
10.0ms	(* (* 0.5 (sin re)) (- (fma 1/60 (pow im 5) (* 2 im))))
6.0ms	(* -1/3 (pow im 3))

series514.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* 0.5 (* (sin re) (* -1/3 (pow im 3))))
99.0ms	(* (sin re) (* -1/3 (pow im 3)))
278.0ms	(* (* 0.5 (sin re)) (- (fma 1/60 (pow im 5) (* 2 im))))
38.0ms	(* -1/3 (pow im 3))

simplify112.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	696	1220
1	3682	1114
2	5002	1114

prune532.0ms

Filtered

188 candidates to 133 candidates (70.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	188	11	199

Merged error: 0.0b

Counts

199 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* -1/3 (pow im 3))
0.2b	(* (* (sqrt 0.5) (sin re)) (- (fma 1/60 (pow im 5) (* 2 im))))
0.3b	(* (sqrt 0.5) (* (* (sqrt 0.5) (sin re)) (- (fma 1/60 (pow im 5) (* 2 im)))))
0.4b	(* (sqrt 0.5) (sin re))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
71×	`associate-r`
59×	`associate-l`
37×	`unswap-sqr`
27×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
23×	`sqrt-prod`
22×	`pow1` `add-cbrt-cube`
13×	`prod-exp`
11×	`pow-prod-down` `cbrt-unprod`
7×	`*-commutative`
6×	`distribute-lft-neg-in` `distribute-neg-in` `distribute-rgt-neg-in` `fma-udef`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-neg-out`
2×	`neg-mul-1` `sqr-pow`
1×	`pow-to-exp` `unpow3` `pow-exp`

Counts

4 → 173

Calls

4 calls:

9.0ms	(* -1/3 (pow im 3))
12.0ms	(* (* (sqrt 0.5) (sin re)) (- (fma 1/60 (pow im 5) (* 2 im))))
22.0ms	(* (sqrt 0.5) (* (* (sqrt 0.5) (sin re)) (- (fma 1/60 (pow im 5) (* 2 im)))))
5.0ms	(* (sqrt 0.5) (sin re))

series949.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* -1/3 (pow im 3))
391.0ms	(* (* (sqrt 0.5) (sin re)) (- (fma 1/60 (pow im 5) (* 2 im))))
471.0ms	(* (sqrt 0.5) (* (* (sqrt 0.5) (sin re)) (- (fma 1/60 (pow im 5) (* 2 im)))))
49.0ms	(* (sqrt 0.5) (sin re))

simplify112.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	643	1617
1	3309	1432
2	5001	1419

prune475.0ms

Filtered

185 candidates to 116 candidates (62.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	181	4	185
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	186	10	196

Merged error: 0b

Counts

196 → 10

regimes236.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	13
1	33	13
2	40	13
3	40	13

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	4677×	body	1280	valid
983.0ms	3930×	body	640	valid
297.0ms	1901×	body	320	valid
228.0ms	4369×	body	80	valid
106.0ms	931×	body	160	valid