Details

Time bar (total: 35.5s)

sample77.0ms

Algorithm
intervals
Results
20.0ms200×body80valid
14.0ms24×body2560valid
9.0ms256×pre80true
9.0ms17×body1280valid
2.0ms4×body640valid
2.0ms5×body320valid
1.0ms2×body5120valid
1.0ms4×body160valid

simplify108.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
108.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize55.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (+ (* x x) (* p (* 4 p))))
0.9b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b
(+ (* x x) (* p (* 4 p)))
0.0b
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 56
Calls
4 calls:
Slowest
25.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
22.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
15.0ms
(+ (* x x) (* p (* 4 p)))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
286.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
119.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
71.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
46.0ms
(+ (* x x) (* p (* 4 p)))

simplify8.3s

Counts
76 → 68
Calls
76 calls:
Slowest
509.0ms
(+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3))
458.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
450.0ms
(sqrt (- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5)))
422.0ms
(sqrt (+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3)))
380.0ms
(- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p))))

prune696.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.5b

localize53.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (+ (* x x) (* p (* p 4))))
16.8b
(sqrt (+ (* x x) (* p (* p 4))))
4.0b
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
4.0b
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 56
Calls
4 calls:
Slowest
15.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
12.0ms
(sqrt (+ (* x x) (* p (* p 4))))
12.0ms
(sqrt (+ (* x x) (* p (* p 4))))
9.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
82.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
61.0ms
(sqrt (+ (* x x) (* p (* p 4))))
57.0ms
(sqrt (+ (* x x) (* p (* p 4))))

simplify6.8s

Counts
76 → 68
Calls
76 calls:
Slowest
424.0ms
(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
394.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))
385.0ms
(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
376.0ms
(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))
375.0ms
(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))

prune846.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.5b

localize54.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (+ (* x x) (* p (* p 4))))
16.8b
(sqrt (+ (* x x) (* p (* p 4))))
4.0b
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
4.0b
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 56
Calls
4 calls:
Slowest
12.0ms
(sqrt (+ (* x x) (* p (* p 4))))
11.0ms
(sqrt (+ (* x x) (* p (* p 4))))
10.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
9.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
89.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
70.0ms
(sqrt (+ (* x x) (* p (* p 4))))
57.0ms
(sqrt (+ (* x x) (* p (* p 4))))

simplify6.7s

Counts
76 → 68
Calls
76 calls:
Slowest
577.0ms
(- (* 0.5 0.5) (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))))
387.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))
380.0ms
(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
353.0ms
(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
351.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))

prune969.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.5b

localize39.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (+ (* x x) (* p (* p 4))))
16.8b
(sqrt (+ (* x x) (* p (* p 4))))
4.0b
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
4.0b
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 56
Calls
4 calls:
Slowest
14.0ms
(sqrt (+ (* x x) (* p (* p 4))))
9.0ms
(sqrt (+ (* x x) (* p (* p 4))))
7.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
5.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
80.0ms
(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
60.0ms
(sqrt (+ (* x x) (* p (* p 4))))
55.0ms
(sqrt (+ (* x x) (* p (* p 4))))

simplify5.6s

Counts
76 → 68
Calls
76 calls:
Slowest
357.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))
335.0ms
(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
335.0ms
(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
311.0ms
(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))
309.0ms
(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))

prune870.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

regimes85.0ms

Accuracy

0% (0.4b remaining)

Error of 13.2b against oracle of 12.7b and baseline of 13.2b

bsearch7.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
990.0ms6081×body80valid
531.0ms742×body2560valid
363.0ms585×body1280valid
265.0ms8000×pre80true
160.0ms313×body640valid
41.0ms60×body5120valid
39.0ms145×body320valid
13.0ms74×body160valid