Details

Time bar (total: 15.5s)

sample59.0ms

Algorithm
intervals
Results
14.0ms202×body80valid
11.0ms24×body2560valid
6.0ms256×pre80true
4.0ms13×body1280valid
4.0ms13×body640valid
1.0ms4×body320valid

simplify99.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01417
12816
24016
34716
44916
55116
65216
done5216

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity add-log-exp
6×add-sqr-sqrt
5×add-cube-cbrt
4×pow1 fma-def
3×add-exp-log expm1-log1p-u flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 48
Calls
3 calls:
40.0ms
(+ (* (* 4.0 p) p) (* x x))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
41.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series275.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(+ (* (* 4.0 p) p) (* x x))
101.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
107.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
57 → 57
Iterations

Useful iterations: done (1.8s)

IterNodesCost
085833
1218726
2699658
32170637
done5001633

prune313.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
17.2b
(sqrt (fma 4.0 (pow p 2) (* x x)))
17.2b
(sqrt (fma 4.0 (pow p 2) (* x x)))
17.2b
(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
4×add-exp-log cbrt-prod expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×flip3-+ pow1/3 flip-+ distribute-lft-out
Counts
4 → 61
Calls
4 calls:
20.0ms
(cbrt (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
3.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
4.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
4.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
479.0ms
(cbrt (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
62.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
102.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
92.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify2.9s

Counts
73 → 73
Iterations

Useful iterations: 5 (1.7s)

IterNodesCost
075999
1152907
2308856
3638840
41521838
54126836
done5000836

prune500.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))))
7.3b
(+ 1.0 (/ x (* (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))))))
17.2b
(sqrt (fma 4.0 (pow p 2) (* x x)))
17.2b
(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
21×*-un-lft-identity
19×add-cube-cbrt
18×pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u
3×fma-def
2×rem-sqrt-square
1×+-commutative pow2 flip3-+ pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 124
Calls
4 calls:
36.0ms
(* (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))))
26.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))))))
2.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
2.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))))
114.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x)))))))
86.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
73.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify2.1s

Counts
136 → 136
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01163008
12191696
25611566
318911513
done50001470

prune549.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.5b

localize42.0ms

Local error

Found 4 expressions with local error:

7.8b
(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (fma 4.0 (pow p 2) (* x x))))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x))))) (sqrt (sqrt (cbrt (fma 4.0 (pow p 2) (* x x))))))))
17.2b
(sqrt (fma 4.0 (pow p 2) (* x x)))
18.1b
(cbrt (fma 4.0 (pow p 2) (* x x)))
18.1b
(cbrt (fma 4.0 (pow p 2) (* x x)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-def sqrt-prod
2×pow1/3
1×+-commutative rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sum-log flip-+ distribute-lft-out
Counts
4 → 58
Calls
4 calls:
39.0ms
(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (fma 4.0 (pow p 2) (* x x))))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x))))) (sqrt (sqrt (cbrt (fma 4.0 (pow p 2) (* x x))))))))
3.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
2.0ms
(cbrt (fma 4.0 (pow p 2) (* x x)))
2.0ms
(cbrt (fma 4.0 (pow p 2) (* x x)))

series670.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (fma 4.0 (pow p 2) (* x x))))) (sqrt (sqrt (fma 4.0 (pow p 2) (* x x))))) (sqrt (sqrt (cbrt (fma 4.0 (pow p 2) (* x x))))))))
60.0ms
(sqrt (fma 4.0 (pow p 2) (* x x)))
202.0ms
(cbrt (fma 4.0 (pow p 2) (* x x)))
184.0ms
(cbrt (fma 4.0 (pow p 2) (* x x)))

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01221559
12671481
27281326
327821307
done50001281

prune462.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

regimes133.0ms

Accuracy

0% (1.5b remaining)

Error of 14.8b against oracle of 13.3b and baseline of 14.8b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02544
12944
done2944

end0.0ms

sample2.2s

Algorithm
intervals
Results
611.0ms8000×pre80true
458.0ms5980×body80valid
431.0ms851×body2560valid
257.0ms636×body1280valid
70.0ms299×body640valid
30.0ms151×body320valid
10.0ms83×body160valid