Details

Time bar (total: 12.5s)

sample62.0ms

Algorithm
intervals
Results
13.0ms191×body80valid
12.0ms30×body2560valid
7.0ms21×body1280valid
5.0ms256×pre80true
2.0ms8×body640valid
1.0ms6×body320valid

simplify75.0ms

Counts
1 → 1
Iterations
IterNodes
done41
541
440
338
234
127
014

prune18.0ms

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
21×add-cube-cbrt
18×times-frac
15×sqrt-prod
11×add-cbrt-cube add-exp-log
10×pow1
6×associate-/r* add-log-exp
4×sqrt-div
3×flip3-+ associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp associate-*l* *-commutative div-inv distribute-lft-out unswap-sqr
Counts
4 → 87
Calls
4 calls:
14.0ms
(* (* p p) 4.0)
11.0ms
(/ x (sqrt (+ (* x x) (* (* p p) 4.0))))
48.0ms
(+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))))
11.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (* p p) 4.0)
76.0ms
(/ x (sqrt (+ (* x x) (* (* p p) 4.0))))
133.0ms
(+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))))
73.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

simplify933.0ms

Counts
99 → 99
Iterations
IterNodes
done5001
21514
1335
0144

prune675.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.7b

localize101.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
14.3b
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
14.3b
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
14.3b
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×add-cbrt-cube add-exp-log
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ difference-of-squares
2×times-frac
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 61
Calls
4 calls:
78.0ms
(- (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
12.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
12.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
10.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
75.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
99.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
63.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

simplify974.0ms

Counts
73 → 73
Iterations
IterNodes
done5000
31761
2447
1169
077

prune888.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (pow p 2))
0.2b
(* x (/ 1 (sqrt (+ (* x x) (* 4.0 (pow p 2))))))
3.0b
(+ 1.0 (* x (/ 1 (sqrt (+ (* x x) (* 4.0 (pow p 2)))))))
14.3b
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
32×associate-*r*
24×*-un-lft-identity
22×times-frac add-cube-cbrt
18×add-exp-log
14×sqrt-prod
11×add-cbrt-cube
9×unswap-sqr
7×pow1 prod-exp
6×associate-*l* add-log-exp
4×unpow-prod-down sqrt-div
3×flip3-+ cbrt-unprod flip-+
2×div-exp associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp cbrt-undiv +-commutative rem-sqrt-square rec-exp sum-log sqrt-pow1 pow1/2 1-exp pow-prod-down pow-exp associate-*r/ un-div-inv div-inv
Counts
4 → 102
Calls
4 calls:
12.0ms
(* 4.0 (pow p 2))
33.0ms
(* x (/ 1 (sqrt (+ (* x x) (* 4.0 (pow p 2))))))
4.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* x x) (* 4.0 (pow p 2)))))))
6.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* 4.0 (pow p 2))
74.0ms
(* x (/ 1 (sqrt (+ (* x x) (* 4.0 (pow p 2))))))
121.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* x x) (* 4.0 (pow p 2)))))))
75.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

simplify1.3s

Counts
114 → 114
Iterations
IterNodes
done5000
21698
1473
0183

prune760.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2))))))
9.6b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2)))))) (/ x (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2))))))))
14.3b
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
14.3b
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
4 → 94
Calls
4 calls:
23.0ms
(/ x (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2))))))
9.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2)))))) (/ x (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2))))))))
19.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
12.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ x (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2))))))
101.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2)))))) (/ x (sqrt (sqrt (+ (* x x) (* 4.0 (pow p 2))))))))
64.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))
98.0ms
(sqrt (+ (* x x) (* 4.0 (pow p 2))))

simplify710.0ms

Counts
106 → 106
Iterations
IterNodes
done5001
21407
1364
0163

prune881.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.6b

regimes477.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done29
129
023

end0.0ms

sample2.7s

Algorithm
intervals
Results
672.0ms5972×body80valid
620.0ms8000×pre80true
567.0ms749×body2560valid
270.0ms676×body1280valid
100.0ms321×body640valid
42.0ms159×body320valid
31.0ms46×body5120valid
12.0ms77×body160valid