Details

Time bar (total: 26.1s)

sample113.0ms

Algorithm
intervals
Results
83.0ms473×body80valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.3s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 143
Calls
4 calls:
36.0ms
(* (* (fabs x) (fabs x)) (fabs x))
2.1s
(* (/ 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)))))
80.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series570.0ms

Counts
4 → 10
Calls
4 calls:
47.0ms
(* (* (fabs x) (fabs x)) (fabs x))
474.0ms
(* (/ 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)))))
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.7s

Counts
153 → 153
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02917051
19675061
246983884
done50003881

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.0b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
13×add-sqr-sqrt
11×add-cbrt-cube
10×associate-*r*
9×pow1
8×add-cube-cbrt *-un-lft-identity
6×prod-exp
4×expm1-log1p-u unpow-prod-down associate-*l* cbrt-unprod fma-udef log1p-expm1-u add-log-exp
3×pow-prod-down unswap-sqr
2×*-commutative sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in sqrt-div associate-*r/ associate-*l/ pow-exp
Counts
4 → 70
Calls
4 calls:
1.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
1.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
20.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
47.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
307.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
242.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
127.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
428.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
01301864
12781791
210081543
done50011543

prune475.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (* 0.047619047619047616 (sqrt (pow (fabs x) 7))) (sqrt (pow (fabs x) 7)))))))
0.1b
(* 0.047619047619047616 (sqrt (pow (fabs x) 7)))
7.1b
(sqrt (pow (fabs x) 7))
7.1b
(sqrt (pow (fabs x) 7))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt sqrt-prod
13×add-cube-cbrt *-un-lft-identity associate-*r*
12×unpow-prod-down
11×pow1 add-exp-log add-cbrt-cube
6×rem-sqrt-square sqr-pow
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×sqrt-pow1 pow1/2 *-commutative fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*r/ associate-*l/
Counts
4 → 95
Calls
4 calls:
48.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (* 0.047619047619047616 (sqrt (pow (fabs x) 7))) (sqrt (pow (fabs x) 7)))))))
17.0ms
(* 0.047619047619047616 (sqrt (pow (fabs x) 7)))
5.0ms
(sqrt (pow (fabs x) 7))
4.0ms
(sqrt (pow (fabs x) 7))

series710.0ms

Counts
4 → 12
Calls
4 calls:
461.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (* 0.047619047619047616 (sqrt (pow (fabs x) 7))) (sqrt (pow (fabs x) 7)))))))
100.0ms
(* 0.047619047619047616 (sqrt (pow (fabs x) 7)))
73.0ms
(sqrt (pow (fabs x) 7))
76.0ms
(sqrt (pow (fabs x) 7))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: 2 (251.0ms)

IterNodesCost
01331872
12881553
29391375
done50011375

prune796.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 3.0 (pow (fabs x) 3))
0.3b
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
0.6b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
438×times-frac
235×add-sqr-sqrt
234×add-cube-cbrt *-un-lft-identity
74×associate-/r*
48×unpow-prod-down cube-prod
39×sqrt-prod
24×add-exp-log
16×cube-mult unpow3 add-cbrt-cube sqr-pow
13×div-exp
11×div-inv
9×associate-/l*
7×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-to-exp pow-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 372
Calls
4 calls:
18.0ms
(/ 3.0 (pow (fabs x) 3))
27.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
27.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
3.0ms
(sqrt PI)

series586.0ms

Counts
4 → 10
Calls
4 calls:
52.0ms
(/ 3.0 (pow (fabs x) 3))
462.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
73.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify2.9s

Counts
382 → 382
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
054410863
110739979
237939589
done50009589

prune2.2s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes318.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02430
12930
done2930

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s14065×body80valid