Details

sample110.0ms

Algorithm

intervals

Results

46.0ms	111×	body	1280	valid
19.0ms	75×	body	640	valid
18.0ms	284×	body	80	valid
8.0ms	47×	body	320	valid
3.0ms	29×	body	160	valid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	7
1	62	7
2	108	7
3	177	7
4	279	7
5	770	7
6	1075	7
7	1599	7
8	3585	7
9	4712	7
10	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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-l` `sum-log` `*-commutative`

Counts

2 → 35

Calls

2 calls:

6.0ms	(+ (exp (- 0.0 im)) (exp im))
11.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (exp (- 0.0 im)) (exp im))
69.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

simplify35.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	265	349
1	1200	295
2	5001	294

prune89.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0b

Counts

42 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (- 0.0 im)) (exp im))
0.0b	(* (* 0.5 (sin re)) (cbrt (pow (+ (exp (- 0.0 im)) (exp im)) 3)))
0.0b	(cbrt (pow (+ (exp (- 0.0 im)) (exp im)) 3))
0.0b	(pow (+ (exp (- 0.0 im)) (exp im)) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod` `*-un-lft-identity`
17×	`associate-r`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
10×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out`
6×	`cube-div` `add-log-exp`
4×	`cbrt-div` `flip3-+` `flip-+`
3×	`cube-mult` `pow-unpow` `unpow3` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`associate-*r/`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-l` `pow-exp` `sum-log` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 98

Calls

4 calls:

6.0ms	(+ (exp (- 0.0 im)) (exp im))
14.0ms	(* (* 0.5 (sin re)) (cbrt (pow (+ (exp (- 0.0 im)) (exp im)) 3)))
8.0ms	(cbrt (pow (+ (exp (- 0.0 im)) (exp im)) 3))
8.0ms	(pow (+ (exp (- 0.0 im)) (exp im)) 3)

series162.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (exp (- 0.0 im)) (exp im))
67.0ms	(* (* 0.5 (sin re)) (cbrt (pow (+ (exp (- 0.0 im)) (exp im)) 3)))
22.0ms	(cbrt (pow (+ (exp (- 0.0 im)) (exp im)) 3))
50.0ms	(pow (+ (exp (- 0.0 im)) (exp im)) 3)

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	402	877
1	1863	818
2	5003	807

prune207.0ms

Filtered

110 candidates to 63 candidates (57.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 0b

Counts

113 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp (- 0.0 im)) (exp im)))
0.0b	(sqrt (+ (exp (- 0.0 im)) (exp im)))
0.0b	(* (* 0.5 (sin re)) (* (sqrt (+ (exp (- 0.0 im)) (exp im))) (sqrt (+ (exp (- 0.0 im)) (exp im)))))
1.0b	(* (sqrt (+ (exp (- 0.0 im)) (exp im))) (sqrt (+ (exp (- 0.0 im)) (exp im))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
33×	`pow1`
32×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `sqrt-div`
18×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt` `flip3-+` `flip-+`
12×	`associate-*r/`
11×	`swap-sqr` `pow-prod-down`
10×	`sqrt-pow1` `pow1/2`
9×	`prod-exp` `cbrt-unprod`
8×	`frac-times` `associate-r` `associate-l` `distribute-lft-out`
5×	`pow-prod-up`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`rem-sqrt-square` `*-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 124

Calls

4 calls:

7.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
7.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
23.0ms	(* (* 0.5 (sin re)) (* (sqrt (+ (exp (- 0.0 im)) (exp im))) (sqrt (+ (exp (- 0.0 im)) (exp im)))))
18.0ms	(* (sqrt (+ (exp (- 0.0 im)) (exp im))) (sqrt (+ (exp (- 0.0 im)) (exp im))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
48.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
67.0ms	(* (* 0.5 (sin re)) (* (sqrt (+ (exp (- 0.0 im)) (exp im))) (sqrt (+ (exp (- 0.0 im)) (exp im)))))
23.0ms	(* (sqrt (+ (exp (- 0.0 im)) (exp im))) (sqrt (+ (exp (- 0.0 im)) (exp im))))

simplify57.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	402	1391
1	1630	1175
2	5001	1154

prune289.0ms

Filtered

136 candidates to 74 candidates (54.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	136	3	139

Merged error: 0b

Counts

139 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))))
0.7b	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
0.7b	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
0.7b	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

8.0ms	(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))))
10.0ms	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
9.0ms	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
9.0ms	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))))
151.0ms	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
154.0ms	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
162.0ms	(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	326	1354
1	1149	1231
2	5002	1148

prune253.0ms

Filtered

84 candidates to 63 candidates (75.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Merged error: 0b

Counts

87 → 3

regimes124.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	17	9

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	2968×	body	1280	valid
656.0ms	2474×	body	640	valid
473.0ms	8473×	body	80	valid
214.0ms	1229×	body	320	valid
86.0ms	677×	body	160	valid

Details

sample110.0ms

simplify103.0ms

prune3.0ms

localize10.0ms

rewrite18.0ms

series91.0ms

simplify35.0ms

prune89.0ms

localize13.0ms

rewrite38.0ms

series162.0ms

simplify59.0ms

prune207.0ms

localize12.0ms

rewrite60.0ms

series189.0ms

simplify57.0ms

prune289.0ms

localize14.0ms

rewrite39.0ms

series682.0ms

simplify59.0ms

prune253.0ms

regimes124.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling