Details

Time bar (total: 42.0s)

sample43.0ms

Algorithm
intervals
Results
20.0ms90×body1280valid
6.0ms129×body80valid
4.0ms22×body640valid
1.0ms8×body320valid
1.0ms7×body160valid

simplify361.0ms

Counts
1 → 1
Iterations
IterNodes
done42
642
540
434
332
226
119
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(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))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 log1p-expm1-u
3×associate-/r* fma-def fma-neg sqrt-prod associate-/l*
1×cbrt-undiv +-commutative hypot-udef clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
18.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0ms
(hypot 1.0 x)
6.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series936.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
100.0ms
(hypot 1.0 x)
135.0ms
(/ 1.0 (hypot 1.0 x))
544.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.9s

Counts
99 → 99
Iterations
IterNodes
done5001
22439
1564
0223

prune823.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

localize124.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×associate-/r* times-frac
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u
3×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
1×difference-cubes sub-neg flip3-- fma-neg diff-log cube-unmult prod-diff pow3 flip--
Counts
4 → 86
Calls
4 calls:
8.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
10.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
9.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
38.0ms
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
196.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
132.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
1.3s
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))

simplify2.8s

Counts
98 → 98
Iterations
IterNodes
done5002
23075
1591
0204

prune949.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

localize192.0ms

Local error

Found 4 expressions with local error:

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

rewrite452.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
22×sqrt-prod
19×pow1
14×*-un-lft-identity add-cube-cbrt
12×sqrt-div
11×add-cbrt-cube add-exp-log
9×swap-sqr
8×sqrt-pow1 flip3-- pow1/2 flip-- add-log-exp
7×associate-*r* associate-*l*
6×difference-cubes cube-unmult pow3
5×pow-prod-up
4×expm1-log1p-u frac-times log1p-expm1-u unswap-sqr
3×associate-/r* times-frac pow-prod-down pow-sqr
2×cbrt-undiv sub-neg fma-neg diff-log div-exp prod-diff associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×pow2 clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod *-commutative div-inv associate-/l*
Counts
4 → 119
Calls
4 calls:
9.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
336.0ms
(* (sqrt (- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))) (sqrt (- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))))
56.0ms
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))
45.0ms
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))

series4.2s

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
1.4s
(* (sqrt (- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))) (sqrt (- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))))
1.3s
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))
1.3s
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 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))))))

simplify2.8s

Counts
131 → 131
Iterations
IterNodes
done5000
23569
1720
0270

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.4b

localize438.0ms

Local error

Found 4 expressions with local error:

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

rewrite748.0ms

Algorithm
rewrite-expression-head
Rules
136×frac-times
108×flip3-+ sqrt-div flip-+
67×pow1
44×associate-*l/ associate-*r/
26×add-cbrt-cube add-exp-log
25×pow-prod-up
20×pow-prod-down
14×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity sqrt-pow1 pow1/2 add-cube-cbrt
7×pow-sqr
6×associate-/r* times-frac pow3 add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u
2×clear-num frac-2neg pow-plus div-inv associate-/l*
1×pow2 sub-neg flip3-- fma-neg diff-log swap-sqr associate-*r* associate-*l* prod-diff *-commutative flip--
Counts
4 → 189
Calls
4 calls:
12.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
8.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
220.0ms
(* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 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)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
485.0ms
(- (* (* (* 1.0 (* 1.0 1.0)) (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 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)) (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)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))

series7.1s

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
167.0ms
(/ (* 1.0 0.5) (hypot 1.0 x))
360.0ms
(* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 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)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
6.4s
(- (* (* (* 1.0 (* 1.0 1.0)) (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 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)) (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)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))

simplify9.3s

Counts
201 → 201
Iterations
IterNodes
done5001
11936
0579

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.3b

regimes715.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify23.0ms

Iterations
IterNodes
done40
140
031

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.5s2865×body1280valid
428.0ms4052×body80valid
171.0ms599×body640valid
64.0ms327×body320valid
18.0ms157×body160valid