Details

Time bar (total: 28.8s)

sample141.0ms

Algorithm
intervals
Results
118.0ms425×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2017
42017
31250
2261
175
028

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (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)

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×add-exp-log
36×associate-*l*
35×pow1 add-cbrt-cube
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
19×prod-exp
17×cbrt-unprod
14×associate-*l/ sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+ unswap-sqr
5×div-exp
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp pow3
Counts
4 → 151
Calls
4 calls:
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
2.0s
(* (/ 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)))))
59.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series441.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(* (* (fabs x) (fabs x)) (fabs x))
353.0ms
(* (/ 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)))))
51.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.7s

Counts
161 → 161
Iterations
IterNodes
done2000
22000
11034
0293

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
34×pow1
25×add-sqr-sqrt
20×add-cbrt-cube add-exp-log
18×associate-*l*
16×*-un-lft-identity sqrt-prod
15×add-cube-cbrt
11×times-frac
10×pow-prod-down prod-exp cbrt-unprod
9×associate-*r*
6×pow-plus pow-prod-up
5×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef
2×pow2 pow-sqr
1×distribute-rgt-in distribute-lft-in sqrt-div pow3 associate-*l/ div-inv
Counts
4 → 106
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))
31.0ms
(* (* (fabs x) (fabs x)) (fabs x))
19.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))))
45.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

series623.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))
31.0ms
(* (* (fabs x) (fabs x)) (fabs x))
385.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))))
72.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

simplify1.4s

Counts
118 → 118
Iterations
IterNodes
done2028
32028
2955
1329
0164

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (/ (sqrt 1) (sqrt PI))) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))))
0.3b
(* (sqrt (/ (sqrt 1) (sqrt PI))) (* (sqrt (/ (sqrt 1) (sqrt PI))) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
172×sqrt-prod
86×associate-*l*
81×add-sqr-sqrt
78×times-frac
61×*-un-lft-identity
59×add-cube-cbrt
13×pow1
11×add-cbrt-cube add-exp-log
8×unswap-sqr
6×fma-udef
5×distribute-rgt-in distribute-lft-in sqrt-div
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
1×frac-times associate-*r/
Counts
4 → 171
Calls
4 calls:
14.0ms
(* (sqrt (/ (sqrt 1) (sqrt PI))) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))))
43.0ms
(* (sqrt (/ (sqrt 1) (sqrt PI))) (* (sqrt (/ (sqrt 1) (sqrt PI))) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series928.0ms

Counts
4 → 8
Calls
4 calls:
629.0ms
(* (sqrt (/ (sqrt 1) (sqrt PI))) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))))
299.0ms
(* (sqrt (/ (sqrt 1) (sqrt PI))) (* (sqrt (/ (sqrt 1) (sqrt PI))) (fma 1/5 (pow (fabs x) 5) (fma 2 (fabs x) (fma (pow (fabs x) 7) 1/21 (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.4s

Counts
179 → 179
Iterations
IterNodes
done2004
32004
21201
1424
0190

prune3.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
11×add-cbrt-cube add-exp-log
6×associate-/r* pow-plus pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod associate-/l*
2×pow2 pow-sqr
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp associate-*l* pow3 *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 100
Calls
4 calls:
0.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (+ (fabs x) (fabs x)))
15.0ms
(* (* (fabs x) (fabs x)) (fabs x))
5.0ms
(/ (fma (pow (fabs x) 5) 1/5 (fma 1/21 (pow (fabs x) 7) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (+ (fabs x) (fabs x))))) (sqrt PI))
1.0ms
(sqrt PI)

series476.0ms

Counts
4 → 10
Calls
4 calls:
94.0ms
(fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (+ (fabs x) (fabs x)))
33.0ms
(* (* (fabs x) (fabs x)) (fabs x))
348.0ms
(/ (fma (pow (fabs x) 5) 1/5 (fma 1/21 (pow (fabs x) 7) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (+ (fabs x) (fabs x))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify1.7s

Counts
110 → 110
Iterations
IterNodes
done2004
42004
31868
2615
1264
0144

prune1.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes348.0ms

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

sample5.4s

Algorithm
intervals
Results
4.8s13996×body80valid