Details

Time bar (total: 43.8s)

sample46.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
7.0ms256×pre80true

simplify313.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
313.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize16.0ms

Local error

Found 2 expressions with local error:

13.1b
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))

rewrite62.0ms

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
48.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
13.0ms
(* 4 (* i i))

series169.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
115.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
53.0ms
(* 4 (* i i))

simplify4.3s

Counts
28 → 54
Calls
28 calls:
Slowest
548.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
515.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
422.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))
415.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
378.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))

prune361.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

12.7b
(/ i (- (* 4 (* i i)) 1.0))
0.1b
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
0.0b
(* 4 (* i i))

rewrite184.0ms

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
115.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
40.0ms
(/ i (- (* 4 (* i i)) 1.0))
26.0ms
(* 4 (* i i))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
97.0ms
(/ i (- (* 4 (* i i)) 1.0))
39.0ms
(* 4 (* i i))

simplify7.4s

Counts
92 → 118
Calls
92 calls:
Slowest
621.0ms
(* (* (* (/ i (- (* 4 (* i i)) 1.0)) (/ i (- (* 4 (* i i)) 1.0))) (/ i (- (* 4 (* i i)) 1.0))) (* (* (/ i 4) (/ i 4)) (/ i 4)))
446.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))
369.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))
313.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))
310.0ms
(/ i (- (pow (* 4 (* i i)) 3) (pow 1.0 3)))

prune968.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ i (fma (/ 1.0 i) -4 (* 16 i)))
0.0b
(fma (/ 1.0 i) -4 (* 16 i))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
4.0ms
(/ i (fma (/ 1.0 i) -4 (* 16 i)))
0.0ms
(fma (/ 1.0 i) -4 (* 16 i))

series179.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
95.0ms
(fma (/ 1.0 i) -4 (* 16 i))
83.0ms
(/ i (fma (/ 1.0 i) -4 (* 16 i)))

simplify1.9s

Counts
31 → 47
Calls
31 calls:
Slowest
278.0ms
(/ (* (* i i) i) (* (* (fma (/ 1.0 i) -4 (* 16 i)) (fma (/ 1.0 i) -4 (* 16 i))) (fma (/ 1.0 i) -4 (* 16 i))))
216.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
201.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
188.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
97.0ms
(- (* 16 i) (* 4.0 (/ 1 i)))

prune412.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i))
0.1b
(/ (sqrt i) (/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i)))
0.0b
(fma (/ 1.0 i) -4 (* 16 i))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
155×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
28×associate-/r*
10×add-cbrt-cube add-exp-log
9×div-inv associate-/l*
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×associate-/r/ fma-udef
Counts
3 → 231
Calls
3 calls:
Slowest
12.0ms
(/ (sqrt i) (/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i)))
5.0ms
(/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i))
1.0ms
(fma (/ 1.0 i) -4 (* 16 i))

series243.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
88.0ms
(/ (sqrt i) (/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i)))
78.0ms
(/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i))
76.0ms
(fma (/ 1.0 i) -4 (* 16 i))

simplify22.9s

Counts
351 → 240
Calls
351 calls:
Slowest
578.0ms
(/ (* (cbrt (sqrt i)) (cbrt (sqrt i))) (/ (* (cbrt (fma (/ 1.0 i) -4 (* 16 i))) (cbrt (fma (/ 1.0 i) -4 (* 16 i)))) (sqrt 1)))
458.0ms
(/ (* (* (sqrt i) (sqrt i)) (sqrt i)) (* (* (/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i)) (/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i))) (/ (fma (/ 1.0 i) -4 (* 16 i)) (sqrt i))))
297.0ms
(/ (sqrt 1) (/ (* (cbrt (fma (/ 1.0 i) -4 (* 16 i))) (cbrt (fma (/ 1.0 i) -4 (* 16 i)))) (* (cbrt (sqrt i)) (cbrt (sqrt i)))))
291.0ms
(/ (* (cbrt (sqrt i)) (cbrt (sqrt i))) (/ (* (cbrt (fma (/ 1.0 i) -4 (* 16 i))) (cbrt (fma (/ 1.0 i) -4 (* 16 i)))) (* (cbrt (sqrt i)) (cbrt (sqrt i)))))
288.0ms
(/ (* (* (fma (/ 1.0 i) -4 (* 16 i)) (fma (/ 1.0 i) -4 (* 16 i))) (fma (/ 1.0 i) -4 (* 16 i))) (* (* (sqrt i) (sqrt i)) (sqrt i)))

prune2.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
933.0ms8000×body80valid
265.0ms8000×pre80true