Details

Time bar (total: 17.0s)

sample109.0ms

Algorithm
intervals
Results
37.0ms26×body2560valid
23.0ms192×body80valid
11.0ms256×pre80true
11.0ms18×body1280valid
6.0ms10×body640valid
2.0ms7×body320valid
1.0ms1×body5120valid
1.0ms2×body160valid

simplify116.0ms

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize23.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* x x) (* p (* 4 p))))
0.7b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
0.0b
(* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×associate-*r*
20×*-un-lft-identity times-frac add-cube-cbrt
16×sqrt-prod
9×add-cbrt-cube add-exp-log
8×pow1
6×sqrt-div add-log-exp
4×flip3-+ flip-+ insert-posit16
3×associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative sum-log div-exp pow-prod-down associate-*r/ *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
Slowest
31.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
29.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
19.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series533.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
279.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
94.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
83.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
77.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.7s

Counts
101 → 101

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.5b

localize43.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* x x) (* (* p p) 4)))
0.7b
(log (exp (+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5)))))
0.7b
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5)))
0.0b
(sqrt (log (exp (+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5))))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-pow
13×sqrt-prod
12×exp-prod
11×add-sqr-sqrt
9×add-cube-cbrt
8×pow1
6×associate-/r/ add-log-exp
4×log-prod add-cbrt-cube add-exp-log insert-posit16
3×distribute-rgt-out distribute-rgt1-in distribute-lft-out
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
1×+-commutative sum-log rem-log-exp exp-sum
Counts
4 → 72
Calls
4 calls:
Slowest
101.0ms
(log (exp (+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5)))))
100.0ms
(sqrt (log (exp (+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5))))))
18.0ms
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5)))
6.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(sqrt (log (exp (+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5))))))
106.0ms
(log (exp (+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5)))))
104.0ms
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p p) 4))) 0.5)))
55.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

simplify716.0ms

Counts
84 → 84

prune870.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.5b

localize53.0ms

Local error

Found 4 expressions with local error:

19.7b
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
14.5b
(sqrt (+ (* x x) (* p (* 4 p))))
14.5b
(sqrt (+ (* x x) (* p (* 4 p))))
14.5b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*r/
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 cbrt-div *-un-lft-identity add-cube-cbrt
6×sqrt-div
5×frac-times associate-*l/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 66
Calls
4 calls:
Slowest
337.0ms
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
8.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
5.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
63.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
56.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
55.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.6s

Counts
78 → 78

prune975.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 13.5b

localize64.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* x x) (* (* p p) 4)))
14.5b
(sqrt (+ (* x x) (* (* p p) 4)))
14.5b
(sqrt (+ (* x x) (* (* p p) 4)))
13.7b
(/ (* x (* x x)) (* (+ (* x x) (* (* p p) 4)) (sqrt (+ (* x x) (* (* p p) 4)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
25×add-cbrt-cube add-exp-log
12×sqrt-div
10×add-sqr-sqrt
9×flip3-+ prod-exp sqrt-prod cbrt-unprod flip-+
8×associate-/r/
7×pow1 *-un-lft-identity add-cube-cbrt
6×cbrt-undiv div-exp
4×frac-times insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*l/ associate-*r/
1×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
Counts
4 → 82
Calls
4 calls:
Slowest
29.0ms
(/ (* x (* x x)) (* (+ (* x x) (* (* p p) 4)) (sqrt (+ (* x x) (* (* p p) 4)))))
12.0ms
(sqrt (+ (* x x) (* (* p p) 4)))
8.0ms
(sqrt (+ (* x x) (* (* p p) 4)))
8.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (* x (* x x)) (* (+ (* x x) (* (* p p) 4)) (sqrt (+ (* x x) (* (* p p) 4)))))
55.0ms
(sqrt (+ (* x x) (* (* p p) 4)))
52.0ms
(sqrt (+ (* x x) (* (* p p) 4)))
50.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

simplify3.4s

Counts
94 → 94

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 13.5b

regimes186.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch3.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
660.0ms5951×body80valid
540.0ms8000×pre80true
536.0ms774×body2560valid
341.0ms651×body1280valid
156.0ms336×body640valid
39.0ms63×body5120valid
39.0ms157×body320valid
11.0ms68×body160valid