Details

Time bar (total: 2.5m)

sample42.0ms

Algorithm
intervals
Results
19.0ms91×body1280valid
5.0ms117×body80valid
5.0ms26×body640valid
2.0ms20×body320valid
0.0ms2×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.8b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 61
Calls
4 calls:
1.0ms
(hypot 1.0 x)
3.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series198.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
86.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
106.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0201433
1602413
21984411
35001411

prune327.0ms

Filtered
73 candidates to 52 candidates (28.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New68573
Fresh000
Picked101
Done000
Total69574

Merged error: 17.4b

Counts
74 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.1b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-*r/ associate-/r* associate-/l* add-log-exp
4×associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 sqrt-div div-exp clear-num frac-sub flip-- div-inv
1×flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-+
Counts
4 → 85
Calls
4 calls:
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series141.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
41.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify39.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0299576
11026547
25001544

prune540.0ms

Filtered
97 candidates to 70 candidates (27.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New96197
Fresh044
Picked101
Done000
Total975102

Merged error: 17.4b

Counts
102 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.1b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log associate-*r/ add-cbrt-cube
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×times-frac
8×associate-*l/ frac-sub
7×pow1
6×flip3-- flip3-+ flip-- flip-+ associate-/l/ add-log-exp
5×cbrt-undiv div-exp
4×prod-exp associate-/r* cbrt-unprod associate-/l*
2×frac-2neg sqrt-pow1 sqrt-div clear-num associate-/r/ div-inv associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in pow1/2 diff-log pow-prod-down sqrt-prod
Counts
4 → 87
Calls
4 calls:
27.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
16.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series228.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
5.0ms
(/ 1.0 (hypot 1.0 x))
87.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
51.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify103.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06621495
137651260
250021260

prune837.0ms

Filtered
99 candidates to 73 candidates (26.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New97299
Fresh134
Picked011
Done000
Total986104

Merged error: 17.4b

Counts
104 → 6

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.1b
(/ (+ (* (neg (* (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3))) 0.5)) (+ (pow 1.0 6) (pow (* 0.5 (+ 0.5 1.0)) 3))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x)))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3)))))
0.1b
(* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x)))
1.1b
(+ (* (neg (* (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3))) 0.5)) (+ (pow 1.0 6) (pow (* 0.5 (+ 0.5 1.0)) 3))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x))))

rewrite688.0ms

Algorithm
rewrite-expression-head
Rules
2638×associate-*r/
2082×associate-*l/
1760×frac-add
1528×frac-times
1396×flip3-+ flip-+
755×flip3-- flip--
672×distribute-neg-frac
450×associate-/l/
56×associate-/r/
14×add-exp-log add-cbrt-cube
12×pow1
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow-prod-down prod-exp cbrt-unprod
3×times-frac associate-*l* associate-/l*
2×cbrt-undiv associate-+l+ sqrt-pow1 sqrt-div div-exp
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow1/2 associate-*r* clear-num associate-/r* sum-log sqrt-prod *-commutative div-inv
Counts
4 → 1075
Calls
4 calls:
6.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
93.0ms
(/ (+ (* (neg (* (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3))) 0.5)) (+ (pow 1.0 6) (pow (* 0.5 (+ 0.5 1.0)) 3))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x)))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3)))))
65.0ms
(* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x)))
38.0ms
(+ (* (neg (* (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3))) 0.5)) (+ (pow 1.0 6) (pow (* 0.5 (+ 0.5 1.0)) 3))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
145.0ms
(/ (+ (* (neg (* (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3))) 0.5)) (+ (pow 1.0 6) (pow (* 0.5 (+ 0.5 1.0)) 3))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x)))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3)))))
45.0ms
(* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x)))
100.0ms
(+ (* (neg (* (+ (+ (pow 1.0 6) (pow 0.5 6)) (* (pow 1.0 3) (pow 0.5 3))) 0.5)) (+ (pow 1.0 6) (pow (* 0.5 (+ 0.5 1.0)) 3))) (* (+ (* (* 1.0 1.0) (- (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))) (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0)))) (* (- (pow (pow 1.0 3) 3) (pow (pow 0.5 3) 3)) (hypot 1.0 x))))

simplify1.0s

Algorithm
egg-herbie
Counts
1087 → 1087
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05001109218

prune2.5m

Filtered
1087 candidates to 1068 candidates (1.7%)

Profiling

Loading profile data...