Details

Time bar (total: 13.4s)

sample115.0ms

Algorithm
intervals
Results
28.0ms185×body80valid
24.0ms26×body2560valid
21.0ms28×body1280valid
13.0ms256×pre80true
4.0ms7×body640valid
3.0ms6×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify123.0ms

Counts
1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize55.0ms

Local error

Found 4 expressions with local error:

12.4b
(sqrt (+ (* x x) (* p (* 4 p))))
0.4b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b
(+ (* x x) (* p (* 4 p)))
0.0b
(* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×associate-*r*
20×times-frac
19×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×pow1
4×flip3-+ sqrt-div flip-+ insert-posit16
3×associate-*l* unswap-sqr
2×+-commutative sum-log prod-exp associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*r/ *-commutative div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
33.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
22.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
16.0ms
(+ (* x x) (* p (* 4 p)))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
93.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
54.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
41.0ms
(+ (* x x) (* p (* 4 p)))

simplify1.5s

Counts
97 → 97

prune944.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.1b

localize31.0ms

Local error

Found 4 expressions with local error:

12.4b
(sqrt (+ (* x x) (* p (* 4 p))))
0.4b
(log (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
0.4b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b
(+ (* x x) (* p (* 4 p)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
6×pow1
4×log-prod add-cbrt-cube add-exp-log log-pow insert-posit16
3×exp-prod flip3-+ sqrt-prod flip-+
2×+-commutative sum-log sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp exp-sum
Counts
4 → 57
Calls
4 calls:
Slowest
61.0ms
(log (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
14.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
8.0ms
(+ (* x x) (* p (* 4 p)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
95.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
86.0ms
(log (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
46.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
40.0ms
(+ (* x x) (* p (* 4 p)))

simplify838.0ms

Counts
69 → 69

prune842.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.1b

localize71.0ms

Local error

Found 4 expressions with local error:

12.4b
(sqrt (+ (* x x) (* p (* 4 p))))
12.4b
(sqrt (+ (* x x) (* p (* 4 p))))
12.4b
(sqrt (+ (* x x) (* p (* 4 p))))
0.5b
(* (cbrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) (cbrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
16×cbrt-prod
15×*-un-lft-identity add-cube-cbrt
14×pow1
12×cbrt-div
9×flip3-+ sqrt-prod flip-+
6×pow1/3 sqrt-div swap-sqr associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 pow1/2
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 97
Calls
4 calls:
Slowest
94.0ms
(* (cbrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) (cbrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
13.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
305.0ms
(* (cbrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) (cbrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
70.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
59.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
50.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify880.0ms

Counts
109 → 109

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.1b

localize79.0ms

Local error

Found 4 expressions with local error:

12.4b
(sqrt (+ (* (* p 4) p) (* x x)))
12.4b
(sqrt (+ (* (* p 4) p) (* x x)))
12.4b
(sqrt (+ (* (* p 4) p) (* x x)))
2.8b
(+ (/ 0.5 (* (/ (sqrt (+ (* (* p 4) p) (* x x))) (* x x)) (/ (+ (* (* p 4) p) (* x x)) x))) 0.5)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 61
Calls
4 calls:
Slowest
42.0ms
(+ (/ 0.5 (* (/ (sqrt (+ (* (* p 4) p) (* x x))) (* x x)) (/ (+ (* (* p 4) p) (* x x)) x))) 0.5)
25.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
21.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
18.0ms
(sqrt (+ (* (* p 4) p) (* x x)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
83.0ms
(+ (/ 0.5 (* (/ (sqrt (+ (* (* p 4) p) (* x x))) (* x x)) (/ (+ (* (* p 4) p) (* x x)) x))) 0.5)
58.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
54.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
48.0ms
(sqrt (+ (* (* p 4) p) (* x x)))

simplify999.0ms

Counts
73 → 73

prune903.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.0b

regimes108.0ms

Accuracy

0% (1.4b remaining)

Error of 14.2b against oracle of 12.8b and baseline of 14.2b

bsearch9.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
917.0ms6032×body80valid
560.0ms766×body2560valid
332.0ms8000×pre80true
290.0ms605×body1280valid
111.0ms309×body640valid
82.0ms56×body5120valid
42.0ms156×body320valid
35.0ms76×body160valid