Details

Time bar (total: 41.6s)

sample51.0ms

Algorithm
intervals
Results
31.0ms256×body80valid
8.0ms256×pre80true

simplify174.0ms

Calls
1 calls:
Slowest
173.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize15.0ms

Local error

Found 2 expressions with local error:

15.4b
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
0.3b
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

rewrite24.0ms

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
13.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
8.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

series95.0ms

Calls
2 calls:
Slowest
55.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
40.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

simplify30.7s

Calls
200 calls:
Slowest
634.0ms
(/ (* (* 2 i) (* 2 i)) (/ i 2))
559.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
480.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
443.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (sqrt (/ i 2))))
441.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ 1 2))

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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)))
3.0ms
(- (* 8 i) (/ 2.0 i))

series71.0ms

Calls
2 calls:
Slowest
38.0ms
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))
33.0ms
(- (* 8 i) (/ 2.0 i))

simplify2.6s

Calls
40 calls:
Slowest
551.0ms
(/ (* (* (/ i 2) (/ i 2)) (/ i 2)) (* (* (- (* 8 i) (/ 2.0 i)) (- (* 8 i) (/ 2.0 i))) (- (* 8 i) (/ 2.0 i))))
206.0ms
(+ (* (* 8 i) (* 8 i)) (+ (* (/ 2.0 i) (/ 2.0 i)) (* (* 8 i) (/ 2.0 i))))
192.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
130.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
117.0ms
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))

prune380.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

16.3b
(/ (* 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)

rewrite22.0ms

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
12.0ms
(* (/ (* i i) (- (/ (* i i) 1/4) 1.0)) 1/4)
7.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
2.0ms
(/ (* i i) 1/4)

series95.0ms

Calls
3 calls:
Slowest
49.0ms
(* (/ (* i i) (- (/ (* i i) 1/4) 1.0)) 1/4)
34.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
12.0ms
(/ (* i i) 1/4)

simplify2.4s

Calls
31 calls:
Slowest
397.0ms
(/ (* i i) (- (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (* 1.0 1.0)))
246.0ms
(+ (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (+ (* 1.0 1.0) (* (/ (* i i) 1/4) 1.0)))
170.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (- (/ (* i i) 1/4) 1.0) (- (/ (* i i) 1/4) 1.0)) (- (/ (* i i) 1/4) 1.0)))
168.0ms
(- (+ (* 1.0 (pow i 2)) (+ (* 4.0 (pow i 4)) (* 16.0 (pow i 6)))))
165.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))

prune516.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (/ 0.015625 i) i)
0.1b
(/ 0.00390625 (pow i 4))
0.0b
(+ (/ (/ 0.015625 i) i) (+ 1/16 (/ 0.00390625 (pow i 4))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×associate-/l*
3×pow1 associate-/r* add-cbrt-cube add-exp-log insert-posit16 div-inv
2×clear-num frac-2neg flip3-+ frac-add flip-+
1×+-commutative associate-+r+ sum-log distribute-lft-out associate-/l/
Calls
3 calls:
Slowest
7.0ms
(+ (/ (/ 0.015625 i) i) (+ 1/16 (/ 0.00390625 (pow i 4))))
3.0ms
(/ (/ 0.015625 i) i)
1.0ms
(/ 0.00390625 (pow i 4))

series69.0ms

Calls
3 calls:
Slowest
31.0ms
(/ 0.00390625 (pow i 4))
24.0ms
(+ (/ (/ 0.015625 i) i) (+ 1/16 (/ 0.00390625 (pow i 4))))
14.0ms
(/ (/ 0.015625 i) i)

simplify1.1s

Calls
21 calls:
Slowest
242.0ms
(+ (* (/ 0.015625 i) (- 1/16 (/ 0.00390625 (pow i 4)))) (* i (- (* 1/16 1/16) (* (/ 0.00390625 (pow i 4)) (/ 0.00390625 (pow i 4))))))
193.0ms
(+ (* (/ 0.015625 i) (+ (* 1/16 1/16) (- (* (/ 0.00390625 (pow i 4)) (/ 0.00390625 (pow i 4))) (* 1/16 (/ 0.00390625 (pow i 4)))))) (* i (+ (pow 1/16 3) (pow (/ 0.00390625 (pow i 4)) 3))))
170.0ms
(* i (+ (* 1/16 1/16) (- (* (/ 0.00390625 (pow i 4)) (/ 0.00390625 (pow i 4))) (* 1/16 (/ 0.00390625 (pow i 4))))))
106.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
95.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))

prune501.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8000×body80valid
278.0ms8000×pre80true