Details

Time bar (total: 47.0s)

sample116.0ms

Algorithm
intervals
Results
68.0ms459×body80valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5000
31250
2261
175
028

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite15.3s

Algorithm
rewrite-expression-head
Rules
257×add-exp-log
184×prod-exp
147×add-cbrt-cube
98×cbrt-unprod
69×pow1
49×pow-prod-down
39×associate-*l*
27×add-sqr-sqrt times-frac div-exp
26×*-un-lft-identity add-cube-cbrt
15×cbrt-undiv
12×rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l/ *-commutative sqrt-prod div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 193
Calls
4 calls:
14.1s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0s
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
93.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series234.0ms

Counts
4 → 10
Calls
4 calls:
90.0ms
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
85.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
58.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.2s

Counts
203 → 203
Iterations
IterNodes
done5000
22422
1961
0329

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite6.2s

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
76×prod-exp
75×add-cbrt-cube
48×associate-*l*
46×add-sqr-sqrt
44×cbrt-unprod
40×times-frac
39×associate-*l/
36×pow1 frac-add
35×*-un-lft-identity
33×add-cube-cbrt
22×frac-times pow-prod-down associate-*r/
15×div-exp
14×flip3-+ sqrt-prod flip-+
9×cbrt-undiv
6×rec-exp 1-exp
5×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 197
Calls
4 calls:
5.1s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
980.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
117.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series675.0ms

Counts
4 → 10
Calls
4 calls:
529.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
77.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
69.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.2s

Counts
207 → 207
Iterations
IterNodes
done5000
11402
0411

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 7) 21)
0.1b
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ (pow (fabs x) 7) 21)))))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ (pow (fabs x) 7) 21))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
32×times-frac
31×*-un-lft-identity
30×add-cube-cbrt
25×pow1
17×associate-*l*
16×add-exp-log sqrt-prod
13×add-cbrt-cube
12×unpow-prod-down
7×associate-/l*
6×pow-plus associate-*r* pow-prod-up
5×unswap-sqr
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×associate-/r* div-exp fma-udef
2×pow2 pow-sqr *-commutative div-inv
1×distribute-rgt-in pow-to-exp cbrt-undiv clear-num frac-2neg distribute-lft-in sqrt-div pow3 associate-*l/ pow-exp
Counts
4 → 130
Calls
4 calls:
9.0ms
(/ (pow (fabs x) 7) 21)
30.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ (pow (fabs x) 7) 21)))))
33.0ms
(* (* (fabs x) (fabs x)) (fabs x))
0.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ (pow (fabs x) 7) 21))

series645.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (pow (fabs x) 7) 21)
376.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ (pow (fabs x) 7) 21)))))
43.0ms
(* (* (fabs x) (fabs x)) (fabs x))
137.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ (pow (fabs x) 7) 21))

simplify2.7s

Counts
142 → 142
Iterations
IterNodes
done5000
33103
21076
1416
0218

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ 1 (/ 21 (pow (fabs x) 7)))))))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ 1 (/ 21 (pow (fabs x) 7))))
0.2b
(/ 1 (/ 21 (pow (fabs x) 7)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
170×times-frac
106×add-sqr-sqrt
97×*-un-lft-identity
96×add-cube-cbrt
36×unpow-prod-down
33×add-exp-log
26×pow1
25×associate-/r*
17×div-exp associate-*l*
16×add-cbrt-cube sqrt-prod
12×sqr-pow
6×pow-plus associate-*r* pow-prod-up div-inv
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp cbrt-undiv pow-exp fma-udef associate-/l*
2×pow2 pow-sqr *-commutative
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in sqrt-div pow3 associate-*l/ associate-/r/ pow-flip inv-pow
Counts
4 → 215
Calls
4 calls:
36.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ 1 (/ 21 (pow (fabs x) 7)))))))
41.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ 1 (/ 21 (pow (fabs x) 7))))
29.0ms
(/ 1 (/ 21 (pow (fabs x) 7)))

series718.0ms

Counts
4 → 12
Calls
4 calls:
415.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ 1 (/ 21 (pow (fabs x) 7)))))))
36.0ms
(* (* (fabs x) (fabs x)) (fabs x))
178.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (/ 1 (/ 21 (pow (fabs x) 7))))
89.0ms
(/ 1 (/ 21 (pow (fabs x) 7)))

simplify2.7s

Counts
227 → 227
Iterations
IterNodes
done5002
22108
1853
0364

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes99.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.2s13746×body80valid