Details

Time bar (total: 29.0s)

sample53.0ms

Algorithm
intervals
Results
28.0ms101×body1280valid
6.0ms125×body80valid
4.0ms19×body640valid
1.0ms6×body320valid
0.0ms5×body160valid

simplify28.0ms

Counts
1 → 1
Iterations
IterNodes
done30
430
328
224
119
09

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize18.0ms

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 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
2.2b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- pow1/2 diff-log div-exp pow-prod-down sqrt-prod div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
19.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
36.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
47.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
11.0ms
(/ 1.0 (hypot 1.0 x))
115.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.8s

Counts
78 → 78
Iterations
IterNodes
done5001
32076
2663
1238
0112

prune451.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.3b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
12×flip3-+ times-frac flip-+
10×pow1
8×add-cbrt-cube add-exp-log add-log-exp
6×sqrt-div cube-unmult associate-*l* associate-*r/ associate-/r/
5×difference-cubes pow3
4×frac-times frac-add sqrt-prod associate-/l*
3×associate-/r* associate-*r*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 pow-plus flip3-- pow1/2 associate-*l/ pow-prod-up flip-- associate--r+ unswap-sqr associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv distribute-lft-out
Counts
4 → 104
Calls
4 calls:
25.0ms
(+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))
92.0ms
(* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))
186.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
33.0ms
(- (* (* 1.0 1.0) 1.0) (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))
105.0ms
(* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))
276.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
127.0ms
(- (* (* 1.0 1.0) 1.0) (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))

simplify2.8s

Counts
116 → 116
Iterations
IterNodes
done5001
23023
1686
0208

prune875.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.3b

localize142.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))
0.5b
(/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
0.5b
(/ (* (* 1.0 1.0) 1.0) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
2.2b
(- (/ (* (* 1.0 1.0) 1.0) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))))) (/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))))))

rewrite741.0ms

Algorithm
rewrite-expression-head
Rules
32×flip3-+ flip-+
24×associate-/r/
20×add-cbrt-cube associate-*r/ add-exp-log
18×add-sqr-sqrt
16×frac-add
13×*-un-lft-identity
12×sqrt-div
11×add-cube-cbrt
10×pow1
8×frac-times associate-/l/
7×distribute-rgt-out--
6×associate-/r* times-frac associate-*l* add-log-exp
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×associate-*l/ sqrt-prod div-inv
3×associate-*r*
2×clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 pow-prod-up associate-/l* unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log cube-unmult pow-prod-down *-commutative frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 124
Calls
4 calls:
83.0ms
(* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))
95.0ms
(/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
78.0ms
(/ (* (* 1.0 1.0) 1.0) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
480.0ms
(- (/ (* (* 1.0 1.0) 1.0) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))))) (/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))
253.0ms
(/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
134.0ms
(/ (* (* 1.0 1.0) 1.0) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
524.0ms
(- (/ (* (* 1.0 1.0) 1.0) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))))) (/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))))))

simplify4.1s

Counts
136 → 136
Iterations
IterNodes
done5001
23531
1750
0237

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.1b

localize274.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3)
0.5b
(/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3)))
0.5b
(- (* (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))) (* (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
1.7b
(- (/ (* (* 1.0 1.0) 1.0) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3))) (/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
204×associate-*r/
122×flip3-+ flip-+
68×frac-times
65×frac-sub
36×associate-*l/
26×cube-div
18×associate-/r/
15×*-un-lft-identity
12×frac-add
11×add-sqr-sqrt
10×add-cbrt-cube add-exp-log
9×add-cube-cbrt
8×distribute-rgt-in distribute-lft-in distribute-rgt-out-- add-log-exp associate-/l/
6×sqrt-div
5×pow1 associate-/r* times-frac sub-div
4×associate--l+ associate--r+
3×pow-unpow unpow-prod-down cube-prod div-inv
2×cbrt-undiv sub-neg flip3-- diff-log div-exp sum-cubes flip-- distribute-lft-out
1×cube-mult pow-to-exp clear-num pow-pow frac-2neg unpow3 pow-exp prod-exp cbrt-unprod associate-/l* distribute-lft-out-- rem-cube-cbrt difference-of-squares sqr-pow
Counts
4 → 176
Calls
4 calls:
24.0ms
(pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3)
172.0ms
(/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3)))
320.0ms
(- (* (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))) (* (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
985.0ms
(- (/ (* (* 1.0 1.0) 1.0) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3))) (/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3))))

series2.8s

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3)
833.0ms
(/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3)))
389.0ms
(- (* (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))) (* (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))))))))
1.4s
(- (/ (* (* 1.0 1.0) 1.0) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3))) (/ (* (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))) (+ (pow (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x))) 3) (pow (* 1.0 (+ 1.0 (sqrt (+ (* 1.0 0.5) (/ (* 1.0 0.5) (hypot 1.0 x)))))) 3))))

simplify4.4s

Counts
188 → 188
Iterations
IterNodes
done5002
11981
0540

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.1b

regimes165.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify99.0ms

Iterations
IterNodes
done99
199
067

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.9s2822×body1280valid
273.0ms4068×body80valid
194.0ms654×body640valid
59.0ms294×body320valid
20.0ms162×body160valid