Details

Time bar (total: 12.0s)

sample86.0ms

Algorithm
intervals
Results
19.0ms256×pre80true
15.0ms30×body2560valid
14.0ms191×body80valid
9.0ms21×body1280valid
2.0ms8×body640valid
1.0ms6×body320valid

simplify70.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.1b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u fma-def flip3-+ sqrt-div flip-+ log1p-expm1-u
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv distribute-lft-out
Counts
4 → 91
Calls
4 calls:
27.0ms
(+ (* (* 4.0 p) p) (* x x))
30.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
55.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
21.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(+ (* (* 4.0 p) p) (* x x))
105.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
127.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
71.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts
103 → 103
Iterations
IterNodes
done5001
21516
1320
0135

prune835.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize101.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (/ x (sqrt (fma p (* p 4.0) (* x x)))) 1.0)
14.3b
(sqrt (fma p (* p 4.0) (* x x)))
14.3b
(sqrt (fma p (* p 4.0) (* x x)))
14.3b
(sqrt (fma p (* p 4.0) (* x x)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
83×*-un-lft-identity
81×add-cube-cbrt
74×times-frac
66×prod-diff
46×sqrt-prod
22×fma-neg
7×pow1
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 151
Calls
4 calls:
33.0ms
(- (/ 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)))
2.0ms
(sqrt (fma p (* p 4.0) (* x x)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (/ x (sqrt (fma p (* p 4.0) (* x x)))) 1.0)
75.0ms
(sqrt (fma p (* p 4.0) (* x x)))
115.0ms
(sqrt (fma p (* p 4.0) (* x x)))
101.0ms
(sqrt (fma p (* p 4.0) (* x x)))

simplify2.1s

Counts
163 → 163
Iterations
IterNodes
done5001
33602
2809
1333
0165

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma p (* p 4.0) (* x x))
0.2b
(* x (/ 1 (sqrt (fma p (* p 4.0) (* x x)))))
3.0b
(+ 1.0 (* x (/ 1 (sqrt (fma p (* p 4.0) (* x x))))))
14.3b
(sqrt (fma p (* p 4.0) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
22×*-un-lft-identity times-frac associate-*r*
20×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
7×pow1
6×add-log-exp
5×unswap-sqr
4×expm1-log1p-u prod-exp log1p-expm1-u
3×fma-def associate-*l*
2×div-exp cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sum-log sqrt-pow1 flip3-+ pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative flip-+ fma-udef div-inv
Counts
4 → 90
Calls
4 calls:
0.0ms
(fma p (* p 4.0) (* x x))
29.0ms
(* x (/ 1 (sqrt (fma p (* p 4.0) (* x x)))))
5.0ms
(+ 1.0 (* x (/ 1 (sqrt (fma p (* p 4.0) (* x x))))))
1.0ms
(sqrt (fma p (* p 4.0) (* x x)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(fma p (* p 4.0) (* x x))
67.0ms
(* x (/ 1 (sqrt (fma p (* p 4.0) (* x x)))))
97.0ms
(+ 1.0 (* x (/ 1 (sqrt (fma p (* p 4.0) (* x x))))))
96.0ms
(sqrt (fma p (* p 4.0) (* x x)))

simplify672.0ms

Counts
102 → 102
Iterations
IterNodes
done5001
21159
1339
0138

prune629.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (fma p (* p 4.0) (* x x)))))
9.6b
(+ 1.0 (* (/ 1 (sqrt (sqrt (fma p (* p 4.0) (* x x))))) (/ x (sqrt (sqrt (fma p (* p 4.0) (* x x)))))))
14.3b
(sqrt (fma p (* p 4.0) (* x x)))
14.3b
(sqrt (fma p (* p 4.0) (* x x)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
31×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
27×times-frac
9×associate-/r*
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-+ div-exp flip-+ div-inv
Counts
4 → 99
Calls
4 calls:
6.0ms
(/ x (sqrt (sqrt (fma p (* p 4.0) (* x x)))))
5.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (fma p (* p 4.0) (* x x))))) (/ x (sqrt (sqrt (fma p (* p 4.0) (* x x)))))))
1.0ms
(sqrt (fma p (* p 4.0) (* x x)))
2.0ms
(sqrt (fma p (* p 4.0) (* x x)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ x (sqrt (sqrt (fma p (* p 4.0) (* x x)))))
122.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (fma p (* p 4.0) (* x x))))) (/ x (sqrt (sqrt (fma p (* p 4.0) (* x x)))))))
76.0ms
(sqrt (fma p (* p 4.0) (* x x)))
87.0ms
(sqrt (fma p (* p 4.0) (* x x)))

simplify624.0ms

Counts
111 → 111
Iterations
IterNodes
done5001
21096
1308
0149

prune682.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 13.7b

regimes191.0ms

Accuracy

0% (0.2b remaining)

Error of 13.7b against oracle of 13.5b and baseline of 13.7b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done23
123
020

end0.0ms

sample1.8s

Algorithm
intervals
Results
735.0ms5972×body80valid
290.0ms749×body2560valid
205.0ms676×body1280valid
191.0ms8000×pre80true
65.0ms321×body640valid
48.0ms46×body5120valid
24.0ms159×body320valid
10.0ms77×body160valid