Details

Time bar (total: 21.2s)

sample36.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify187.0ms

Calls
1 calls:
Slowest
187.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize20.0ms

Local error

Found 2 expressions with local error:

13.4b
(/ (* (/ i 2) (/ i 2)) (- (* (* 2 i) (* 2 i)) 1.0))
0.0b
(- (* (* 2 i) (* 2 i)) 1.0)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×associate-/r* times-frac associate-/l/
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp associate-/r/ insert-posit16 log1p-expm1-u flip-- add-log-exp
1×frac-times clear-num sub-neg frac-2neg fma-neg associate-*l/ prod-exp associate-*r/ cbrt-unprod div-inv associate-/l*
Calls
2 calls:
Slowest
13.0ms
(/ (* (/ i 2) (/ i 2)) (- (* (* 2 i) (* 2 i)) 1.0))
6.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

series182.0ms

Calls
2 calls:
Slowest
107.0ms
(/ (* (/ i 2) (/ i 2)) (- (* (* 2 i) (* 2 i)) 1.0))
75.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

simplify2.7s

Calls
26 calls:
Slowest
394.0ms
(- (+ (log (/ i 2)) (log (/ i 2))) (log (- (* (* 2 i) (* 2 i)) 1.0)))
357.0ms
(- (log (* (/ i 2) (/ i 2))) (log (- (* (* 2 i) (* 2 i)) 1.0)))
286.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
272.0ms
(+ (* (* (* 2 i) (* 2 i)) (* (* 2 i) (* 2 i))) (+ (* 1.0 1.0) (* (* (* 2 i) (* 2 i)) 1.0)))
267.0ms
(/ (* (* (* (/ i 2) (/ i 2)) (/ i 2)) (* (* (/ i 2) (/ i 2)) (/ i 2))) (* (* (- (* (* 2 i) (* 2 i)) 1.0) (- (* (* 2 i) (* 2 i)) 1.0)) (- (* (* 2 i) (* 2 i)) 1.0)))

prune348.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-*r*
10×add-cbrt-cube add-exp-log div-inv
5×pow1
4×associate-*l* associate-/r/ associate-/l*
3×expm1-log1p-u associate-/r* flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×frac-times clear-num sub-neg frac-2neg fma-neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Calls
3 calls:
Slowest
31.0ms
(* (/ i 2) (/ (/ i 2) (- (* (* 2 i) (* 2 i)) 1.0)))
18.0ms
(/ (/ i 2) (- (* (* 2 i) (* 2 i)) 1.0))
12.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

series296.0ms

Calls
3 calls:
Slowest
130.0ms
(/ (/ i 2) (- (* (* 2 i) (* 2 i)) 1.0))
97.0ms
(* (/ i 2) (/ (/ i 2) (- (* (* 2 i) (* 2 i)) 1.0)))
68.0ms
(- (* (* 2 i) (* 2 i)) 1.0)

simplify7.2s

Calls
72 calls:
Slowest
445.0ms
(/ (/ 1 2) (sqrt (- (* (* 2 i) (* 2 i)) 1.0)))
441.0ms
(+ (log (/ i 2)) (- (log (/ i 2)) (log (- (* (* 2 i) (* 2 i)) 1.0))))
403.0ms
(- (+ (* 0.5 i) (+ (* 2.0 (pow i 3)) (* 8.0 (pow i 5)))))
280.0ms
(+ (log (/ i 2)) (log (/ (/ i 2) (- (* (* 2 i) (* 2 i)) 1.0))))
277.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))

prune799.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ i (fma (/ 1.0 i) -2 (* 8 i)))
0.0b
(fma (/ 1.0 i) -2 (* 8 i))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt associate-/r* *-un-lft-identity add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×clear-num frac-2neg fma-udef div-inv
Calls
2 calls:
Slowest
1.0ms
(/ i (fma (/ 1.0 i) -2 (* 8 i)))
0.0ms
(fma (/ 1.0 i) -2 (* 8 i))

series213.0ms

Calls
2 calls:
Slowest
110.0ms
(fma (/ 1.0 i) -2 (* 8 i))
103.0ms
(/ i (fma (/ 1.0 i) -2 (* 8 i)))

simplify896.0ms

Calls
9 calls:
Slowest
327.0ms
(- (+ (* 0.5 (pow i 2)) (+ (* 2.0 (pow i 4)) (* 8.0 (pow i 6)))))
121.0ms
(+ (* 0.03125 (/ 1 (pow i 2))) (+ 1/8 (* 0.0078125 (/ 1 (pow i 4)))))
103.0ms
(+ (* 0.03125 (/ 1 (pow i 2))) (+ 1/8 (* 0.0078125 (/ 1 (pow i 4)))))
90.0ms
(- (* 8 i) (* 2.0 (/ 1 i)))
86.0ms
(- (* 8 i) (* 2.0 (/ 1 i)))

prune242.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-*r*
10×div-inv
9×add-cbrt-cube add-exp-log
4×pow1 associate-*l* associate-/l*
3×associate-/r*
2×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Calls
2 calls:
Slowest
6.0ms
(* (/ i 2) (/ (/ i 2) (fma (* 2 i) (* 2 i) (- 1.0))))
4.0ms
(/ (/ i 2) (fma (* 2 i) (* 2 i) (- 1.0)))

series244.0ms

Calls
2 calls:
Slowest
127.0ms
(* (/ i 2) (/ (/ i 2) (fma (* 2 i) (* 2 i) (- 1.0))))
116.0ms
(/ (/ i 2) (fma (* 2 i) (* 2 i) (- 1.0)))

simplify5.7s

Calls
64 calls:
Slowest
454.0ms
(+ (log (/ i 2)) (- (log (/ i 2)) (log (fma (* 2 i) (* 2 i) (- 1.0)))))
376.0ms
(- (+ (* 0.5 i) (+ (* 2.0 (pow i 3)) (* 8.0 (pow i 5)))))
296.0ms
(+ (log (/ i 2)) (log (/ (/ i 2) (fma (* 2 i) (* 2 i) (- 1.0)))))
259.0ms
(* (* (* (/ i 2) (/ i 2)) (/ i 2)) (/ (* (* (/ i 2) (/ i 2)) (/ i 2)) (* (* (fma (* 2 i) (* 2 i) (- 1.0)) (fma (* 2 i) (* 2 i) (- 1.0))) (fma (* 2 i) (* 2 i) (- 1.0)))))
251.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))

prune592.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s8000×body80valid
215.0ms8000×pre80true