Details

Time bar (total: 12.5s)

sample82.0ms

Algorithm
intervals
Results
19.0ms196×body80valid
12.0ms20×body2560valid
8.0ms256×pre80true
7.0ms15×body1280valid
6.0ms14×body640valid
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify90.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize16.0ms

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))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite240.0ms

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:
37.0ms
(+ (* (* 4.0 p) p) (* x x))
42.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
80.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (* (* 4.0 p) p) (* x x))
77.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
99.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
91 → 91

prune446.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.1b

localize23.0ms

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)))))
3.9b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite184.0ms

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:
23.0ms
(+ (* (* 4.0 p) p) (* x x))
108.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
37.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (* (* 4.0 p) p) (* x x))
88.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
99.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
94.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.0s

Counts
98 → 98

prune464.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite508.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×add-sqr-sqrt
22×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×log-prod exp-prod sqrt-div
3×flip3-+ flip-+ associate-/l*
2×associate-/r/ distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum clear-num sum-log div-inv
Counts
4 → 85
Calls
4 calls:
44.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
293.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
107.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
85.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
98.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify986.0ms

Counts
97 → 97

prune514.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.6b
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
25×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
16×unpow-prod-down
9×add-exp-log
8×associate-/l*
6×pow1 sqrt-prod add-cbrt-cube add-log-exp
5×distribute-lft-out
4×flip3-+ sqrt-div cube-prod flip-+ unpow2 sqr-pow
3×div-exp associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num sum-log sum-cubes div-inv
Counts
4 → 98
Calls
4 calls:
171.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
44.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
40.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
40.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
74.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
83.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
70.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify755.0ms

Counts
110 → 110

prune533.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

regimes217.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify581.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
610.0ms8000×pre80true
471.0ms6047×body80valid
367.0ms723×body2560valid
222.0ms590×body1280valid
80.0ms333×body640valid
36.0ms77×body5120valid
28.0ms160×body320valid
8.0ms70×body160valid