Details

Time bar (total: 21.4s)

sample63.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
9.0ms256×pre80true

simplify272.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
272.0ms
(/ (/ (* (* 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: 15.8b

localize27.0ms

Local error

Found 2 expressions with local error:

15.8b
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))

rewrite63.0ms

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
44.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
19.0ms
(* 4 (* i i))

series156.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
116.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
40.0ms
(* 4 (* i i))

simplify4.5s

Counts
28 → 54
Calls
28 calls:
Slowest
576.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
502.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
399.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
398.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
386.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))

prune481.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

15.2b
(/ i (- (* 4 (* i i)) 1.0))
0.1b
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
0.0b
(* 4 (* i i))

rewrite146.0ms

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
89.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
29.0ms
(/ i (- (* 4 (* i i)) 1.0))
25.0ms
(* 4 (* i i))

series250.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
111.0ms
(/ i (- (* 4 (* i i)) 1.0))
94.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
45.0ms
(* 4 (* i i))

simplify7.5s

Counts
92 → 118
Calls
92 calls:
Slowest
479.0ms
(+ (* (* 4 (* i i)) (* 4 (* i i))) (+ (* 1.0 1.0) (* (* 4 (* i i)) 1.0)))
443.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))
411.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))
379.0ms
(/ i (- (pow (* 4 (* i i)) 3) (pow 1.0 3)))
310.0ms
(* (* (* 4 4) 4) (* (* (* i i) i) (* (* i i) i)))

prune812.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ i (fma (/ 1.0 i) -4 (* 16 i)))

rewrite4.0ms

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)))

series105.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
105.0ms
(/ i (fma (/ 1.0 i) -4 (* 16 i)))

simplify2.0s

Counts
28 → 33
Calls
28 calls:
Slowest
285.0ms
(/ (* (* i i) i) (* (* (fma (/ 1.0 i) -4 (* 16 i)) (fma (/ 1.0 i) -4 (* 16 i))) (fma (/ 1.0 i) -4 (* 16 i))))
265.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
250.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
236.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))
70.0ms
(- (log i) (log (fma (/ 1.0 i) -4 (* 16 i))))

prune328.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.7b
(/ (+ 0.015625 (/ 0.00390625 (* i i))) (* i i))
0.7b
(/ 0.00390625 (* i i))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×add-cbrt-cube add-exp-log
10×*-un-lft-identity
7×times-frac associate-/l*
6×add-sqr-sqrt add-cube-cbrt
4×cbrt-undiv div-exp
2×expm1-log1p-u pow1 clear-num associate-/r* frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv distribute-lft-out add-log-exp associate-/l/
1×flip3-+ flip-+
Counts
2 → 52
Calls
2 calls:
Slowest
48.0ms
(/ (+ 0.015625 (/ 0.00390625 (* i i))) (* i i))
7.0ms
(/ 0.00390625 (* i i))

series150.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
117.0ms
(/ (+ 0.015625 (/ 0.00390625 (* i i))) (* i i))
33.0ms
(/ 0.00390625 (* i i))

simplify2.5s

Counts
34 → 58
Calls
34 calls:
Slowest
341.0ms
(/ (* (* 0.00390625 0.00390625) 0.00390625) (* (* (* i i) (* i i)) (* i i)))
275.0ms
(+ (pow 0.015625 3) (pow (/ 0.00390625 (* i i)) 3))
241.0ms
(/ (* (* 0.00390625 0.00390625) 0.00390625) (* (* (* i i) i) (* (* i i) i)))
214.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (* 0.00390625 (/ 1 (pow i 4))))
202.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (* 0.00390625 (/ 1 (pow i 4))))

prune310.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.2s8000×body80valid
202.0ms8000×pre80true