Details

Time bar (total: 17.3s)

sample58.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
9.0ms256×pre80true

simplify293.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize12.0ms

Local error

Found 2 expressions with local error:

19.7b
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
7×pow1 prod-exp cbrt-unprod
4×add-sqr-sqrt cbrt-undiv div-exp
3×*-un-lft-identity associate-*l* pow-prod-down add-cube-cbrt
2×expm1-log1p-u associate-*l/ associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
1×clear-num associate-/r* frac-2neg times-frac flip3-- associate-*r* *-commutative div-inv flip-- associate-/l* unswap-sqr
Counts
2 → 48
Calls
2 calls:
Slowest
45.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
13.0ms
(* 4 (* i i))

series205.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
163.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
42.0ms
(* 4 (* i i))

simplify4.4s

Counts
28 → 54
Calls
28 calls:
Slowest
635.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
602.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
397.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
394.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
370.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))

prune450.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

19.0b
(/ i (- (* 4 (* i i)) 1.0))
0.1b
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
0.0b
(* 4 (* i i))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
26×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube add-exp-log
18×associate-*l*
14×associate-*r*
10×pow1
7×prod-exp cbrt-unprod
5×cbrt-undiv div-exp unswap-sqr
4×pow-prod-down associate-/r/
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
2×flip3-- *-commutative flip--
1×frac-times clear-num frac-2neg associate-*l/ associate-*r/
Counts
3 → 109
Calls
3 calls:
Slowest
96.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
28.0ms
(/ i (- (* 4 (* i i)) 1.0))
13.0ms
(* 4 (* i i))

series245.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
108.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
107.0ms
(/ i (- (* 4 (* i i)) 1.0))
30.0ms
(* 4 (* i i))

simplify6.9s

Counts
92 → 118
Calls
92 calls:
Slowest
518.0ms
(* (* (* (/ i (- (* 4 (* i i)) 1.0)) (/ i (- (* 4 (* i i)) 1.0))) (/ i (- (* 4 (* i i)) 1.0))) (* (* (/ i 4) (/ i 4)) (/ i 4)))
428.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))
348.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))
306.0ms
(/ i (- (pow (* 4 (* i i)) 3) (pow 1.0 3)))
283.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))

prune767.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.1b
(/ i (fma (/ 1.0 i) -4 (* 16 i)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
4.0ms
(/ i (fma (/ 1.0 i) -4 (* 16 i)))

series129.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
129.0ms
(/ i (fma (/ 1.0 i) -4 (* 16 i)))

simplify1.8s

Counts
28 → 33
Calls
28 calls:
Slowest
281.0ms
(/ (* (* i i) i) (* (* (fma (/ 1.0 i) -4 (* 16 i)) (fma (/ 1.0 i) -4 (* 16 i))) (fma (/ 1.0 i) -4 (* 16 i))))
218.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
212.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
172.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
77.0ms
(/ 1 (* (cbrt (fma (/ 1.0 i) -4 (* 16 i))) (cbrt (fma (/ 1.0 i) -4 (* 16 i)))))

prune299.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

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
982.0ms8000×body80valid
247.0ms8000×pre80true