Details

Time bar (total: 17.9s)

sample80.0ms

Algorithm
intervals
Results
17.0ms194×body80valid
11.0ms19×body2560valid
10.0ms21×body1280valid
7.0ms256×pre80true
3.0ms8×body640valid
2.0ms3×body5120valid
2.0ms8×body320valid
1.0ms3×body160valid

simplify49.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt sqrt-div sqrt-prod
3×add-exp-log sqrt-pow1 flip3-+ add-cbrt-cube flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log distribute-lft-out
Counts
3 → 40
Calls
3 calls:
77.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
112.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
26.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series523.0ms

Counts
3 → 9
Calls
3 calls:
349.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
99.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.9s

Counts
49 → 49

prune219.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.2b
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 *-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×add-log-exp
5×sqrt-prod log-pow
4×add-exp-log exp-prod sqrt-div add-cbrt-cube
3×log-prod sqrt-pow1 flip3-+ flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square rem-log-exp pow-prod-down sum-log distribute-lft-out
Counts
4 → 56
Calls
4 calls:
80.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
3.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
71.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series883.0ms

Counts
4 → 12
Calls
4 calls:
343.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
349.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
94.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
96.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
68 → 68

prune391.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite726.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt add-log-exp
8×add-cube-cbrt exp-prod
6×pow1
5×log-pow
4×add-exp-log log-prod add-cbrt-cube
3×sqrt-prod distribute-lft-out
2×flip3-+ sqrt-div exp-sum sum-log flip-+ rem-exp-log
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp
Counts
4 → 58
Calls
4 calls:
254.0ms
(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
73.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
353.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
44.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
109.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
87.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
82.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts
70 → 70

prune310.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
8.3b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×pow1 sqrt-prod
6×add-log-exp
5×log-pow
4×add-exp-log exp-prod sqrt-div add-cbrt-cube
3×log-prod flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative rem-log-exp sum-log distribute-lft-out
Counts
4 → 58
Calls
4 calls:
3.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
83.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
43.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series653.0ms

Counts
4 → 12
Calls
4 calls:
388.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
95.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
93.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.3s

Counts
70 → 70

prune397.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

regimes606.0ms

Accuracy

-0.4% (1.2b remaining)

Error of 14.3b against oracle of 13.1b and baseline of 14.3b

bsearch0.0ms

simplify2.0s

end0.0ms

sample2.1s

Algorithm
intervals
Results
441.0ms6018×body80valid
440.0ms296×body640valid
436.0ms779×body2560valid
260.0ms608×body1280valid
187.0ms8000×pre80true
30.0ms171×body320valid
27.0ms55×body5120valid
9.0ms73×body160valid