Details

sample93.0ms

Algorithm

intervals

Results

39.0ms	98×	body	1280	valid
18.0ms	87×	body	640	valid
12.0ms	286×	body	80	valid
5.0ms	38×	body	320	valid
2.0ms	23×	body	160	valid

simplify831.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	23	11
2	56	11
3	82	11
4	184	11
5	250	11
6	322	11
7	561	11
8	677	11
9	713	11
10	839	11
11	856	11
done	856	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)))

rewrite38.0ms

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:

10.0ms	(+ (exp (- im)) (exp im))
26.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(+ (exp (- im)) (exp im))
58.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify2.6s

Counts

41 → 41

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	87	548
1	247	530
2	927	441
3	4088	437
done	5000	437

prune97.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-cbrt-cube`
5×	`add-exp-log`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`times-frac` `associate-/r*`
2×	`pow1` `cbrt-undiv` `div-exp`
1×	`+-commutative` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

2 → 32

Calls

2 calls:

9.0ms	(+ (/ (* 0.5 (cos re)) (exp im)) (* (exp im) (* 0.5 (cos re))))
5.0ms	(/ (* 0.5 (cos re)) (exp im))

series121.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(+ (/ (* 0.5 (cos re)) (exp im)) (* (exp im) (* 0.5 (cos re))))
38.0ms	(/ (* 0.5 (cos re)) (exp im))

simplify2.0s

Counts

38 → 38

Iterations

Useful iterations: 3 (857.0ms)

Iter	Nodes	Cost
0	87	582
1	238	546
2	846	469
3	4205	446
done	5000	446

prune98.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp im))
0.0b	(/ (cos re) (sqrt (exp im)))
0.0b	(/ 0.5 (sqrt (exp im)))
0.1b	(* (/ 0.5 (sqrt (exp im))) (/ (cos re) (sqrt (exp im))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
84×	`times-frac`
62×	`add-cube-cbrt` `*-un-lft-identity`
51×	`sqrt-prod`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`sqrt-pow1` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`exp-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 167

Calls

4 calls:

1.0ms	(sqrt (exp im))
7.0ms	(/ (cos re) (sqrt (exp im)))
3.0ms	(/ 0.5 (sqrt (exp im)))
27.0ms	(* (/ 0.5 (sqrt (exp im))) (/ (cos re) (sqrt (exp im))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp im))
41.0ms	(/ (cos re) (sqrt (exp im)))
34.0ms	(/ 0.5 (sqrt (exp im)))
43.0ms	(* (/ 0.5 (sqrt (exp im))) (/ (cos re) (sqrt (exp im))))

simplify933.0ms

Counts

179 → 179

Iterations

Useful iterations: done (928.0ms)

Iter	Nodes	Cost
0	203	2348
1	500	2172
2	1502	1930
done	5001	1910

prune453.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (sqrt (exp (- im))) 0.5) (/ (cos re) (sqrt (exp im)))) (* (exp im) (* 0.5 (cos re))))
0.0b	(sqrt (exp im))
0.0b	(/ (cos re) (sqrt (exp im)))
0.1b	(* (* (sqrt (exp (- im))) 0.5) (/ (cos re) (sqrt (exp im))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt`
34×	`add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
22×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div`
3×	`cbrt-undiv` `exp-prod` `div-exp` `pow-prod-down` `associate-/l*`
2×	`neg-sub0` `exp-neg` `frac-times` `exp-diff` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `flip3-+` `pow1/2` `associate-r/` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

4 → 112

Calls

4 calls:

56.0ms	(+ (* (* (sqrt (exp (- im))) 0.5) (/ (cos re) (sqrt (exp im)))) (* (exp im) (* 0.5 (cos re))))
1.0ms	(sqrt (exp im))
5.0ms	(/ (cos re) (sqrt (exp im)))
57.0ms	(* (* (sqrt (exp (- im))) 0.5) (/ (cos re) (sqrt (exp im))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (* (* (sqrt (exp (- im))) 0.5) (/ (cos re) (sqrt (exp im)))) (* (exp im) (* 0.5 (cos re))))
15.0ms	(sqrt (exp im))
42.0ms	(/ (cos re) (sqrt (exp im)))
75.0ms	(* (* (sqrt (exp (- im))) 0.5) (/ (cos re) (sqrt (exp im))))

simplify971.0ms

Counts

124 → 124

Iterations

Useful iterations: done (968.0ms)

Iter	Nodes	Cost
0	198	1902
1	502	1690
2	2061	1531
done	5000	1529

prune364.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes102.0ms

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
535.0ms	2479×	body	640	valid
373.0ms	8509×	body	80	valid
187.0ms	1290×	body	320	valid
62.0ms	634×	body	160	valid