Details

Time bar (total: 11.0s)

sample91.0ms

Algorithm
intervals
Results
37.0ms99×body1280valid
16.0ms77×body640valid
15.0ms290×body80valid
5.0ms38×body320valid
2.0ms18×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01011
12311
25811
310011
420911
529211
641211
795711
8162811
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)))

rewrite43.0ms

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:
14.0ms
(+ (exp (- im)) (exp im))
28.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series86.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(+ (exp (- im)) (exp im))
58.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify760.0ms

Counts
48 → 48
Iterations

Useful iterations: done (759.0ms)

IterNodesCost
091586
1256566
2987476
done5000475

prune140.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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)))

rewrite23.0ms

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))
8.0ms
(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
10.0ms
(* (exp im) (* 0.5 (cos re)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ (cos re) (exp im))
82.0ms
(+ (* (/ (cos re) (exp im)) 0.5) (* (exp im) (* 0.5 (cos re))))
41.0ms
(* (exp im) (* 0.5 (cos re)))

simplify2.1s

Counts
72 → 72
Iterations

Useful iterations: 3 (643.0ms)

IterNodesCost
0123884
1305811
21059717
34969714
done5000714

prune194.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-exp-log add-cbrt-cube
12×associate-*l*
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow-prod-down prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u
3×exp-prod
2×associate-*r* *-commutative
1×+-commutative rem-sqrt-square fma-def flip3-+ pow1/2 sum-log flip-+
Counts
4 → 81
Calls
4 calls:
1.0ms
(sqrt (exp im))
12.0ms
(* (sqrt (exp im)) (* 0.5 (cos re)))
10.0ms
(+ (* (/ (cos re) (exp im)) 0.5) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
34.0ms
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(sqrt (exp im))
51.0ms
(* (sqrt (exp im)) (* 0.5 (cos re)))
81.0ms
(+ (* (/ (cos re) (exp im)) 0.5) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
40.0ms
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

simplify597.0ms

Counts
93 → 93
Iterations

Useful iterations: done (595.0ms)

IterNodesCost
01301308
1335988
21145843
done5000832

prune242.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp im) (exp (- im)))
0.0b
(* (+ (exp im) (exp (- im))) (* 0.5 (cos re)))
0.3b
(pow (* (+ (exp im) (exp (- im))) (* 0.5 (cos re))) 3)
0.5b
(cbrt (pow (* (+ (exp im) (exp (- im))) (* 0.5 (cos re))) 3))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log add-cbrt-cube
12×*-un-lft-identity
8×cbrt-prod add-sqr-sqrt add-cube-cbrt
6×pow-prod-down associate-*l/ prod-exp cbrt-unprod add-log-exp
4×cube-div expm1-log1p-u flip3-+ associate-*l* flip-+ log1p-expm1-u
3×pow-unpow pow-pow fma-def pow-exp rem-cube-cbrt
2×cube-mult unpow-prod-down cbrt-div unpow3 cube-prod distribute-lft-out sqr-pow
1×+-commutative pow-to-exp pow1/3 associate-*r* sum-log *-commutative rem-cbrt-cube
Counts
4 → 90
Calls
4 calls:
6.0ms
(+ (exp im) (exp (- im)))
27.0ms
(* (+ (exp im) (exp (- im))) (* 0.5 (cos re)))
12.0ms
(pow (* (+ (exp im) (exp (- im))) (* 0.5 (cos re))) 3)
3.0ms
(cbrt (pow (* (+ (exp im) (exp (- im))) (* 0.5 (cos re))) 3))

series215.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (exp im) (exp (- im)))
57.0ms
(* (+ (exp im) (exp (- im))) (* 0.5 (cos re)))
79.0ms
(pow (* (+ (exp im) (exp (- im))) (* 0.5 (cos re))) 3)
57.0ms
(cbrt (pow (* (+ (exp im) (exp (- im))) (* 0.5 (cos re))) 3))

simplify514.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (125.0ms)

IterNodesCost
01441566
13631322
213471223
done50001223

prune316.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
11720
done1720

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s3006×body1280valid
566.0ms2570×body640valid
379.0ms8549×body80valid
189.0ms1264×body320valid
57.0ms590×body160valid