Details

Time bar (total: 13.8s)

sample31.0ms

Algorithm
intervals
Results
15.0ms92×body1280valid
4.0ms137×body80valid
3.0ms17×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22512
33112
43312
53912
64212
done4212

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
12×prod-diff
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r* sqrt-prod associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 60
Calls
2 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series540.0ms

Counts
2 → 6
Calls
2 calls:
125.0ms
(/ 1.0 (hypot 1.0 x))
414.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify684.0ms

Counts
66 → 66
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
01841680
14391305
215861081
done50011081

prune206.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.5b

localize12.0ms

Local error

Found 4 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
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.8b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg flip3-+ fma-neg diff-log div-sub prod-diff flip-+
Counts
4 → 112
Calls
4 calls:
15.0ms
(/ (- (* 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)))))))
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
1.7s
(/ (- (* 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)))))))
119.0ms
(/ 1.0 (hypot 1.0 x))
157.0ms
(/ 1.0 (hypot 1.0 x))
151.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.4s

Counts
124 → 124
Iterations

Useful iterations: 2 (407.0ms)

IterNodesCost
02973324
18763167
241522900
done50002900

prune522.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.5b

localize35.0ms

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))
0.8b
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
64×prod-diff
51×add-sqr-sqrt
47×*-un-lft-identity
45×add-cube-cbrt
27×times-frac
23×sqr-pow
19×unpow-prod-down cube-prod
17×cube-mult unpow3
10×add-exp-log add-cbrt-cube
9×associate-/r* associate-/l*
8×fma-neg difference-of-squares
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×difference-cubes sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 183
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series845.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1.0 (hypot 1.0 x))
113.0ms
(/ 1.0 (hypot 1.0 x))
120.0ms
(/ 1.0 (hypot 1.0 x))
506.0ms
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify1.4s

Counts
195 → 195
Iterations

Useful iterations: 2 (301.0ms)

IterNodesCost
02587363
16194597
223433505
done50013505

prune970.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 12.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.8b
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
1.3b
(log (exp (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
112×prod-diff
84×add-sqr-sqrt
74×*-un-lft-identity
70×add-cube-cbrt
69×unpow-prod-down
61×log-prod
58×exp-sum
41×sqr-pow
18×times-frac
14×cube-mult unpow3 cube-prod
12×difference-of-squares
11×log-pow
10×exp-prod
8×add-exp-log add-cbrt-cube
7×fma-neg
6×associate-/r* associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv sub-neg frac-2neg div-exp clear-num div-inv distribute-lft-out--
1×log-div flip3-- exp-diff diff-log rem-log-exp flip--
Counts
4 → 225
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
37.0ms
(log (exp (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))

series1.3s

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1.0 (hypot 1.0 x))
145.0ms
(/ 1.0 (hypot 1.0 x))
545.0ms
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
519.0ms
(log (exp (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))

simplify1.4s

Counts
237 → 237
Iterations

Useful iterations: 2 (388.0ms)

IterNodesCost
040711554
17676954
224735171
done50015171

prune914.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 12.5b

regimes233.0ms

Accuracy

0% (0.2b remaining)

Error of 14.8b against oracle of 14.6b and baseline of 14.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02576
12876
done2876

end0.0ms

sample978.0ms

Algorithm
intervals
Results
562.0ms2825×body1280valid
143.0ms4065×body80valid
100.0ms637×body640valid
36.0ms331×body320valid
10.0ms142×body160valid