Details

Time bar (total: 32.4s)

sample89.0ms

Algorithm
intervals
Results
45.0ms73×body1280valid
16.0ms144×body80valid
10.0ms21×body640valid
3.0ms10×body320valid
2.0ms8×body160valid

simplify14.0ms

Counts
1 → 1
Iterations
IterNodes
325
225
121
09

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b
(/ 1/2 (hypot 1 x))
2.6b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×times-frac
8×sqrt-prod
6×add-cbrt-cube add-exp-log add-log-exp
5×pow1
4×insert-posit16 difference-of-squares
3×associate-/r* associate-/l* distribute-lft-out--
2×sqrt-div distribute-lft-out
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log div-exp flip-+ div-inv flip--
Counts
4 → 73
Calls
4 calls:
0.0ms
(hypot 1 x)
9.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
3.0ms
(/ 1/2 (hypot 1 x))
39.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series128.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(hypot 1 x)
50.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
10.0ms
(/ 1/2 (hypot 1 x))
66.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify3.4s

Counts
85 → 85
Iterations
IterNodes
43528
31199
2424
1209
0113

prune795.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
2.0b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×times-frac
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
4×pow1 insert-posit16 distribute-lft-out
2×cbrt-undiv clear-num frac-2neg div-exp sqrt-prod div-inv difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 87
Calls
4 calls:
3.0ms
(/ 1/2 (hypot 1 x))
4.0ms
(/ 1/2 (hypot 1 x))
16.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
7.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series114.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1/2 (hypot 1 x))
5.0ms
(/ 1/2 (hypot 1 x))
47.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
56.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify8.3s

Counts
99 → 99
Iterations
IterNodes
44651
31373
2479
1214
0107

prune982.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))
0.2b
(/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
1.9b
(- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
27×*-un-lft-identity
20×add-cbrt-cube add-exp-log
18×pow1 times-frac
17×add-cube-cbrt
8×associate-/l*
6×prod-exp cbrt-unprod add-log-exp
5×pow-prod-up distribute-lft-out-- difference-of-squares
4×cbrt-undiv associate-/r* div-exp insert-posit16
3×associate-*l* pow-prod-down
2×clear-num frac-2neg flip3-- associate-/r/ div-inv flip-- associate-/l/
1×pow2 sub-neg flip3-+ pow-plus diff-log div-sub cube-unmult associate-*r* pow-sqr *-commutative flip-+ unswap-sqr
Counts
4 → 105
Calls
4 calls:
61.0ms
(/ (- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
16.0ms
(* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))
12.0ms
(/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
19.0ms
(- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))

series371.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(/ (- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
43.0ms
(* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))
37.0ms
(/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
87.0ms
(- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))

simplify4.3s

Counts
117 → 117
Iterations
IterNodes
36809
21395
1431
0171

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1/8 (* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x))))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.1b
(* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x))))
0.5b
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
1.9b
(- 1/8 (* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x)))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
37×add-sqr-sqrt
32×add-cbrt-cube
31×times-frac
25×*-un-lft-identity
23×add-cube-cbrt
17×div-exp prod-exp
13×associate-*l*
10×cbrt-undiv
9×cbrt-unprod
7×associate-*r*
6×pow1 associate-/l* add-log-exp unswap-sqr
4×associate-/r* insert-posit16 div-inv
3×rec-exp 1-exp
2×clear-num frac-2neg flip3-- associate-/r/ flip-- associate-/l/
1×frac-times sub-neg flip3-+ diff-log div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 125
Calls
4 calls:
32.0ms
(/ (- 1/8 (* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x))))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
29.0ms
(* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x))))
6.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
4.0ms
(- 1/8 (* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x)))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (- 1/8 (* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x))))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
53.0ms
(* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x))))
20.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
89.0ms
(- 1/8 (* (/ 1 (hypot 1 x)) (/ 1/8 (* (hypot 1 x) (hypot 1 x)))))

simplify6.3s

Counts
137 → 137
Iterations
IterNodes
37831
21857
1590
0213

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

regimes107.0ms

Accuracy

0% (0.3b remaining)

Error of 14.6b against oracle of 14.4b and baseline of 14.6b

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
241
141
028

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.2s2852×body1280valid
424.0ms4052×body80valid
301.0ms624×body640valid
117.0ms317×body320valid
29.0ms155×body160valid