Details

Time bar (total: 6.3s)

sample43.0ms

Algorithm
intervals
Results
9.0ms190×body80valid
6.0ms19×body2560valid
5.0ms22×body1280valid
4.0ms256×pre80true
2.0ms9×body640valid
2.0ms11×body320valid
0.0ms4×body160valid
0.0ms1×body5120valid

simplify4.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
58.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
29.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
56.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
43.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
86.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Counts
93 → 93

prune300.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.2b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
3.2b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 122
Calls
4 calls:
76.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
39.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
84.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
65.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Counts
134 → 134

prune356.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.2b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
3.2b
(+ 1.0 (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1))
13.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
38×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative distribute-lft-out inv-pow
Counts
4 → 123
Calls
4 calls:
77.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
33.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
7.0ms
(+ 1.0 (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1))
29.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
87.0ms
(+ 1.0 (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Counts
135 → 135

prune405.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
13.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt
6×pow1 sqrt-prod add-log-exp
5×distribute-lft-out
4×unpow-prod-down flip3-+ sqrt-div cube-prod flip-+
3×times-frac associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/
1×+-commutative frac-2neg prod-exp clear-num sum-log sum-cubes cbrt-unprod div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
140.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
34.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
28.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
56.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Counts
82 → 82

prune373.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.1b

regimes565.0ms

Accuracy

0% (0.5b remaining)

Error of 13.3b against oracle of 12.8b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
643.0ms731×body2560valid
404.0ms6042×body80valid
221.0ms627×body1280valid
205.0ms8000×pre80true
63.0ms330×body640valid
24.0ms63×body5120valid
20.0ms142×body320valid
6.0ms65×body160valid