Details

Time bar (total: 20.1s)

sample58.0ms

Algorithm
intervals
Results
42.0ms271×body80valid

simplify140.0ms

Calls
1 calls:
Slowest
140.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize19.0ms

Local error

Found 2 expressions with local error:

28.6b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
1.0b
(- (* b c) (* a d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Calls
2 calls:
Slowest
17.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
5.0ms
(- (* b c) (* a d))

series196.0ms

Calls
2 calls:
Slowest
125.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
71.0ms
(- (* b c) (* a d))

simplify2.5s

Calls
37 calls:
Slowest
471.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
364.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
348.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
216.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
194.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))

prune566.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.1b

localize8.0ms

Local error

Found 4 expressions with local error:

32.2b
(sqrt (+ (* c c) (* d d)))
32.2b
(sqrt (+ (* c c) (* d d)))
18.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.0b
(- (* b c) (* a d))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×pow1 insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
12.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
5.0ms
(- (* b c) (* a d))
2.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))

series336.0ms

Calls
4 calls:
Slowest
173.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
66.0ms
(sqrt (+ (* c c) (* d d)))
53.0ms
(- (* b c) (* a d))
44.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.5s

Calls
76 calls:
Slowest
347.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
293.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
261.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
223.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
179.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 26.4b

localize12.0ms

Local error

Found 4 expressions with local error:

32.2b
(sqrt (+ (* c c) (* d d)))
32.2b
(sqrt (+ (* c c) (* d d)))
18.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.0b
(- (* b c) (* a d))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×pow1 insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
12.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
5.0ms
(sqrt (+ (* c c) (* d d)))
5.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(- (* b c) (* a d))

series261.0ms

Calls
4 calls:
Slowest
129.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
45.0ms
(- (* b c) (* a d))
44.0ms
(sqrt (+ (* c c) (* d d)))
44.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.4s

Calls
76 calls:
Slowest
313.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
312.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
291.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
188.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
172.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 26.4b

localize13.0ms

Local error

Found 4 expressions with local error:

32.2b
(sqrt (+ (* c c) (* d d)))
32.2b
(sqrt (+ (* c c) (* d d)))
32.2b
(sqrt (+ (* c c) (* d d)))
18.4b
(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
12×add-sqr-sqrt
9×*-un-lft-identity flip3-+ add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod flip-+
8×associate-/r/
4×frac-times pow1 insert-posit16 add-log-exp
3×rem-sqrt-square times-frac pow1/2 associate-/l*
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/l/
1×clear-num associate-/r* frac-2neg flip3-- div-sub prod-exp cbrt-unprod div-inv flip--
Calls
4 calls:
Slowest
29.0ms
(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
5.0ms
(sqrt (+ (* c c) (* d d)))
3.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))

series300.0ms

Calls
4 calls:
Slowest
162.0ms
(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
48.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.5s

Calls
54 calls:
Slowest
286.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
269.0ms
(* (sqrt (sqrt (- (* c c) (* d d)))) (sqrt (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))))
268.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
251.0ms
(* (sqrt (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))) (sqrt (sqrt (- (* c c) (* d d)))))
197.0ms
(sqrt (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))))

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 26.4b

regimes491.0ms

Accuracy

0% (2.7b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch3.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
1.1s8474×body80valid