Details

Time bar (total: 39.4s)

sample68.0ms

Algorithm
intervals
Results
45.0ms256×body80valid
10.0ms256×pre80true

simplify275.0ms

Calls
1 calls:
Slowest
275.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize21.0ms

Local error

Found 3 expressions with local error:

14.7b
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
0.3b
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
0.0b
(- (* (* 2 i) (* 2 i)) 1.0)

rewrite48.0ms

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
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
14.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
12.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

series104.0ms

Calls
3 calls:
Slowest
52.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
29.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
23.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

simplify31.5s

Calls
203 calls:
Slowest
600.0ms
(/ (* (* 2 i) (* 2 i)) (/ i 2))
516.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
511.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
474.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (sqrt (/ i 2))))
435.0ms
(- (log (/ i 2)) (log (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1/4 (- (/ i 1/4) (/ 1.0 i)))
0.1b
(* i (/ 1/4 (- (/ i 1/4) (/ 1.0 i))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-*r*
6×add-sqr-sqrt *-un-lft-identity associate-/r/
5×associate-/r*
4×add-cube-cbrt
2×pow1 flip3-- add-cbrt-cube add-exp-log frac-sub insert-posit16 div-inv flip-- add-log-exp
1×clear-num frac-2neg associate-*r/ *-commutative distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
3.0ms
(/ 1/4 (- (/ i 1/4) (/ 1.0 i)))
1.0ms
(* i (/ 1/4 (- (/ i 1/4) (/ 1.0 i))))

series77.0ms

Calls
2 calls:
Slowest
49.0ms
(* i (/ 1/4 (- (/ i 1/4) (/ 1.0 i))))
28.0ms
(/ 1/4 (- (/ i 1/4) (/ 1.0 i)))

simplify1.6s

Calls
22 calls:
Slowest
289.0ms
(- (+ (* 0.25 i) (+ (* 1.0 (pow i 3)) (* 4.0 (pow i 5)))))
202.0ms
(+ (* 0.00390625 (/ 1 (pow i 5))) (+ (* 0.015625 (/ 1 (pow i 3))) (* 1/16 (/ 1 i))))
177.0ms
(+ (* (/ i 1/4) (/ i 1/4)) (+ (* (/ 1.0 i) (/ 1.0 i)) (* (/ i 1/4) (/ 1.0 i))))
172.0ms
(+ (* (/ i 1/4) (/ i 1/4)) (+ (* (/ 1.0 i) (/ 1.0 i)) (* (/ i 1/4) (/ 1.0 i))))
171.0ms
(+ (* 0.00390625 (/ 1 (pow i 5))) (+ (* 0.015625 (/ 1 (pow i 3))) (* 1/16 (/ 1 i))))

prune330.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

15.6b
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
0.0b
(/ (* i i) 1/4)
0.0b
(- (/ (* i i) 1/4) 1.0)

rewrite27.0ms

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
15.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
6.0ms
(- (/ (* i i) 1/4) 1.0)
5.0ms
(/ (* i i) 1/4)

series66.0ms

Calls
3 calls:
Slowest
28.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
23.0ms
(- (/ (* i i) 1/4) 1.0)
15.0ms
(/ (* i i) 1/4)

simplify1.3s

Calls
22 calls:
Slowest
298.0ms
(+ (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (+ (* 1.0 1.0) (* (/ (* i i) 1/4) 1.0)))
189.0ms
(- (+ (* 1.0 (pow i 2)) (+ (* 4.0 (pow i 4)) (* 16.0 (pow i 6)))))
136.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))
108.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))
92.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (- (/ (* i i) 1/4) 1.0) (- (/ (* i i) 1/4) 1.0)) (- (/ (* i i) 1/4) 1.0)))

prune398.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ 0.015625 i) i)
0.1b
(/ 0.00390625 (pow i 4))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt associate-/l*
3×associate-/r* div-inv
2×pow1 clear-num frac-2neg add-cbrt-cube add-exp-log insert-posit16 add-log-exp
1×associate-/l/
Calls
2 calls:
Slowest
6.0ms
(/ (/ 0.015625 i) i)
1.0ms
(/ 0.00390625 (pow i 4))

series25.0ms

Calls
2 calls:
Slowest
14.0ms
(/ 0.00390625 (pow i 4))
11.0ms
(/ (/ 0.015625 i) i)

simplify63.0ms

Calls
11 calls:
Slowest
8.0ms
(/ 0.00390625 (pow i 4))
8.0ms
(/ 0.015625 (pow i 2))
8.0ms
(/ 0.015625 (pow i 2))
8.0ms
(/ 0.015625 (pow i 2))
6.0ms
(sqrt (/ 0.015625 i))

prune346.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s8000×body80valid
222.0ms8000×pre80true