Details

Time bar (total: 13.8s)

sample46.0ms

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

simplify82.0ms

Counts
1 → 1
Iterations
IterNodes
done52
652
551
449
347
240
128
014

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:
19.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.0ms
(fma p (* 4.0 p) (* x x))
12.0ms
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
1.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

series557.0ms

Counts
4 → 12
Calls
4 calls:
350.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
45.0ms
(fma p (* 4.0 p) (* x x))
84.0ms
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
78.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.3s

Counts
69 → 69
Iterations
IterNodes
done5001
31899
2468
1169
090

prune526.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
44×fma-def
36×*-un-lft-identity times-frac
34×add-sqr-sqrt
32×add-cube-cbrt
24×sqrt-prod
8×add-log-exp
6×pow1
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-+ div-inv distribute-lft-out
Counts
4 → 102
Calls
4 calls:
27.0ms
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
29.0ms
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
1.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
1.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
93.0ms
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
63.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
70.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

simplify2.1s

Counts
114 → 114
Iterations
IterNodes
done5001
41932
3686
2274
1119
056

prune972.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

localize91.0ms

Local error

Found 4 expressions with local error:

2.9b
(/ (* x x) (fma (* p p) 4.0 (* x x)))
2.9b
(/ (* x x) (fma (* p p) 4.0 (* x x)))
13.2b
(sqrt (fma (* p p) 4.0 (* x x)))
13.2b
(sqrt (fma (* p p) 4.0 (* x x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 associate-/r* times-frac sqrt-prod
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
8.0ms
(/ (* x x) (fma (* p p) 4.0 (* x x)))
8.0ms
(/ (* x x) (fma (* p p) 4.0 (* x x)))
1.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
1.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ (* x x) (fma (* p p) 4.0 (* x x)))
55.0ms
(/ (* x x) (fma (* p p) 4.0 (* x x)))
64.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
63.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

simplify1.5s

Counts
88 → 88
Iterations
IterNodes
done5002
2986
1153
066

prune740.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.8b

localize92.0ms

Local error

Found 4 expressions with local error:

2.9b
(/ (* x x) (fma (* p p) 4.0 (* x x)))
13.2b
(sqrt (fma (* p p) 4.0 (* x x)))
13.2b
(sqrt (fma (* p p) 4.0 (* x x)))
15.4b
(fma (* 1.0 1.0) 1.0 (* (/ x (sqrt (fma (* p p) 4.0 (* x x)))) (expm1 (log1p (/ (* x x) (fma (* p p) 4.0 (* x x)))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* times-frac
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×clear-num frac-2neg prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 63
Calls
4 calls:
11.0ms
(/ (* x x) (fma (* p p) 4.0 (* x x)))
2.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
2.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
0.0ms
(fma (* 1.0 1.0) 1.0 (* (/ x (sqrt (fma (* p p) 4.0 (* x x)))) (expm1 (log1p (/ (* x x) (fma (* p p) 4.0 (* x x)))))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (* x x) (fma (* p p) 4.0 (* x x)))
82.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
69.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
188.0ms
(fma (* 1.0 1.0) 1.0 (* (/ x (sqrt (fma (* p p) 4.0 (* x x)))) (expm1 (log1p (/ (* x x) (fma (* p p) 4.0 (* x x)))))))

simplify1.6s

Counts
75 → 75
Iterations
IterNodes
done5000
21057
1179
082

prune738.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.8b

regimes235.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done28
128
025

end0.0ms

sample2.2s

Algorithm
intervals
Results
729.0ms774×body2560valid
466.0ms6025×body80valid
280.0ms620×body1280valid
160.0ms8000×pre80true
70.0ms166×body320valid
64.0ms268×body640valid
64.0ms70×body5120valid
9.0ms77×body160valid