Details

Time bar (total: 10.7s)

sample45.0ms

Algorithm
intervals
Results
9.0ms191×body80valid
8.0ms30×body2560valid
4.0ms256×pre80true
4.0ms18×body1280valid
2.0ms10×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify37.0ms

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize37.0ms

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)))

rewrite48.0ms

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:
23.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.0ms
(fma p (* 4.0 p) (* x x))
20.0ms
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
2.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
58.0ms
(fma p (* 4.0 p) (* x x))
95.0ms
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
85.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

simplify812.0ms

Counts
69 → 69
Iterations
IterNodes
done5001
31899
2468
1169
090

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b
(log1p (sqrt (* (+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0) 0.5)))
0.5b
(expm1 (log1p (sqrt (* (+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0) 0.5))))
0.6b
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
13.2b
(sqrt (fma (* p p) 4.0 (* x x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
22×fma-def
20×*-un-lft-identity
19×add-sqr-sqrt
18×times-frac add-cube-cbrt
12×sqrt-prod
6×add-log-exp
5×expm1-log1p-u pow1
4×add-cbrt-cube add-exp-log log1p-expm1-u
1×+-commutative rem-sqrt-square log1p-udef expm1-log1p sum-log sqrt-pow1 flip3-+ pow1/2 log1p-expm1 flip-+ div-inv distribute-lft-out expm1-udef
Counts
4 → 73
Calls
4 calls:
0.0ms
(log1p (sqrt (* (+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0) 0.5)))
0.0ms
(expm1 (log1p (sqrt (* (+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0) 0.5))))
24.0ms
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
2.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

series1.7s

Counts
4 → 12
Calls
4 calls:
868.0ms
(log1p (sqrt (* (+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0) 0.5)))
644.0ms
(expm1 (log1p (sqrt (* (+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0) 0.5))))
95.0ms
(+ (/ x (sqrt (fma (* p p) 4.0 (* x x)))) 1.0)
63.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

simplify1.1s

Counts
85 → 85
Iterations
IterNodes
done5001
42129
3795
2345
1164
088

prune477.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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-cbrt-cube add-exp-log add-log-exp
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u
3×fma-def
2×rem-sqrt-square
1×pow2 +-commutative sum-log rem-square-sqrt flip3-+ pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 124
Calls
4 calls:
19.0ms
(* (sqrt (sqrt (fma (* p p) 4.0 (* x x)))) (sqrt (sqrt (fma (* p p) 4.0 (* x x)))))
16.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (fma (* p p) 4.0 (* x x)))) (sqrt (sqrt (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)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (sqrt (sqrt (fma (* p p) 4.0 (* x x)))) (sqrt (sqrt (fma (* p p) 4.0 (* x x)))))
80.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (fma (* p p) 4.0 (* x x)))) (sqrt (sqrt (fma (* p p) 4.0 (* x x)))))))
57.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
61.0ms
(sqrt (fma (* p p) 4.0 (* x x)))

simplify827.0ms

Counts
136 → 136
Iterations
IterNodes
done5001
21163
1248
0116

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
1.0ms
(sqrt (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)))
1.0ms
(sqrt (fma p (* p 4.0) (* x x)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (fma (* p p) 4.0 (* x x)))
65.0ms
(sqrt (fma p (* p 4.0) (* x x)))
68.0ms
(sqrt (fma p (* p 4.0) (* x x)))
67.0ms
(sqrt (fma p (* p 4.0) (* x x)))

simplify1.1s

Counts
72 → 72
Iterations
IterNodes
done5001
81285
7510
6333
5254
4220
3162
2106
163
044

prune506.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.8b

regimes155.0ms

Accuracy

83.1% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 14.9b

bsearch58.0ms

Steps
ItersRangePoint
6
-3.4645914939386396e-106
-2.2560484909930867e-107
-2.3256956640037286e-106

simplify4.0ms

Iterations
IterNodes
done40
140
034

end0.0ms

sample1.6s

Algorithm
intervals
Results
673.0ms6025×body80valid
287.0ms774×body2560valid
169.0ms620×body1280valid
150.0ms8000×pre80true
80.0ms268×body640valid
25.0ms70×body5120valid
22.0ms166×body320valid
7.0ms77×body160valid