Details

Time bar (total: 21.1s)

sample41.0ms

Algorithm
intervals
Results
18.0ms82×body1280valid
6.0ms139×body80valid
3.0ms19×body640valid
2.0ms13×body320valid
0.0ms3×body160valid

simplify47.0ms

Counts
1 → 1
Iterations
IterNodes
done37
637
535
430
328
224
119
09

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize12.0ms

Local error

Found 1 expressions with local error:

1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 14
Calls
1 calls:
5.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series101.0ms

Counts
1 → 3
Calls
1 calls:
101.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts
17 → 17
Iterations
IterNodes
done5001
31443
2287
188
043

prune103.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* 1.0 (+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))))
0.0b
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (+ (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* 1.0 (+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))
0.0b
(+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
0.8b
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt add-log-exp
12×times-frac
11×flip3-+ flip-+
10×cube-unmult
8×frac-add associate-*r/
6×add-cbrt-cube add-exp-log associate-/r/
5×difference-cubes
4×pow1 sum-log associate-/l*
3×associate-/r*
2×distribute-rgt-in +-commutative associate-+r+ distribute-lft-in flip3-- flip-- associate--r+ associate-/l/
1×cbrt-undiv associate-+l+ clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv distribute-lft-out
Counts
4 → 86
Calls
4 calls:
79.0ms
(+ (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* 1.0 (+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))))
134.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (+ (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* 1.0 (+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))
28.0ms
(+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
34.0ms
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))

series647.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(+ (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* 1.0 (+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))))
311.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (+ (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* 1.0 (+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))
74.0ms
(+ 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
134.0ms
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))

simplify3.1s

Counts
98 → 98
Iterations
IterNodes
done5000
23110
1573
0181

prune723.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
0.0b
(+ (+ (/ 0.5 (hypot 1.0 x)) 1.5) (* 1.0 (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.0b
(* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
0.8b
(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
38×flip3-+ flip-+
32×frac-times
27×*-un-lft-identity
25×pow1
20×associate-*r/
14×add-sqr-sqrt
11×add-cbrt-cube add-exp-log add-log-exp
10×associate-*l/
9×add-cube-cbrt
8×associate-*l*
7×distribute-lft-out
6×swap-sqr pow-prod-up
5×distribute-rgt-in distribute-lft-in associate-*r*
4×sqrt-div pow-prod-down frac-add prod-exp cbrt-unprod
3×sum-log
2×pow2 pow-plus pow-sqr *-commutative unswap-sqr
1×+-commutative associate-+l+ sub-neg flip3-- diff-log cube-unmult flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 126
Calls
4 calls:
76.0ms
(* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
73.0ms
(+ (+ (/ 0.5 (hypot 1.0 x)) 1.5) (* 1.0 (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
120.0ms
(* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
4.0ms
(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
133.0ms
(+ (+ (/ 0.5 (hypot 1.0 x)) 1.5) (* 1.0 (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
104.0ms
(* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
117.0ms
(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))

simplify1.3s

Counts
138 → 138
Iterations
IterNodes
done5001
1679
0215

prune774.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
0.0b
(* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
0.0b
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5)))) (+ (+ (* 1.0 1.0) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) 1.0)))
0.8b
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

rewrite3.5s

Algorithm
rewrite-expression-head
Rules
135×flip3-+ flip-+
112×frac-times
108×associate-*l/
54×associate-/r/
52×sqrt-div frac-add
42×pow1
32×associate-*r/
18×*-un-lft-identity
16×add-sqr-sqrt add-cbrt-cube add-exp-log
14×add-cube-cbrt
12×pow-plus pow-prod-up
9×times-frac
8×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod add-log-exp
4×pow2 pow-sqr associate--r+
3×associate-/r* associate-/l*
2×flip3-- associate-*l* pow3 *-commutative flip-- distribute-lft-out unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 214
Calls
4 calls:
122.0ms
(* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
191.0ms
(* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
2.4s
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5)))) (+ (+ (* 1.0 1.0) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) 1.0)))
740.0ms
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

series1.0s

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
97.0ms
(* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
663.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5)))) (+ (+ (* 1.0 1.0) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) 1.0)))
201.0ms
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

simplify3.2s

Counts
226 → 226
Iterations
IterNodes
done5000
11457
0475

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.4b

regimes132.0ms

Accuracy

0% (0.0b remaining)

Error of 14.7b against oracle of 14.7b and baseline of 14.7b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done36
236
134
024

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s2843×body1280valid
314.0ms4049×body80valid
264.0ms638×body640valid
75.0ms135×body160valid
59.0ms335×body320valid