Details

Time bar (total: 48.6s)

sample51.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
9.0ms256×pre80true

simplify207.0ms

Calls
1 calls:
Slowest
207.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize30.0ms

Local error

Found 2 expressions with local error:

13.7b
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
0.3b
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
69×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
44×div-inv
21×associate-/r*
9×add-cbrt-cube add-exp-log
7×associate-/r/ associate-/l*
4×cbrt-undiv div-exp
3×associate-/l/
2×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×flip3-- div-sub flip--
Calls
2 calls:
Slowest
25.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
17.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

series93.0ms

Calls
2 calls:
Slowest
60.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
33.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

simplify31.0s

Calls
200 calls:
Slowest
723.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ 1 2))
617.0ms
(/ (* (* 2 i) (* 2 i)) (/ i 2))
554.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
454.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
448.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (/ i 2) (- (* 8 i) (/ 1.0 (/ i 2))))
0.0b
(- (* 8 i) (/ 1.0 (/ i 2)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×div-inv
4×add-cbrt-cube add-exp-log associate-/l* add-log-exp
3×associate-/r*
2×pow1 flip3-- associate-/r/ insert-posit16 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp associate-/l/
Calls
2 calls:
Slowest
6.0ms
(/ (/ i 2) (- (* 8 i) (/ 1.0 (/ i 2))))
6.0ms
(- (* 8 i) (/ 1.0 (/ i 2)))

series69.0ms

Calls
2 calls:
Slowest
42.0ms
(/ (/ i 2) (- (* 8 i) (/ 1.0 (/ i 2))))
26.0ms
(- (* 8 i) (/ 1.0 (/ i 2)))

simplify3.4s

Calls
40 calls:
Slowest
245.0ms
(+ (* (* 8 i) (* 8 i)) (+ (* (/ 1.0 (/ i 2)) (/ 1.0 (/ i 2))) (* (* 8 i) (/ 1.0 (/ i 2)))))
176.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
144.0ms
(/ (exp (* 8 i)) (exp (/ 1.0 (/ i 2))))
132.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
126.0ms
(/ (* (* (/ i 2) (/ i 2)) (/ i 2)) (* (* (- (* 8 i) (/ 1.0 (/ i 2))) (- (* 8 i) (/ 1.0 (/ i 2)))) (- (* 8 i) (/ 1.0 (/ i 2)))))

prune447.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i)))
0.2b
(* (/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i))) (/ (sqrt (/ i 2)) 2))
0.0b
(- (* i 4) (/ 1.0 i))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×sqrt-prod
27×associate-*l*
10×add-cbrt-cube add-exp-log div-inv
7×associate-/l*
5×pow1 add-log-exp
4×associate-*r* associate-/r/
3×associate-/r* flip3-- insert-posit16 flip--
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×frac-times clear-num sub-neg frac-2neg sqrt-div diff-log pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Calls
3 calls:
Slowest
11.0ms
(* (/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i))) (/ (sqrt (/ i 2)) 2))
7.0ms
(/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i)))
2.0ms
(- (* i 4) (/ 1.0 i))

series239.0ms

Calls
3 calls:
Slowest
137.0ms
(* (/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i))) (/ (sqrt (/ i 2)) 2))
67.0ms
(/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i)))
35.0ms
(- (* i 4) (/ 1.0 i))

simplify6.3s

Calls
104 calls:
Slowest
1.1s
(* (* (* (/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i))) (/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i)))) (/ (sqrt (/ i 2)) (- (* i 4) (/ 1.0 i)))) (* (* (/ (sqrt (/ i 2)) 2) (/ (sqrt (/ i 2)) 2)) (/ (sqrt (/ i 2)) 2)))
311.0ms
(/ (sqrt (/ i 2)) (- (pow (* i 4) 3) (pow (/ 1.0 i) 3)))
285.0ms
(/ (* (* (sqrt (/ i 2)) (sqrt (/ i 2))) (sqrt (/ i 2))) (* (* (- (* i 4) (/ 1.0 i)) (- (* i 4) (/ 1.0 i))) (- (* i 4) (/ 1.0 i))))
283.0ms
(* (/ (* (* (sqrt (/ i 2)) (sqrt (/ i 2))) (sqrt (/ i 2))) (* (* (- (* i 4) (/ 1.0 i)) (- (* i 4) (/ 1.0 i))) (- (* i 4) (/ 1.0 i)))) (* (* (/ (sqrt (/ i 2)) 2) (/ (sqrt (/ i 2)) 2)) (/ (sqrt (/ i 2)) 2)))
263.0ms
(/ (sqrt (/ i 2)) (- (* (* i 4) (* i 4)) (* (/ 1.0 i) (/ 1.0 i))))

prune964.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

14.6b
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
0.0b
(/ (* i i) 1/4)
0.0b
(* (/ (* i i) (- (/ (* i i) 1/4) 1.0)) 1/4)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×times-frac
5×add-cbrt-cube add-exp-log
4×associate-/r/
3×pow1 associate-/r* insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg flip3-- flip-- associate-/l*
1×cbrt-undiv div-exp associate-*l/ *-commutative
Calls
3 calls:
Slowest
18.0ms
(* (/ (* i i) (- (/ (* i i) 1/4) 1.0)) 1/4)
7.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
5.0ms
(/ (* i i) 1/4)

series117.0ms

Calls
3 calls:
Slowest
51.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
47.0ms
(* (/ (* i i) (- (/ (* i i) 1/4) 1.0)) 1/4)
19.0ms
(/ (* i i) 1/4)

simplify2.5s

Calls
31 calls:
Slowest
345.0ms
(/ (* i i) (- (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (* 1.0 1.0)))
299.0ms
(+ (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (+ (* 1.0 1.0) (* (/ (* i i) 1/4) 1.0)))
252.0ms
(- (+ (* 1.0 (pow i 2)) (+ (* 4.0 (pow i 4)) (* 16.0 (pow i 6)))))
212.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
165.0ms
(/ (* i i) (- (pow (/ (* i i) 1/4) 3) (pow 1.0 3)))

prune419.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s8000×body80valid
264.0ms8000×pre80true