Details

Time bar (total: 20.7s)

sample56.0ms

Algorithm
intervals
Results
27.0ms90×body1280valid
7.0ms129×body80valid
6.0ms22×body640valid
1.0ms8×body320valid
1.0ms7×body160valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09258
119258
226258
332258
434258
540258
642258
done42258

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize33.0ms

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))))))

rewrite39.0ms

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:
17.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms
(hypot 1.0 x)
7.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series882.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
84.0ms
(hypot 1.0 x)
154.0ms
(/ 1.0 (hypot 1.0 x))
509.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.2s

Counts
99 → 99
Iterations

Useful iterations: done (2.1s)

IterNodesCost
022339431
156433627
2243930530
done500130385

prune555.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
4×expm1-log1p-u pow1 log1p-expm1-u
3×fma-def
2×cbrt-undiv clear-num frac-2neg div-exp div-inv associate--r+
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ flip3-- fma-neg diff-log prod-diff flip-+ flip-- distribute-lft-out
Counts
4 → 93
Calls
4 calls:
9.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series845.0ms

Counts
4 → 12
Calls
4 calls:
435.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
142.0ms
(/ 1.0 (hypot 1.0 x))
115.0ms
(/ 1.0 (hypot 1.0 x))
153.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.2s

Counts
105 → 105
Iterations

Useful iterations: 2 (925.0ms)

IterNodesCost
019436396
154531006
2267329751
done500129751

prune618.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize119.0ms

Local error

Found 4 expressions with local error:

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

rewrite461.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
10×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
6×add-log-exp
4×distribute-rgt-in expm1-log1p-u pow1 distribute-lft-in log1p-expm1-u associate--r+
3×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×difference-cubes sub-neg flip3-- fma-neg diff-log cube-unmult prod-diff pow3 flip--
Counts
4 → 108
Calls
4 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(/ 1.0 (hypot 1.0 x))
447.0ms
(- (* (* 1.0 1.0) (* (* 1.0 1.0) (* 1.0 1.0))) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series874.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 1.0 (hypot 1.0 x))
105.0ms
(/ 1.0 (hypot 1.0 x))
107.0ms
(/ 1.0 (hypot 1.0 x))
521.0ms
(- (* (* 1.0 1.0) (* (* 1.0 1.0) (* 1.0 1.0))) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.9s

Counts
120 → 120
Iterations

Useful iterations: done (2.8s)

IterNodesCost
017242622
150937568
2296935919
done500135816

prune947.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
2.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
54×*-un-lft-identity
36×add-cube-cbrt sqrt-prod
24×prod-diff
19×pow1
12×sqrt-div swap-sqr
9×times-frac
8×sqrt-pow1 flip3-- add-cbrt-cube pow1/2 associate-*r* associate-*l* add-exp-log flip-- distribute-lft-out-- add-log-exp
6×fma-neg difference-of-squares
5×pow-prod-up
4×expm1-log1p-u frac-times log1p-expm1-u unswap-sqr
3×associate-/r* pow-prod-down pow-sqr associate-/l*
2×sub-neg diff-log associate-*l/ associate-*r/
1×pow2 cbrt-undiv clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod div-exp prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 158
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
57.0ms
(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
9.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ 1.0 (hypot 1.0 x))
466.0ms
(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
443.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
488.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.5s

Counts
170 → 170
Iterations

Useful iterations: done (2.5s)

IterNodesCost
024887380
156572969
2252367697
done500167297

prune895.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes549.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.6b

bsearch3.0ms

simplify22.0ms

Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
0381512
1461512
done461512

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.6s2865×body1280valid
278.0ms4052×body80valid
185.0ms599×body640valid
61.0ms327×body320valid
16.0ms157×body160valid