Details

Time bar (total: 45.6s)

sample210.0ms

Algorithm
intervals
Results
87.0ms87×body1280valid
55.0ms83×body640valid
32.0ms250×body80valid
16.0ms38×body320valid
5.0ms18×body160valid

simplify186.0ms

Calls
1 calls:
Slowest
185.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
9×times-frac
7×add-cbrt-cube
6×add-exp-log
5×pow1 add-log-exp
3×associate-/r* associate-*r* associate-*l* insert-posit16 associate-/l*
2×flip3-+ associate-*l/ flip-+
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Calls
3 calls:
Slowest
84.0ms
(* (+ (/ 0.5 (exp im)) (* (exp im) 0.5)) (cos re))
18.0ms
(+ (/ 0.5 (exp im)) (* (exp im) 0.5))
5.0ms
(/ 0.5 (exp im))

series207.0ms

Calls
3 calls:
Slowest
110.0ms
(* (+ (/ 0.5 (exp im)) (* (exp im) 0.5)) (cos re))
68.0ms
(+ (/ 0.5 (exp im)) (* (exp im) 0.5))
29.0ms
(/ 0.5 (exp im))

simplify2.7s

Calls
47 calls:
Slowest
441.0ms
(* (+ (/ 0.5 (exp im)) (* (exp im) 0.5)) (cos re))
438.0ms
(/ (* (* 0.5 0.5) 0.5) (* (* (exp im) (exp im)) (exp im)))
286.0ms
(* (+ (pow (/ 0.5 (exp im)) 3) (pow (* (exp im) 0.5) 3)) (cos re))
215.0ms
(* (- (* (/ 0.5 (exp im)) (/ 0.5 (exp im))) (* (* (exp im) 0.5) (* (exp im) 0.5))) (cos re))
209.0ms
(* (* (* (+ (/ 0.5 (exp im)) (* (exp im) 0.5)) (+ (/ 0.5 (exp im)) (* (exp im) 0.5))) (+ (/ 0.5 (exp im)) (* (exp im) 0.5))) (* (* (cos re) (cos re)) (cos re)))

prune678.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (sqrt (/ 0.5 (exp im))) (sqrt (/ 0.5 (exp im))))
0.0b
(sqrt (/ 0.5 (exp im)))
0.0b
(sqrt (/ 0.5 (exp im)))
0.0b
(/ 0.5 (exp im))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt sqrt-prod
71×times-frac
58×*-un-lft-identity add-cube-cbrt
21×pow1
18×swap-sqr
16×associate-*r* associate-*l*
10×sqrt-pow1 pow1/2
9×unswap-sqr
8×add-cbrt-cube
7×add-exp-log div-inv
6×sqrt-div
5×pow-prod-up
4×rem-sqrt-square insert-posit16 add-log-exp
3×associate-/r* pow-prod-down pow-sqr associate-/l*
1×pow2 frac-times cbrt-undiv clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (/ 0.5 (exp im))) (sqrt (/ 0.5 (exp im))))
5.0ms
(/ 0.5 (exp im))
3.0ms
(sqrt (/ 0.5 (exp im)))
3.0ms
(sqrt (/ 0.5 (exp im)))

series223.0ms

Calls
4 calls:
Slowest
100.0ms
(* (sqrt (/ 0.5 (exp im))) (sqrt (/ 0.5 (exp im))))
57.0ms
(sqrt (/ 0.5 (exp im)))
51.0ms
(sqrt (/ 0.5 (exp im)))
14.0ms
(/ 0.5 (exp im))

simplify4.0s

Calls
185 calls:
Slowest
384.0ms
(/ (* (* 0.5 0.5) 0.5) (* (* (exp im) (exp im)) (exp im)))
359.0ms
(- (+ (pow (sqrt 0.5) 2) (* 1/2 (* (pow (sqrt 0.5) 2) (pow im 2)))) (* (pow (sqrt 0.5) 2) im))
297.0ms
(- (+ (* 1/8 (* (sqrt 0.5) (pow im 2))) (sqrt 0.5)) (* 1/2 (* (sqrt 0.5) im)))
255.0ms
(- (+ (* 1/8 (* (sqrt 0.5) (pow im 2))) (sqrt 0.5)) (* 1/2 (* (sqrt 0.5) im)))
189.0ms
(* (* (* (sqrt (/ 0.5 (exp im))) (sqrt (/ 0.5 (exp im)))) (sqrt (/ 0.5 (exp im)))) (* (* (sqrt (/ 0.5 (exp im))) (sqrt (/ 0.5 (exp im)))) (sqrt (/ 0.5 (exp im)))))

prune2.0s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (exp im) (sqrt 0.5))
1.0b
(* (sqrt (/ 0.5 (exp im))) (sqrt (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))))
0.0b
(/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))
0.0b
(sqrt (/ 0.5 (exp im)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
573×times-frac
479×sqrt-prod
384×add-sqr-sqrt
295×*-un-lft-identity add-cube-cbrt
140×associate-*r*
28×associate-/r*
24×unswap-sqr
18×div-inv
16×associate-*l*
13×add-cbrt-cube
11×add-exp-log
9×pow1 associate-/l*
5×sqrt-div
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 pow-prod-down
2×rem-sqrt-square clear-num frac-2neg associate-/r/
1×frac-times sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
57.0ms
(* (sqrt (/ 0.5 (exp im))) (sqrt (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))))
22.0ms
(/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))
12.0ms
(/ (exp im) (sqrt 0.5))
7.0ms
(sqrt (/ 0.5 (exp im)))

series361.0ms

Calls
4 calls:
Slowest
110.0ms
(/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))
96.0ms
(* (sqrt (/ 0.5 (exp im))) (sqrt (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))))
94.0ms
(sqrt (/ 0.5 (exp im)))
61.0ms
(/ (exp im) (sqrt 0.5))

simplify19.6s

Calls
585 calls:
Slowest
421.0ms
(/ (* (* (sqrt 0.5) (sqrt 0.5)) (sqrt 0.5)) (/ (* (* (exp im) (exp im)) (exp im)) (* (* (sqrt 0.5) (sqrt 0.5)) (sqrt 0.5))))
361.0ms
(- (+ (pow (sqrt 0.5) 2) (* 1/2 (* (pow (sqrt 0.5) 2) (pow im 2)))) (* (pow (sqrt 0.5) 2) im))
342.0ms
(- (+ (pow (sqrt 0.5) 2) (* 1/2 (* (pow (sqrt 0.5) 2) (pow im 2)))) (* (pow (sqrt 0.5) 2) im))
276.0ms
(- (+ (* 1/8 (* (sqrt 0.5) (pow im 2))) (sqrt 0.5)) (* 1/2 (* (sqrt 0.5) im)))
263.0ms
(/ (sqrt 1) (/ (* (cbrt (exp im)) (cbrt (exp im))) (* (cbrt (sqrt 0.5)) (cbrt (sqrt 0.5)))))

prune6.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.1s2964×body1280valid
1.9s2514×body640valid
1.6s8546×body80valid
942.0ms1273×body320valid
610.0ms679×body160valid