Details

sample87.0ms

Algorithm

intervals

Results

37.0ms	87×	body	1280	valid
18.0ms	63×	body	640	valid
12.0ms	256×	body	80	valid
5.0ms	32×	body	320	valid
1.0ms	14×	body	160	valid

simplify29.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	26	12
2	62	12
3	117	12
4	191	12
5	363	12
6	681	12
7	855	12
8	1330	12
9	2557	12
10	4729	12
done	5001	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 25

Calls

1 calls:

74.0ms

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

series71.0ms

Counts

1 → 3

Calls

1 calls:

71.0ms

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

simplify432.0ms

Counts

28 → 28

Iterations

Useful iterations: done (431.0ms)

Iter	Nodes	Cost
0	81	450
1	240	439
2	997	365
done	5002	364

prune70.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp (- 0.0 im)) 3)
0.2b	(/ (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3) (pow (exp im) 3))) (+ (* (exp (- 0.0 im)) (exp (- 0.0 im))) (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))))
0.3b	(* (exp (- 0.0 im)) (exp im))
5.5b	(- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`exp-sum`
30×	`add-cube-cbrt`
28×	`prod-diff`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `cube-prod` `associate-l`
13×	`add-exp-log`
10×	`exp-diff`
9×	`exp-prod`
8×	`associate-/r/`
7×	`pow1`
6×	`pow-pow` `frac-add` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `times-frac` `div-exp` `associate-r` `associate-l/` `associate-/r`
2×	`frac-times` `flip3-+` `pow-prod-up` `flip-+` `associate-/l/` `distribute-lft-out--`
1×	`cube-div` `cube-mult` `pow-to-exp` `distribute-rgt-out--` `frac-2neg` `fma-neg` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `div-inv` `associate-/l` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 139

Calls

4 calls:

13.0ms	(pow (exp (- 0.0 im)) 3)
212.0ms	(/ (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3) (pow (exp im) 3))) (+ (* (exp (- 0.0 im)) (exp (- 0.0 im))) (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))))
40.0ms	(* (exp (- 0.0 im)) (exp im))
7.0ms	(- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (exp (- 0.0 im)) 3)
227.0ms	(/ (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3) (pow (exp im) 3))) (+ (* (exp (- 0.0 im)) (exp (- 0.0 im))) (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))))
57.0ms	(* (exp (- 0.0 im)) (exp im))
47.0ms	(- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))

simplify2.0s

Counts

151 → 151

Iterations

Useful iterations: 2 (344.0ms)

Iter	Nodes	Cost
0	305	3830
1	900	3094
2	4258	2282
done	5000	2282

prune551.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp im) 3)
0.1b	(pow (exp (- 0.0 im)) 3)
0.2b	(* (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3) (pow (exp im) 3))) (/ 1 (fma (exp im) (- (exp im) (exp (- 0.0 im))) (pow (exp (- 0.0 im)) 2))))
5.5b	(- (exp im) (exp (- 0.0 im)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

87×	`prod-diff`
71×	`add-sqr-sqrt` `*-un-lft-identity`
67×	`add-cube-cbrt`
55×	`exp-sum`
43×	`add-exp-log`
27×	`add-cbrt-cube`
24×	`prod-exp`
17×	`unpow-prod-down` `cube-prod`
15×	`pow1`
13×	`associate-r`
12×	`cbrt-unprod`
10×	`pow-pow`
9×	`times-frac`
8×	`exp-prod`
6×	`sub-neg` `pow-unpow` `div-exp` `pow-prod-down` `add-log-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `fma-neg` `1-exp`
2×	`cube-mult` `frac-times` `pow-to-exp` `flip3-+` `unpow3` `associate-*l/` `pow-exp` `flip-+` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`cube-div` `flip3--` `exp-diff` `diff-log` `associate-l` `un-div-inv` `*-commutative` `flip--` `div-inv`

Counts

4 → 193

Calls

4 calls:

2.0ms	(pow (exp im) 3)
13.0ms	(pow (exp (- 0.0 im)) 3)
259.0ms	(* (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3) (pow (exp im) 3))) (/ 1 (fma (exp im) (- (exp im) (exp (- 0.0 im))) (pow (exp (- 0.0 im)) 2))))
20.0ms	(- (exp im) (exp (- 0.0 im)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (exp im) 3)
26.0ms	(pow (exp (- 0.0 im)) 3)
218.0ms	(* (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3) (pow (exp im) 3))) (/ 1 (fma (exp im) (- (exp im) (exp (- 0.0 im))) (pow (exp (- 0.0 im)) 2))))
42.0ms	(- (exp im) (exp (- 0.0 im)))

simplify3.1s

Counts

205 → 205

Iterations

Useful iterations: 2 (419.0ms)

Iter	Nodes	Cost
0	399	6705
1	1114	5141
2	4733	3620
done	5000	3620

prune524.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 re (* 0.5 (* re (pow im 2))))
0.0b	(* 0.5 (* re (pow im 2)))
0.1b	(* 0.16666666666666666 (pow re 3))
8.0b	(* re (pow im 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-exp-log`
21×	`associate-r`
13×	`prod-exp` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`unpow-prod-down` `unswap-sqr`
6×	`pow1`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `*-commutative`
2×	`unpow2`
1×	`cube-mult` `unpow3` `pow-prod-down` `fma-udef`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma 1.0 re (* 0.5 (* re (pow im 2))))
8.0ms	(* 0.5 (* re (pow im 2)))
6.0ms	(* 0.16666666666666666 (pow re 3))
6.0ms	(* re (pow im 2))

series178.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma 1.0 re (* 0.5 (* re (pow im 2))))
32.0ms	(* 0.5 (* re (pow im 2)))
35.0ms	(* 0.16666666666666666 (pow re 3))
33.0ms	(* re (pow im 2))

simplify619.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	138	914
1	309	833
2	1215	734
done	5001	734

prune230.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes142.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	35
1	27	35
done	27	35

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2934×	body	1280	valid
575.0ms	2478×	body	640	valid
445.0ms	8581×	body	80	valid
189.0ms	1247×	body	320	valid
70.0ms	618×	body	160	valid