Details

Time bar (total: 25.1s)

sample186.0ms

Algorithm
intervals
Results
155.0ms444×body80valid

simplify931.0ms

Counts
1 → 1
Iterations
IterNodes
done2000
31250
2261
175
028

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.3s

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
36×pow1
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
15×div-exp associate-*l/
14×sqrt-prod
12×frac-add
9×cbrt-undiv
6×frac-times rec-exp flip3-+ 1-exp associate-*r/ flip-+
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 → 181
Calls
4 calls:
612.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.7s
(* (/ 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 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
53.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series561.0ms

Counts
4 → 10
Calls
4 calls:
96.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
390.0ms
(* (/ 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 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
75.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.1s

Counts
191 → 191
Iterations
IterNodes
done2001
11236
0362

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt PI)))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
141×sqrt-prod
126×times-frac
78×*-un-lft-identity
66×add-cube-cbrt
31×associate-*r* associate-*l*
28×add-exp-log unswap-sqr
18×add-cbrt-cube
9×associate-/r* div-exp
8×pow1 prod-exp
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 203
Calls
4 calls:
9.0ms
(/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt PI)))
35.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt PI))))
2.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series950.0ms

Counts
4 → 8
Calls
4 calls:
616.0ms
(/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt PI)))
333.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.6s

Counts
211 → 211
Iterations
IterNodes
done2000
21954
1605
0229

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (/ 1 (sqrt (sqrt (sqrt PI)))) (sqrt (sqrt PI))) (/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt (sqrt PI)))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
1392×sqrt-prod
1087×times-frac
968×add-sqr-sqrt
438×*-un-lft-identity
378×add-cube-cbrt
364×associate-*l*
140×unswap-sqr
40×associate-*r*
39×add-exp-log
25×add-cbrt-cube
17×div-exp
11×div-inv
10×prod-exp
9×pow1 cbrt-undiv
6×cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×rec-exp 1-exp
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 623
Calls
4 calls:
66.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt PI)))) (sqrt (sqrt PI))) (/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt (sqrt PI)))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series729.0ms

Counts
4 → 6
Calls
4 calls:
729.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt PI)))) (sqrt (sqrt PI))) (/ (fma (* (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) 1/21 (fma 1/5 (* (fabs x) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (sqrt (sqrt PI)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.6s

Counts
629 → 629
Iterations
IterNodes
done2001
11365
0431

prune3.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7)))
0.3b
(* (pow (/ 1 PI) 1/4) (fma (pow (fabs x) 5) 1/5 (fma (fabs x) 2 (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7))))))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (* (pow (/ 1 PI) 1/4) (fma (pow (fabs x) 5) 1/5 (fma (fabs x) 2 (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7)))))))
1.0b
(sqrt PI)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
103×add-exp-log
58×prod-exp
48×associate-*l*
44×add-sqr-sqrt
38×times-frac
34×*-un-lft-identity
33×add-cube-cbrt
30×sqrt-prod
24×div-exp
20×pow-exp
18×add-cbrt-cube
16×unpow-prod-down
12×rec-exp 1-exp
7×pow1 cbrt-unprod fma-udef
5×distribute-rgt-in pow-to-exp distribute-lft-in unswap-sqr
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv *-commutative div-inv sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/
Counts
4 → 153
Calls
4 calls:
0.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7)))
15.0ms
(* (pow (/ 1 PI) 1/4) (fma (pow (fabs x) 5) 1/5 (fma (fabs x) 2 (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7))))))
72.0ms
(* (/ 1 (sqrt (sqrt PI))) (* (pow (/ 1 PI) 1/4) (fma (pow (fabs x) 5) 1/5 (fma (fabs x) 2 (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7)))))))
2.0ms
(sqrt PI)

series1.2s

Counts
4 → 10
Calls
4 calls:
137.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7)))
625.0ms
(* (pow (/ 1 PI) 1/4) (fma (pow (fabs x) 5) 1/5 (fma (fabs x) 2 (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7))))))
408.0ms
(* (/ 1 (sqrt (sqrt PI))) (* (pow (/ 1 PI) 1/4) (fma (pow (fabs x) 5) 1/5 (fma (fabs x) 2 (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* 1/21 (pow (fabs x) 7)))))))
0.0ms
(sqrt PI)

simplify756.0ms

Counts
163 → 163
Iterations
IterNodes
done2001
1601
0246

prune1.1s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes353.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations
IterNodes
done46
146
028

end0.0ms

sample4.9s

Algorithm
intervals
Results
4.6s13875×body80valid