Details

Time bar (total: 24.2s)

sample95.0ms

Algorithm
intervals
Results
60.0ms456×body80valid

simplify2.1s

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 155
Calls
4 calls:
1.8s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
971.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
75.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series557.0ms

Counts
4 → 10
Calls
4 calls:
416.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
79.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
61.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify632.0ms

Counts
165 → 165

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7))
0.1b
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
0.1b
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7))))))

rewrite449.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
55×associate-*l*
48×times-frac
45×add-exp-log
42×*-un-lft-identity
41×add-cube-cbrt
29×associate-*r*
24×unswap-sqr
21×add-cbrt-cube
19×prod-exp
16×associate-*l/ sqrt-prod
15×unpow-prod-down
12×frac-add
9×div-exp sqr-pow
7×sqrt-div cbrt-unprod
6×pow1 frac-times pow-to-exp flip3-+ associate-*r/ pow-exp flip-+
5×cube-prod
4×*-commutative div-inv add-log-exp
3×cbrt-undiv
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down
Counts
4 → 185
Calls
4 calls:
22.0ms
(* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7))
31.0ms
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
25.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))
359.0ms
(* (sqrt (/ 1 PI)) (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7))))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7))
420.0ms
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
48.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))
394.0ms
(* (sqrt (/ 1 PI)) (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7))))))

simplify627.0ms

Counts
197 → 197

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
0.1b
(* (sqrt (/ 1 PI)) (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)))
0.1b
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7)))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×associate-*l*
53×add-exp-log
45×times-frac
41×*-un-lft-identity
40×add-cube-cbrt
29×sqrt-prod
26×prod-exp
25×add-cbrt-cube
23×associate-*r*
18×unswap-sqr
10×unpow-prod-down associate-*l/ cbrt-unprod
9×div-exp
8×pow1
7×sqrt-div
6×pow-to-exp pow-exp sqr-pow
5×frac-times cube-prod associate-*r/
4×flip3-+ frac-add *-commutative flip-+ div-inv add-log-exp
3×cbrt-undiv
2×pow-prod-down
1×distribute-rgt-in cube-mult distribute-lft-in unpow3
Counts
4 → 177
Calls
4 calls:
20.0ms
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
46.0ms
(* (sqrt (/ 1 PI)) (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)))
21.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))
126.0ms
(* (sqrt (/ 1 PI)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7)))))

series578.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
174.0ms
(* (sqrt (/ 1 PI)) (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)))
57.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))
281.0ms
(* (sqrt (/ 1 PI)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (/ 857828500451523.0 18014398509481984.0) (pow (fabs x) 7)))))

simplify563.0ms

Counts
189 → 189

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(/ (* 1.0 (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
43×prod-exp cbrt-unprod
34×pow1
26×associate-*l*
24×add-sqr-sqrt times-frac
23×add-cube-cbrt *-un-lft-identity
21×pow-prod-down
10×cbrt-undiv div-exp
9×sqrt-prod
8×associate-*l/
6×associate-*r/ frac-add associate-/r* associate-/l/
4×add-log-exp
3×flip3-+ flip-+ div-inv
2×associate-*r* *-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l*
Counts
4 → 132
Calls
4 calls:
888.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
78.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
801.0ms
(/ (* 1.0 (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (sqrt PI))
1.0ms
(sqrt PI)

series628.0ms

Counts
4 → 10
Calls
4 calls:
104.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
69.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
454.0ms
(/ (* 1.0 (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify1.9s

Counts
142 → 142

prune781.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes194.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0s

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.0s13874×body80valid