Details

Time bar (total: 7.2s)

sample68.0ms

Algorithm
intervals
Results
13.0ms30×body2560valid
13.0ms180×body80valid
8.0ms22×body1280valid
6.0ms256×pre80true
3.0ms12×body640valid
2.0ms8×body320valid
2.0ms3×body5120valid
0.0ms1×body160valid

simplify3.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
20×add-sqr-sqrt
19×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 sqrt-div
3×flip3-+ flip-+ associate-/l*
2×associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv distribute-lft-out
Counts
3 → 68
Calls
3 calls:
31.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
83.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series264.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
105.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify146.0ms

Counts
77 → 77

prune350.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.6b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite159.0ms

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:
59.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
37.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
36.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
71.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify119.0ms

Counts
81 → 81

prune826.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.6b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
24×associate-*r*
22×times-frac
20×*-un-lft-identity
18×add-cube-cbrt
14×sqrt-prod
12×add-exp-log
8×add-cbrt-cube
6×pow1
5×add-log-exp unswap-sqr
4×sqrt-div prod-exp
3×flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
3 → 75
Calls
3 calls:
93.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
39.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Counts
84 → 84

prune374.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 16.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.9b
(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 94
Calls
4 calls:
33.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
111.0ms
(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
65.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify165.0ms

Counts
106 → 106

prune620.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

regimes231.0ms

Accuracy

0% (1.1b remaining)

Error of 14.6b against oracle of 13.4b and baseline of 14.6b

bsearch0.0ms

simplify97.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
682.0ms742×body2560valid
550.0ms5985×body80valid
253.0ms676×body1280valid
193.0ms8000×pre80true
115.0ms321×body640valid
53.0ms138×body320valid
29.0ms62×body5120valid
9.0ms76×body160valid