Details

sample109.0ms

Algorithm

intervals

Results

44.0ms	98×	body	1280	valid
20.0ms	87×	body	640	valid
17.0ms	286×	body	80	valid
7.0ms	38×	body	320	valid
3.0ms	23×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	23	11
2	58	11
3	98	11
4	204	11
5	272	11
6	357	11
7	600	11
8	700	11
9	736	11
10	863	11
11	880	11
done	880	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-sqr-sqrt` `add-cube-cbrt` `associate-r` `add-log-exp`
3×	`fma-def` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3-+` `associate-*r/` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-l` `sum-log` `*-commutative`

Counts

2 → 42

Calls

2 calls:

9.0ms	(+ (exp (- im)) (exp im))
30.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series85.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (exp (- im)) (exp im))
57.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	91	586
1	256	566
2	969	488
3	4245	471
done	5001	471

prune136.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
0.0b	(/ (cos re) (exp im))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

8.0ms	(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
4.0ms	(/ (cos re) (exp im))

series109.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
28.0ms	(/ (cos re) (exp im))

simplify1.4s

Counts

49 → 49

Iterations

Useful iterations: 3 (498.0ms)

Iter	Nodes	Cost
0	96	661
1	237	621
2	727	546
3	2894	539
done	5000	539

prune129.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (/ (cos re) (exp im)) 0.5 (* (exp im) (* 0.5 (cos re))))
0.0b	(/ (cos re) (exp im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-cbrt-cube`
3×	`add-exp-log` `associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (/ (cos re) (exp im)) 0.5 (* (exp im) (* 0.5 (cos re))))
6.0ms	(/ (cos re) (exp im))

series106.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(fma (/ (cos re) (exp im)) 0.5 (* (exp im) (* 0.5 (cos re))))
27.0ms	(/ (cos re) (exp im))

simplify1.4s

Counts

45 → 45

Iterations

Useful iterations: 4 (545.0ms)

Iter	Nodes	Cost
0	82	527
1	156	511
2	339	441
3	879	440
4	2769	439
done	5001	439

prune118.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp im) (cos re) (/ (cos re) (exp im)))
0.0b	(/ (cos re) (exp im))
0.1b	(log1p (expm1 (* (fma (exp im) (cos re) (/ (cos re) (exp im))) 0.5)))
0.6b	(expm1 (* (fma (exp im) (cos re) (/ (cos re) (exp im))) 0.5))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-cbrt-cube`
5×	`add-exp-log` `log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `fma-udef` `div-inv` `expm1-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(fma (exp im) (cos re) (/ (cos re) (exp im)))
4.0ms	(/ (cos re) (exp im))
0.0ms	(log1p (expm1 (* (fma (exp im) (cos re) (/ (cos re) (exp im))) 0.5)))
0.0ms	(expm1 (* (fma (exp im) (cos re) (/ (cos re) (exp im))) 0.5))

series326.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (exp im) (cos re) (/ (cos re) (exp im)))
26.0ms	(/ (cos re) (exp im))
113.0ms	(log1p (expm1 (* (fma (exp im) (cos re) (/ (cos re) (exp im))) 0.5)))
116.0ms	(expm1 (* (fma (exp im) (cos re) (/ (cos re) (exp im))) 0.5))

simplify2.2s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	112	934
1	212	885
2	546	793
3	1533	787
4	4896	784
done	5000	784

prune198.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
done	13	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2984×	body	1280	valid
540.0ms	2479×	body	640	valid
378.0ms	8509×	body	80	valid
190.0ms	1290×	body	320	valid
60.0ms	634×	body	160	valid