Details

Time bar (total: 11.1s)

sample35.0ms

Algorithm
intervals
Results
15.0ms92×body1280valid
4.0ms126×body80valid
4.0ms14×body320valid
2.0ms19×body640valid
0.0ms5×body160valid

simplify35.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22612
33212
43412
54012
64212
done4212

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity prod-diff
10×add-cube-cbrt
5×pow1
4×sqrt-prod add-log-exp
3×fma-neg
2×add-exp-log expm1-log1p-u sqrt-pow1 sqrt-div associate-*r/ add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- flip3-+ pow1/2 diff-log pow-prod-down flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
2 → 46
Calls
2 calls:
15.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series587.0ms

Counts
2 → 6
Calls
2 calls:
250.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
337.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify684.0ms

Counts
52 → 52
Iterations

Useful iterations: done (682.0ms)

IterNodesCost
01461691
13721291
211331091
done5000958

prune140.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.1b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×associate-/r* distribute-lft-out
3×expm1-log1p-u log1p-expm1-u associate-/l*
2×flip3-- sqrt-pow1 flip3-+ sqrt-div associate-*r/ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv sub-neg frac-2neg pow1/2 fma-neg diff-log div-sub div-exp prod-diff pow-prod-down clear-num sqrt-prod div-inv
Counts
3 → 69
Calls
3 calls:
26.0ms
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
13.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.5s

Counts
3 → 9
Calls
3 calls:
1.1s
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
244.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
112.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.4s

Counts
78 → 78
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02852984
18842816
236462600
done50012592

prune274.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 17.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt 0.5) x)
0.5b
(/ 0.5 (* (pow x 2) (* (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 3) 1.0)))
0.6b
(/ (sqrt 0.5) (* (* (pow x 2) (sqrt 1.0)) (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 2)))
0.7b
(/ (sqrt 0.5) (pow x 2))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log
75×times-frac
57×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
45×sqrt-prod
42×prod-exp
30×div-exp
26×add-cbrt-cube
21×unpow-prod-down associate-/l*
15×pow-to-exp pow-exp
13×associate-/r*
8×cbrt-undiv
7×unpow2 sqr-pow
6×cbrt-unprod
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv add-log-exp
Counts
4 → 195
Calls
4 calls:
7.0ms
(/ (sqrt 0.5) x)
23.0ms
(/ 0.5 (* (pow x 2) (* (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 3) 1.0)))
29.0ms
(/ (sqrt 0.5) (* (* (pow x 2) (sqrt 1.0)) (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 2)))
10.0ms
(/ (sqrt 0.5) (pow x 2))

series630.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (sqrt 0.5) x)
255.0ms
(/ 0.5 (* (pow x 2) (* (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 3) 1.0)))
287.0ms
(/ (sqrt 0.5) (* (* (pow x 2) (sqrt 1.0)) (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 2)))
44.0ms
(/ (sqrt 0.5) (pow x 2))

simplify854.0ms

Counts
207 → 207
Iterations

Useful iterations: 2 (331.0ms)

IterNodesCost
02953270
16342934
221082631
done50012631

prune952.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (sqrt 0.5) (* (* (pow x 2) (sqrt 1.0)) (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 2)))
0.7b
(/ (sqrt 0.5) (pow x 2))
3.2b
(exp (log (/ (sqrt 0.5) (pow x 2))))
28.4b
(log (/ (sqrt 0.5) (pow x 2)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
104×log-prod
99×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
81×sqrt-prod
57×unpow-prod-down
55×add-exp-log
52×exp-sum
21×prod-exp
19×div-exp unpow2 sqr-pow
15×add-cbrt-cube
12×associate-/l*
9×pow-to-exp pow-exp associate-/r*
6×pow1
4×cbrt-undiv expm1-log1p-u exp-prod rem-log-exp log1p-expm1-u div-inv add-log-exp
3×cbrt-unprod
2×log-div frac-2neg clear-num log-pow
1×exp-diff rem-exp-log
Counts
4 → 253
Calls
4 calls:
30.0ms
(/ (sqrt 0.5) (* (* (pow x 2) (sqrt 1.0)) (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 2)))
13.0ms
(/ (sqrt 0.5) (pow x 2))
12.0ms
(exp (log (/ (sqrt 0.5) (pow x 2))))
7.0ms
(log (/ (sqrt 0.5) (pow x 2)))

series562.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(/ (sqrt 0.5) (* (* (pow x 2) (sqrt 1.0)) (pow (fma (sqrt 1.0) (sqrt 0.5) 1.0) 2)))
50.0ms
(/ (sqrt 0.5) (pow x 2))
44.0ms
(exp (log (/ (sqrt 0.5) (pow x 2))))
177.0ms
(log (/ (sqrt 0.5) (pow x 2)))

simplify768.0ms

Counts
265 → 265
Iterations

Useful iterations: done (759.0ms)

IterNodesCost
03624337
16503658
216803217
done50003154

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 17.4b

regimes313.0ms

Accuracy

0% (0.1b remaining)

Error of 15.1b against oracle of 15.0b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01326
11526
done1526

end0.0ms

sample850.0ms

Algorithm
intervals
Results
464.0ms2875×body1280valid
120.0ms4016×body80valid
82.0ms619×body640valid
27.0ms316×body320valid
10.0ms174×body160valid