Details

Time bar (total: 28.1s)

sample58.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
9.0ms256×pre80true

simplify298.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
298.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize33.0ms

Local error

Found 2 expressions with local error:

15.1b
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))

rewrite93.0ms

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
66.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
26.0ms
(* 4 (* i i))

series176.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
132.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
44.0ms
(* 4 (* i i))

simplify4.4s

Counts
28 → 54
Calls
28 calls:
Slowest
530.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
507.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
459.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))
454.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
384.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))

prune387.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

14.5b
(/ (* (- (* 4 (* i i)) 1.0) 4) i)
0.1b
(/ i (/ (* (- (* 4 (* i i)) 1.0) 4) i))
0.0b
(* 4 (* i i))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
23×add-sqr-sqrt
22×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
10×associate-/r*
8×pow1
7×cbrt-undiv div-exp
6×div-inv
5×prod-exp cbrt-unprod
4×associate-/l*
3×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-*l/ associate-/l/
1×flip3-- associate-*r* associate-/r/ *-commutative flip-- unswap-sqr
Counts
3 → 99
Calls
3 calls:
Slowest
55.0ms
(/ (* (- (* 4 (* i i)) 1.0) 4) i)
14.0ms
(/ i (/ (* (- (* 4 (* i i)) 1.0) 4) i))
13.0ms
(* 4 (* i i))

series315.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
182.0ms
(/ (* (- (* 4 (* i i)) 1.0) 4) i)
104.0ms
(/ i (/ (* (- (* 4 (* i i)) 1.0) 4) i))
28.0ms
(* 4 (* i i))

simplify12.4s

Counts
91 → 108
Calls
91 calls:
Slowest
553.0ms
(/ 1 (/ (- (* 4 (* i i)) 1.0) (sqrt i)))
493.0ms
(* (- (pow (* 4 (* i i)) 3) (pow 1.0 3)) 4)
476.0ms
(/ (* (* i i) i) (/ (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)) (* (* i i) i)))
416.0ms
(/ (* (* i i) i) (/ (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)) (* (* i i) i)))
317.0ms
(- (log i) (log (/ (* (- (* 4 (* i i)) 1.0) 4) i)))

prune704.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ i (- (* 16 i) (/ 4.0 i)))
0.0b
(- (* 16 i) (/ 4.0 i))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×prod-diff
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 flip3-- associate-/r/ insert-posit16 log1p-expm1-u div-inv flip--
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp
Counts
2 → 61
Calls
2 calls:
Slowest
25.0ms
(/ i (- (* 16 i) (/ 4.0 i)))
18.0ms
(- (* 16 i) (/ 4.0 i))

series215.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
121.0ms
(/ i (- (* 16 i) (/ 4.0 i)))
94.0ms
(- (* 16 i) (/ 4.0 i))

simplify7.0s

Counts
60 → 67
Calls
60 calls:
Slowest
635.0ms
(fma 16 i (- (* (/ 4.0 (cbrt i)) (/ 1 (* (cbrt i) (cbrt i))))))
541.0ms
(fma (- (/ 4.0 (cbrt i))) (/ 1 (* (cbrt i) (cbrt i))) (* (/ 4.0 (cbrt i)) (/ 1 (* (cbrt i) (cbrt i)))))
310.0ms
(fma 16 i (- (* (/ (cbrt 4.0) (cbrt i)) (/ (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt i) (cbrt i))))))
287.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
287.0ms
(fma 16 i (- (* (/ (cbrt 4.0) i) (/ (* (cbrt 4.0) (cbrt 4.0)) 1))))

prune499.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes14.0ms

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
976.0ms8000×body80valid
234.0ms8000×pre80true