Details

Time bar (total: 15.7s)

sample42.0ms

Algorithm
intervals
Results
9.0ms191×body80valid
9.0ms30×body2560valid
4.0ms18×body1280valid
4.0ms256×pre80true
2.0ms10×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify61.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
014365
128340
240340
347340
449340
551340
652340
done52340

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
0.0b
(fma (* 4.0 p) p (* x x))
0.6b
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 *-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log sqrt-prod log1p-expm1-u
3×fma-def sqrt-pow1
2×flip3-+ pow1/2 sqrt-div associate-*l/ flip-+
1×+-commutative rem-sqrt-square sum-log pow-prod-down fma-udef distribute-lft-out
Counts
4 → 57
Calls
4 calls:
26.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
0.0ms
(fma (* 4.0 p) p (* x x))
14.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
1.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
331.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
59.0ms
(fma (* 4.0 p) p (* x x))
92.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
76.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.5s

Counts
69 → 69
Iterations

Useful iterations: 3 (469.0ms)

IterNodesCost
09018894
116916865
247516740
3184016580
done500116580

prune478.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
0.6b
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1 fma-def sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
4 → 64
Calls
4 calls:
12.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
12.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
1.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
111.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
81.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
71.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.5s

Counts
76 → 76
Iterations

Useful iterations: 3 (226.0ms)

IterNodesCost
05618140
112017024
228216974
370216814
4198316814
done500116814

prune629.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* 4.0 p) p (* x x))
0.5b
(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
0.6b
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt
6×pow1 add-log-exp
5×log-pow
4×expm1-log1p-u exp-prod add-cbrt-cube add-exp-log sqrt-prod log1p-expm1-u
3×log-prod fma-def
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+ fma-udef distribute-lft-out
Counts
4 → 60
Calls
4 calls:
0.0ms
(fma (* 4.0 p) p (* x x))
3.0ms
(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
19.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(fma (* 4.0 p) p (* x x))
341.0ms
(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
100.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
94.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (477.0ms)

IterNodesCost
010422722
118618971
247618871
3174218791
done500118791

prune590.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.8b

localize112.0ms

Local error

Found 4 expressions with local error:

1.2b
(log (cbrt (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5)))))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))
13.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
6×log-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×log-pow
1×pow1/3 rem-log-exp
Counts
4 → 63
Calls
4 calls:
2.0ms
(log (cbrt (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5)))))
1.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series1.0s

Counts
4 → 12
Calls
4 calls:
750.0ms
(log (cbrt (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5)))))
98.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
100.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
94.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.9s

Counts
75 → 75
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
07224612
19823626
214623626
319623626
424823626
532723626
648323626
788723626
8255823626
done500023626

prune680.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

regimes244.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
015460
119460
done19460

end0.0ms

sample1.9s

Algorithm
intervals
Results
492.0ms6025×body80valid
451.0ms8000×pre80true
344.0ms774×body2560valid
285.0ms620×body1280valid
62.0ms268×body640valid
33.0ms70×body5120valid
31.0ms166×body320valid
8.0ms77×body160valid