Details

Time bar (total: 35.3s)

sample94.0ms

Algorithm
intervals
Results
44.0ms98×body1280valid
16.0ms5×body160valid
9.0ms123×body80valid
6.0ms18×body640valid
3.0ms12×body320valid

simplify75.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22612
33212
43412
54012
64212
done4212

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
2.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
12×prod-diff
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-neg associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg hypot-udef flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
1.0ms
(hypot 1.0 x)
27.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms
(/ 1.0 (hypot 1.0 x))
41.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
92.0ms
(hypot 1.0 x)
398.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
157.0ms
(/ 1.0 (hypot 1.0 x))
497.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.3s

Counts
97 → 97
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02252149
15361724
215901489
done50001355

prune481.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (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))
1.8b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 91
Calls
4 calls:
12.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series968.0ms

Counts
4 → 12
Calls
4 calls:
462.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
154.0ms
(/ 1.0 (hypot 1.0 x))
174.0ms
(/ 1.0 (hypot 1.0 x))
177.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.8s

Counts
103 → 103
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01901534
14921450
216621311
done50001302

prune647.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.7b
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
63×*-un-lft-identity
56×prod-diff
53×add-cube-cbrt
45×unpow-prod-down
42×sqr-pow
39×times-frac
30×difference-of-squares
13×associate-/l*
11×add-exp-log add-cbrt-cube
8×cube-mult unpow3 cube-prod
7×pow1 fma-neg
6×associate-/r* add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
2×cbrt-undiv cube-div flip3-- pow-pow frac-2neg div-exp associate-*l/ pow-exp clear-num flip-- div-inv associate-/l/ rem-cube-cbrt
1×pow-to-exp sub-neg flip3-+ diff-log div-sub pow-prod-down prod-exp cbrt-unprod flip-+
Counts
4 → 199
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
67.0ms
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
23.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
30.0ms
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series4.0s

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ 1.0 (hypot 1.0 x))
2.9s
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
385.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
555.0ms
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify981.0ms

Counts
211 → 211
Iterations

Useful iterations: done (963.0ms)

IterNodesCost
052211139
113738703
done50007567

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0b
(* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
0.0b
(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
1.7b
(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity
9×pow1 add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u times-frac associate-*r/ associate-*r* log1p-expm1-u associate-/l*
3×pow-unpow flip3-+ associate-*l* prod-exp cbrt-unprod flip-+ difference-of-squares
2×cbrt-undiv cube-div flip3-- pow-pow div-exp pow-prod-down associate-*l/ pow-exp associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg distribute-lft-in fma-neg diff-log unpow3 div-sub cube-prod prod-diff clear-num associate-/r* *-commutative div-inv distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 98
Calls
4 calls:
20.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
85.0ms
(* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
53.0ms
(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
21.0ms
(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

series19.0s

Counts
4 → 12
Calls
4 calls:
302.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.3s
(* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
15.6s
(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
1.8s
(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

simplify1.4s

Counts
110 → 110
Iterations

Useful iterations: done (1.4s)

IterNodesCost
063410170
120128596
done50007047

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

regimes14.0ms