Details

sample223.0ms

Algorithm

intervals

Results

66.0ms	92×	body	1280	valid
48.0ms	99×	body	640	valid
46.0ms	42×	body	320	valid
28.0ms	291×	body	80	valid
3.0ms	17×	body	160	valid

simplify5.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12
1	26	12
2	63	12
3	120	12
4	197	12
5	244	12
6	355	12
7	423	12
8	700	12
9	1173	12
10	1473	12
11	1509	12
12	1566	12
done	1566	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

14×	`fma-def` `*-un-lft-identity`
11×	`exp-sum`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`prod-diff`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`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` `sub-neg` `distribute-lft-in` `associate-l` `sum-log` `*-commutative`

Counts

2 → 53

Calls

2 calls:

87.0ms	(+ (exp (- 0.0 im)) (exp im))
233.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

series196.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (exp (- 0.0 im)) (exp im))
150.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

simplify4.9s

Counts

59 → 59

Iterations

Useful iterations: 3 (2.8s)

Iter	Nodes	Cost
0	97	642
1	272	622
2	1084	528
3	4758	527
done	5000	527

prune301.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-r`
13×	`pow1` `add-cbrt-cube`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `exp-sum`
9×	`add-exp-log` `prod-diff`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`associate-l` `*-commutative`
1×	`+-commutative` `sub-neg` `fma-def` `flip3-+` `exp-diff` `associate-*r/` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 67

Calls

3 calls:

86.0ms	(* (* 0.5 (sin re)) (exp (- 0.0 im)))
119.0ms	(+ (* (* 0.5 (sin re)) (exp (- 0.0 im))) (* (* 0.5 (sin re)) (exp im)))
53.0ms	(* (* 0.5 (sin re)) (exp im))

series310.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* (* 0.5 (sin re)) (exp (- 0.0 im)))
160.0ms	(+ (* (* 0.5 (sin re)) (exp (- 0.0 im))) (* (* 0.5 (sin re)) (exp im)))
67.0ms	(* (* 0.5 (sin re)) (exp im))

simplify1.8s

Counts

76 → 76

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	161	1115
1	417	943
2	1507	807
done	5000	788

prune350.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

12.0ms	(/ (sin re) (exp im))
24.0ms	(+ (* (/ (sin re) (exp im)) 0.5) (* (* 0.5 (sin re)) (exp im)))
33.0ms	(* (* 0.5 (sin re)) (exp im))

series250.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (sin re) (exp im))
119.0ms	(+ (* (/ (sin re) (exp im)) 0.5) (* (* 0.5 (sin re)) (exp im)))
77.0ms	(* (* 0.5 (sin re)) (exp im))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	129	898
1	326	823
2	1203	729
done	5001	725

prune299.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (exp im) (sin re) (/ (sin re) (exp im)))
0.0b	(/ (sin re) (exp im))

rewrite34.0ms

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:

1.0ms	(fma (exp im) (sin re) (/ (sin re) (exp im)))
31.0ms	(/ (sin re) (exp im))

series178.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(fma (exp im) (sin re) (/ (sin re) (exp im)))
61.0ms	(/ (sin re) (exp im))

simplify5.0s

Counts

45 → 45

Iterations

Useful iterations: 3 (303.0ms)

Iter	Nodes	Cost
0	79	473
1	147	459
2	341	418
3	765	416
4	1792	416
5	4945	416
done	5000	416

prune174.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
done	9	12

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.0s	2971×	body	1280	valid
1.9s	2460×	body	640	valid
1.1s	8550×	body	80	valid
471.0ms	1237×	body	320	valid
238.0ms	592×	body	160	valid