Details

Time bar (total: 26.9s)

sample111.0ms

Algorithm
intervals
Results
65.0ms84×body1280valid
15.0ms133×body80valid
12.0ms23×body640valid
3.0ms8×body320valid
2.0ms8×body160valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
323
223
119
09

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
2.2b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
13×add-cube-cbrt
9×times-frac
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1
4×insert-posit16 difference-of-squares
3×associate-/r* distribute-lft-out associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp div-inv flip--
Counts
4 → 78
Calls
4 calls:
7.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
4.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
48.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series199.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
10.0ms
(/ 1/2 (hypot 1 x))
49.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
76.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify9.4s

Counts
90 → 90
Iterations
IterNodes
45634
31679
2559
1230
0118

prune754.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
1.6b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-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
2×cbrt-undiv clear-num frac-2neg div-exp div-inv difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 85
Calls
4 calls:
12.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
12.0ms
(/ 1/2 (hypot 1 x))
8.0ms
(/ 1/2 (hypot 1 x))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
8.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(/ 1/2 (hypot 1 x))
36.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.9s

Counts
97 → 97
Iterations
IterNodes
32260
2530
1181
091

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.0b

localize63.0ms

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) (/ 1/2 (hypot 1 x)))))
0.0b
(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
0.5b
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
1.6b
(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
27×*-un-lft-identity
23×pow1
20×add-cbrt-cube add-exp-log
18×times-frac
17×add-cube-cbrt
8×associate-/l*
6×pow-plus prod-exp pow-prod-up cbrt-unprod add-log-exp
5×distribute-lft-out-- difference-of-squares
4×cbrt-undiv associate-/r* div-exp insert-posit16
3×associate-*r* pow-prod-down
2×pow2 clear-num frac-2neg flip3-- associate-/r/ pow-sqr div-inv flip-- associate-/l/
1×sub-neg flip3-+ diff-log div-sub associate-*l* pow3 *-commutative flip-+ unswap-sqr
Counts
4 → 109
Calls
4 calls:
74.0ms
(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (+ 1/4 (* (+ (/ 1/2 (hypot 1 x)) 1/2) (/ 1/2 (hypot 1 x)))))
15.0ms
(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
18.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
24.0ms
(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (+ 1/4 (* (+ (/ 1/2 (hypot 1 x)) 1/2) (/ 1/2 (hypot 1 x)))))
48.0ms
(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
50.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
78.0ms
(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

simplify3.8s

Counts
121 → 121
Iterations
IterNodes
35754
21418
1445
0170

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.0b

localize142.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
0.5b
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
0.5b
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
1.6b
(- (* 1/8 1/8) (* (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))) (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
31×add-cbrt-cube add-exp-log
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×cbrt-undiv times-frac div-exp prod-exp cbrt-unprod associate-/l*
6×add-log-exp
4×pow1 insert-posit16
3×clear-num associate-/r* frac-2neg div-inv
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
16.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
19.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
28.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
14.0ms
(- (* 1/8 1/8) (* (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))) (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
55.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
60.0ms
(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
78.0ms
(- (* 1/8 1/8) (* (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))) (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))))

simplify1.7s

Counts
98 → 98
Iterations
IterNodes
33480
2723
1221
084

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.0b

regimes81.0ms

Accuracy

0% (0.3b remaining)

Error of 15.5b against oracle of 15.2b and baseline of 15.5b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
214
114
012

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.8s2878×body1280valid
941.0ms4009×body80valid
440.0ms646×body640valid
100.0ms319×body320valid
33.0ms148×body160valid