Details

Time bar (total: 45.1s)

sample52.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
15.0ms256×pre80true

simplify245.0ms

Calls
1 calls:
Slowest
245.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize27.0ms

Local error

Found 3 expressions with local error:

12.9b
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
0.1b
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
0.0b
(- (* (* 2 i) (* 2 i)) 1.0)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
70×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
44×div-inv
21×associate-/r*
10×add-cbrt-cube add-exp-log
7×associate-/r/ associate-/l*
4×cbrt-undiv div-exp
3×pow1 insert-posit16 add-log-exp associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×sub-neg div-sub
Calls
3 calls:
Slowest
17.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
8.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
5.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

series381.0ms

Calls
3 calls:
Slowest
183.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
119.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
79.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

simplify30.0s

Calls
203 calls:
Slowest
610.0ms
(/ (* (* 2 i) (* 2 i)) (/ i 2))
526.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
508.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
438.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ 1 2))
416.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (cbrt (/ i 2))))

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))
0.0b
(- (* 8 i) (/ 2.0 i))

rewrite10.0ms

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) (/ 2.0 i)))
2.0ms
(- (* 8 i) (/ 2.0 i))

series209.0ms

Calls
2 calls:
Slowest
120.0ms
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))
89.0ms
(- (* 8 i) (/ 2.0 i))

simplify2.4s

Calls
40 calls:
Slowest
488.0ms
(/ (* (* (/ i 2) (/ i 2)) (/ i 2)) (* (* (- (* 8 i) (/ 2.0 i)) (- (* 8 i) (/ 2.0 i))) (- (* 8 i) (/ 2.0 i))))
189.0ms
(+ (* (* 8 i) (* 8 i)) (+ (* (/ 2.0 i) (/ 2.0 i)) (* (* 8 i) (/ 2.0 i))))
153.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
107.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
104.0ms
(- (* 8 i) (* 2.0 (/ 1 i)))

prune361.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (sqrt (/ i 2)) (/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i))))
0.2b
(/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i)))
0.0b
(- (* 8 i) (/ 2.0 i))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
35×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
32×sqrt-prod
27×associate-*r*
10×add-cbrt-cube add-exp-log div-inv
7×associate-*l* associate-/l*
5×pow1 add-log-exp
4×associate-/r/
3×associate-/r* flip3-- sqrt-div insert-posit16 flip--
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×frac-times clear-num sub-neg frac-2neg diff-log pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Calls
3 calls:
Slowest
14.0ms
(* (sqrt (/ i 2)) (/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i))))
6.0ms
(/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i)))
2.0ms
(- (* 8 i) (/ 2.0 i))

series374.0ms

Calls
3 calls:
Slowest
169.0ms
(* (sqrt (/ i 2)) (/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i))))
123.0ms
(/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i)))
81.0ms
(- (* 8 i) (/ 2.0 i))

simplify5.0s

Calls
108 calls:
Slowest
402.0ms
(* (* (* (sqrt (/ i 2)) (sqrt (/ i 2))) (sqrt (/ i 2))) (* (* (/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i))) (/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i)))) (/ (sqrt (/ i 2)) (- (* 8 i) (/ 2.0 i)))))
271.0ms
(/ (* (* (sqrt (/ i 2)) (sqrt (/ i 2))) (sqrt (/ i 2))) (* (* (- (* 8 i) (/ 2.0 i)) (- (* 8 i) (/ 2.0 i))) (- (* 8 i) (/ 2.0 i))))
239.0ms
(+ (* 1/8 (pow (sqrt 1/2) 2)) (+ (* 0.03125 (/ (pow (sqrt 1/2) 2) (pow i 2))) (* 0.0078125 (/ (pow (sqrt 1/2) 2) (pow i 4)))))
222.0ms
(- (+ (* 2.0 (* (pow i 4) (pow (sqrt 1/2) 2))) (+ (* 0.5 (* (pow i 2) (pow (sqrt 1/2) 2))) (* 8.0 (* (pow i 6) (pow (sqrt 1/2) 2))))))
209.0ms
(+ (* (* 8 i) (* 8 i)) (+ (* (/ 2.0 i) (/ 2.0 i)) (* (* 8 i) (/ 2.0 i))))

prune899.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

13.4b
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
0.0b
(- (/ (* i i) 1/4) 1.0)
0.0b
(/ (* i i) 1/4)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×pow1 associate-/r* times-frac insert-posit16 add-log-exp
2×clear-num frac-2neg flip3-- associate-/r/ div-inv flip-- associate-/l*
1×cbrt-undiv sub-neg div-exp
Calls
3 calls:
Slowest
7.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
4.0ms
(- (/ (* i i) 1/4) 1.0)
2.0ms
(/ (* i i) 1/4)

series232.0ms

Calls
3 calls:
Slowest
101.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
85.0ms
(- (/ (* i i) 1/4) 1.0)
45.0ms
(/ (* i i) 1/4)

simplify1.1s

Calls
22 calls:
Slowest
274.0ms
(+ (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (+ (* 1.0 1.0) (* (/ (* i i) 1/4) 1.0)))
162.0ms
(- (+ (* 1.0 (pow i 2)) (+ (* 4.0 (pow i 4)) (* 16.0 (pow i 6)))))
114.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (- (/ (* i i) 1/4) 1.0) (- (/ (* i i) 1/4) 1.0)) (- (/ (* i i) 1/4) 1.0)))
100.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))
85.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))

prune437.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch5.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
951.0ms8000×body80valid
292.0ms8000×pre80true