Details

Time bar (total: 58.0s)

sample59.0ms

Algorithm
intervals
Results
32.0ms90×body1280valid
8.0ms130×body80valid
7.0ms24×body640valid
1.0ms6×body320valid
1.0ms6×body160valid

simplify53.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
53.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(+ (/ 1/2 (hypot 1 x)) 1/2)
0.0b
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
48×add-sqr-sqrt
34×add-cube-cbrt
21×prod-diff
20×sqrt-prod
19×times-frac
13×fma-def
8×add-log-exp
6×add-cbrt-cube add-exp-log distribute-lft-out
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-neg associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+ hypot-def div-inv
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp flip--
Counts
4 → 125
Calls
4 calls:
Slowest
47.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
9.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
5.0ms
(/ 1/2 (hypot 1 x))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
82.0ms
(/ 1/2 (hypot 1 x))
71.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
70.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify8.4s

Counts
118 → 137
Calls
118 calls:
Slowest
454.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))
404.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
390.0ms
(- (+ (* 3/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))) (* 1/4 (/ 1 (pow x 3))))
320.0ms
(- (+ (* 1/4 (/ 1 (* x (sqrt 1/2)))) (sqrt 1/2)) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
311.0ms
(- (+ (* 3/16 (pow x 4)) 1) (* 1/4 (pow x 2)))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize56.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
49×add-sqr-sqrt
38×sqrt-prod
30×distribute-lft-out
25×add-cube-cbrt
24×times-frac
19×pow1
12×sqrt-div
11×swap-sqr
8×sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ add-log-exp difference-of-squares
7×associate-*r* associate-*l*
6×associate-/r*
5×pow-prod-up
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u associate-/l* unswap-sqr
3×fma-def pow-prod-down pow-sqr
2×flip3-- associate-*l/ associate-*r/ associate-/r/ flip-- associate-/l/
1×pow2 cbrt-undiv +-commutative clear-num sum-log sub-neg rem-square-sqrt frac-2neg pow-plus fma-neg sqrt-unprod diff-log div-sub div-exp prod-diff prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
Slowest
132.0ms
(/ (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
71.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
38.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
20.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
393.0ms
(/ (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
110.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
109.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
68.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify15.1s

Counts
169 → 169
Calls
169 calls:
Slowest
688.0ms
(/ (* (* (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (* (* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
580.0ms
(- (+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1)))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1))))))
559.0ms
(+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1)))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1))))))))
506.0ms
(- (+ (* 1/4 (pow x 2)) (* 5/32 (pow x 6))) (* 3/16 (pow x 4)))
482.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(/ 1/2 (hypot 1 x))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt *-un-lft-identity
80×times-frac
62×add-cube-cbrt
39×prod-diff
32×distribute-lft-out
16×sqrt-prod difference-of-squares
9×associate-/r* associate-/l*
8×add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×fma-def fma-neg
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp associate-/r/ flip-+ flip-- associate-/l/
1×+-commutative sum-log sub-neg diff-log div-sub
Counts
4 → 178
Calls
4 calls:
Slowest
61.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
23.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
8.0ms
(/ 1/2 (hypot 1 x))
8.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series676.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
396.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
110.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
91.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
80.0ms
(/ 1/2 (hypot 1 x))

simplify25.2s

Counts
220 → 190
Calls
220 calls:
Slowest
797.0ms
(fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt 1/2) (hypot 1 x)) (/ (* (cbrt 1/2) (cbrt 1/2)) 1))))
579.0ms
(fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))))
559.0ms
(fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))))
517.0ms
(+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1)))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1))))))))
497.0ms
(/ (* (* (- 1/2 (/ 1/2 (hypot 1 x))) (- 1/2 (/ 1/2 (hypot 1 x)))) (- 1/2 (/ 1/2 (hypot 1 x)))) (* (* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (/ 1/2 (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (/ (/ 1/2 (hypot 1 x)) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.2b
(/ (/ 1/2 (hypot 1 x)) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite677.0ms

Algorithm
rewrite-expression-head
Rules
5224×*-un-lft-identity
4868×times-frac
3460×add-sqr-sqrt
2348×distribute-lft-out
2265×add-cube-cbrt
2016×prod-diff
1174×sqrt-prod
263×div-inv
224×associate-/r/
114×flip3-+ flip-+
24×fma-neg
13×associate-/l*
11×distribute-lft-out--
10×add-log-exp
9×add-cbrt-cube add-exp-log
6×associate-/r* fma-def difference-of-squares
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-undiv distribute-rgt-out-- div-exp
2×+-commutative sum-log
1×clear-num sub-neg frac-2neg flip3-- diff-log frac-sub flip-- sub-div associate-/l/
Counts
4 → 2234
Calls
4 calls:
Slowest
394.0ms
(- (/ 1/2 (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (/ (/ 1/2 (hypot 1 x)) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
49.0ms
(/ (/ 1/2 (hypot 1 x)) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
27.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
17.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
779.0ms
(- (/ 1/2 (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (/ (/ 1/2 (hypot 1 x)) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
409.0ms
(/ (/ 1/2 (hypot 1 x)) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
121.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
105.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))