Details

Time bar (total: 21.8s)

sample87.0ms

Algorithm
intervals
Results
17.0ms183×body80valid
16.0ms27×body2560valid
12.0ms26×body1280valid
8.0ms256×pre80true
4.0ms11×body640valid
2.0ms6×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01417
13116
25016
35216
done5216

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×add-cube-cbrt add-log-exp
3×pow1 fma-def sqrt-prod
2×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
2 → 34
Calls
2 calls:
91.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series241.0ms

Counts
2 → 6
Calls
2 calls:
145.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
96.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.4s

Counts
40 → 40
Iterations

Useful iterations: done (3.4s)

IterNodesCost
071605
1312521
21690468
done5000466

prune227.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.1b

localize37.0ms

Local error

Found 3 expressions with local error:

0.4b
(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
0.4b
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
15.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1 log-pow add-log-exp
4×log-prod exp-prod
3×add-exp-log expm1-log1p-u fma-def sqrt-prod add-cbrt-cube log1p-expm1-u
2×distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp exp-sum sum-log flip-+
Counts
3 → 51
Calls
3 calls:
73.0ms
(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
27.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
3.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series358.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
141.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
97.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify4.9s

Counts
60 → 60
Iterations

Useful iterations: 2 (208.0ms)

IterNodesCost
081868
1213774
2859703
done5000703

prune378.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
8.6b
(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
15.2b
(sqrt (fma (* 4.0 p) p (* x x)))
15.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite51.0ms

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:
26.0ms
(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
15.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
2.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
97.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
83.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
70.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify4.8s

Counts
136 → 136
Iterations

Useful iterations: done (4.8s)

IterNodesCost
01163008
done50001750

prune510.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.4b
(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
0.4b
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
15.2b
(sqrt (fma (* 4.0 p) p (* x x)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1 log-pow add-log-exp
4×log-prod exp-prod
3×add-exp-log expm1-log1p-u fma-def sqrt-prod add-cbrt-cube log1p-expm1-u
2×distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp exp-sum sum-log flip-+
Counts
3 → 51
Calls
3 calls:
77.0ms
(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
23.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
3.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

series305.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
106.0ms
(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
80.0ms
(sqrt (fma (* 4.0 p) p (* x x)))

simplify3.6s

Counts
60 → 60
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
081868
1213774
2859703
done5000703

prune191.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.1b

regimes137.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01518
11818
done1818

end0.0ms

sample1.8s

Algorithm
intervals
Results
515.0ms627×body1280valid
421.0ms6044×body80valid
315.0ms740×body2560valid
154.0ms8000×pre80true
53.0ms286×body640valid
22.0ms59×body5120valid
21.0ms153×body320valid
8.0ms91×body160valid