Details

sample187.0ms

Algorithm

intervals

Results

70.0ms	100×	body	1280	valid
28.0ms	71×	body	640	valid
27.0ms	297×	body	80	valid
22.0ms	30×	body	160	valid
11.0ms	48×	body	320	valid

simplify890.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	760
4	175
3	108
2	61
1	26
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp (- 0.0 im)) (exp im))
0.2b	(* (* (sin re) 0.5) (+ (exp (- 0.0 im)) (exp im)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

45.0ms	(+ (exp (- 0.0 im)) (exp im))
142.0ms	(* (* (sin re) 0.5) (+ (exp (- 0.0 im)) (exp im)))

series139.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (exp (- 0.0 im)) (exp im))
108.0ms	(* (* (sin re) 0.5) (+ (exp (- 0.0 im)) (exp im)))

simplify894.0ms

Counts

41 → 41

Iterations

Iter	Nodes
done	5000
2	1555
1	280
0	93

prune234.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ (exp (- 0.0 im)) (exp im)))
0.2b	(sqrt (+ (exp (- 0.0 im)) (exp im)))
0.4b	(* (* (sqrt (+ (exp (- 0.0 im)) (exp im))) 0.5) (sin re))
0.5b	(* (* (* (sqrt (+ (exp (- 0.0 im)) (exp im))) 0.5) (sin re)) (sqrt (+ (exp (- 0.0 im)) (exp im))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log`
15×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`add-sqr-sqrt`
10×	`associate-r`
9×	`flip3-+` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `flip-+`
4×	`frac-times` `add-log-exp`
3×	`distribute-lft-out`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-r/` `-commutative`

Counts

4 → 85

Calls

4 calls:

48.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
82.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
207.0ms	(* (* (sqrt (+ (exp (- 0.0 im)) (exp im))) 0.5) (sin re))
796.0ms	(* (* (* (sqrt (+ (exp (- 0.0 im)) (exp im))) 0.5) (sin re)) (sqrt (+ (exp (- 0.0 im)) (exp im))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
68.0ms	(sqrt (+ (exp (- 0.0 im)) (exp im)))
127.0ms	(* (* (sqrt (+ (exp (- 0.0 im)) (exp im))) 0.5) (sin re))
92.0ms	(* (* (* (sqrt (+ (exp (- 0.0 im)) (exp im))) 0.5) (sin re)) (sqrt (+ (exp (- 0.0 im)) (exp im))))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	2202
1	415
0	160

prune529.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* im im) (* (pow im 4) 1/12))
0.0b	(* (* (sin re) 0.5) (+ (+ (* im im) (* (pow im 4) 1/12)) 2))
0.1b	(* (pow im 4) 1/12)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
12×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`*-un-lft-identity`
8×	`pow1` `associate-l`
7×	`associate-r` `add-cube-cbrt`
6×	`prod-exp`
5×	`add-log-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`pow-prod-down` `unswap-sqr`
2×	`flip3-+` `associate-r/` `-commutative` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `+-commutative` `sum-log` `distribute-lft-in` `pow-exp` `distribute-lft-out`

Counts

3 → 59

Calls

3 calls:

13.0ms	(+ (* im im) (* (pow im 4) 1/12))
88.0ms	(* (* (sin re) 0.5) (+ (+ (* im im) (* (pow im 4) 1/12)) 2))
10.0ms	(* (pow im 4) 1/12)

series753.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(+ (* im im) (* (pow im 4) 1/12))
192.0ms	(* (* (sin re) 0.5) (+ (+ (* im im) (* (pow im 4) 1/12)) 2))
431.0ms	(* (pow im 4) 1/12)

simplify1.8s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
2	2907
1	412
0	137

prune443.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt im)
0.6b	(cbrt im)
0.6b	(cbrt im)
0.7b	(pow (cbrt im) 4)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `pow1/3` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt im)
1.0ms	(cbrt im)
1.0ms	(cbrt im)
7.0ms	(pow (cbrt im) 4)

series1.1s

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt im)
291.0ms	(cbrt im)
264.0ms	(cbrt im)
331.0ms	(pow (cbrt im) 4)

simplify3.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	3369
2	515
1	156
0	56

prune463.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes244.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.1s	2890×	body	1280	valid
1.3s	2496×	body	640	valid
1.2s	8553×	body	80	valid
513.0ms	1231×	body	320	valid
205.0ms	601×	body	160	valid