Details

Time bar (total: 10.9s)

sample54.0ms

Algorithm
intervals
Results
13.0ms26×body2560valid
9.0ms189×body80valid
5.0ms22×body1280valid
5.0ms256×pre80true
2.0ms11×body640valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify34.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
28.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(+ (* (* 4.0 p) p) (* x x))
51.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms
(+ (* (* 4.0 p) p) (* x x))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.5s

Counts
91 → 91
Iterations

Useful iterations: 3 (435.0ms)

IterNodesCost
01281657
12771506
27731400
320701385
done50011385

prune275.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b
(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt
7×sqrt-prod
6×pow1 add-log-exp
5×times-frac
4×sqrt-div
3×flip3-+ associate-/r* flip-+ difference-of-squares
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/
1×sub-neg flip3-- frac-2neg diff-log prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
4 → 69
Calls
4 calls:
50.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms
(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms
(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
81 → 81
Iterations

Useful iterations: 3 (773.0ms)

IterNodesCost
01251406
13011299
29361151
335401144
done50001144

prune450.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.5b

localize35.0ms

Local error

Found 4 expressions with local error:

15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.4b
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))
16.4b
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))
16.4b
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
9.0ms
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))
9.0ms
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))
9.0ms
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
136.0ms
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))
130.0ms
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))
132.0ms
(cbrt (+ (* 4.0 (pow p 2)) (pow x 2)))

simplify2.0s

Counts
66 → 66
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
0961141
12161073
2516965
31252939
43112921
done5001921

prune469.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×flip3-+ sqrt-div prod-exp flip-+
3×associate-*l*
2×+-commutative div-exp sum-log associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
16.0ms
(+ (* (* 4.0 p) p) (* x x))
70.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* (* 4.0 p) p) (* x x))
58.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.4s

Counts
98 → 98
Iterations

Useful iterations: 3 (615.0ms)

IterNodesCost
01521717
13771427
29741271
326411254
done50011254

prune254.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.5b

regimes193.0ms

Accuracy

0% (0.4b remaining)

Error of 13.7b against oracle of 13.2b and baseline of 13.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03175
14175
done4175

end0.0ms

sample840.0ms

Algorithm
intervals
Results
194.0ms5998×body80valid
171.0ms822×body2560valid
106.0ms613×body1280valid
98.0ms8000×pre80true
44.0ms326×body640valid
19.0ms177×body320valid
4.0ms64×body160valid