Details

Time bar (total: 12.3s)

sample89.0ms

Algorithm
intervals
Results
39.0ms99×body1280valid
16.0ms77×body640valid
13.0ms290×body80valid
5.0ms38×body320valid
2.0ms18×body160valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01011
12311
25811
310811
425311
538911
653011
780911
8132311
done500011

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)))

rewrite41.0ms

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:
10.0ms
(+ (exp (- im)) (exp im))
31.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series85.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(+ (exp (- im)) (exp im))
59.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify460.0ms

Counts
48 → 48
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
091586
1263566
21062476
done5001476

prune123.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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-*l* 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-*r* clear-num sum-log *-commutative flip-+ div-inv
Counts
3 → 63
Calls
3 calls:
4.0ms
(/ (cos re) (exp im))
7.0ms
(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
9.0ms
(* (exp im) (* 0.5 (cos re)))

series168.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ (cos re) (exp im))
80.0ms
(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
57.0ms
(* (exp im) (* 0.5 (cos re)))

simplify429.0ms

Counts
72 → 72
Iterations

Useful iterations: done (427.0ms)

IterNodesCost
0123884
1308811
21149717
done5000714

prune180.0ms

Pruning

3 alts after pruning (3 fresh and 0 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))) (sqrt (exp im)))
0.0b
(+ (* (/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im))) 0.5) (* (exp im) (* 0.5 (cos re))))
0.0b
(* (exp im) (* 0.5 (cos re)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
145×add-sqr-sqrt
144×add-cube-cbrt *-un-lft-identity
135×sqrt-prod
22×associate-/l*
14×add-cbrt-cube
12×add-exp-log
10×pow1
8×div-inv
6×associate-/r* add-log-exp
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u
3×cbrt-undiv exp-prod div-exp associate-*l* pow-prod-down prod-exp cbrt-unprod
1×+-commutative rem-sqrt-square fma-def frac-2neg flip3-+ pow1/2 associate-*r* clear-num sum-log *-commutative flip-+ associate-/l/
Counts
4 → 229
Calls
4 calls:
1.0ms
(sqrt (exp im))
13.0ms
(/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im)))
22.0ms
(+ (* (/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im))) 0.5) (* (exp im) (* 0.5 (cos re))))
9.0ms
(* (exp im) (* 0.5 (cos re)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(sqrt (exp im))
28.0ms
(/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im)))
83.0ms
(+ (* (/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im))) 0.5) (* (exp im) (* 0.5 (cos re))))
92.0ms
(* (exp im) (* 0.5 (cos re)))

simplify1.5s

Counts
241 → 241
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03274843
17934201
230603785
done50003784

prune446.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
145×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
138×sqrt-prod
23×add-exp-log add-cbrt-cube
22×associate-/l*
18×pow1
12×associate-*l*
9×pow-prod-down prod-exp cbrt-unprod
8×div-inv
6×associate-/r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv div-exp
2×associate-*r* *-commutative
1×+-commutative fma-def frac-2neg flip3-+ clear-num sum-log flip-+ associate-/l/
Counts
4 → 240
Calls
4 calls:
14.0ms
(* (sqrt (exp im)) (* 0.5 (cos re)))
13.0ms
(/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im)))
22.0ms
(+ (* (/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im))) 0.5) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
31.0ms
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

series211.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sqrt (exp im)) (* 0.5 (cos re)))
29.0ms
(/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im)))
87.0ms
(+ (* (/ (/ (cos re) (sqrt (exp im))) (sqrt (exp im))) 0.5) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
42.0ms
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

simplify1.5s

Counts
252 → 252
Iterations

Useful iterations: 2 (267.0ms)

IterNodesCost
03385356
18344484
231934001
done50004001

prune483.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
11825
done1825

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s3006×body1280valid
559.0ms2570×body640valid
385.0ms8549×body80valid
182.0ms1264×body320valid
56.0ms590×body160valid