Details

Time bar (total: 23.6s)

sample99.0ms

Algorithm
intervals
Results
71.0ms428×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 3 (254.0ms)

IterNodesCost
02867
17066
225047
3104235
done500035

prune388.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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)

rewrite1.9s

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:
38.0ms
(* (* (fabs x) (fabs x)) (fabs x))
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)))))
84.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series601.0ms

Counts
4 → 10
Calls
4 calls:
52.0ms
(* (* (fabs x) (fabs x)) (fabs x))
495.0ms
(* (/ 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)))))
55.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify760.0ms

Counts
153 → 153
Iterations

Useful iterations: done (751.0ms)

IterNodesCost
02917051
110345353
done50014174

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
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)))))
0.1b
(* 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))))))

rewrite79.0ms

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:
0.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.0ms
(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)))))
12.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
64.0ms
(* (* 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:
216.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
325.0ms
(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)))))
109.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
464.0ms
(* (* 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))))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01301864
13091799
217601553
done50011549

prune620.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
0.2b
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.3b
(/ (+ (fma 2.0 (fabs x) (* (pow (fabs x) 3) (/ 2.0 3.0))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
43×times-frac
39×add-cube-cbrt *-un-lft-identity
32×add-exp-log
25×associate-*l*
21×associate-*r*
16×add-cbrt-cube
15×sqrt-prod
14×unswap-sqr
12×prod-exp
10×unpow-prod-down
7×div-exp
6×associate-/r* sqr-pow
5×pow1 cube-prod
4×expm1-log1p-u pow-to-exp pow-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cbrt-undiv div-inv associate-/l*
2×*-commutative associate-/l/
1×unpow-prod-up cube-mult rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 unpow3 associate-*r/ associate-*l/ clear-num flip-+
Counts
4 → 156
Calls
4 calls:
45.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
31.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
48.0ms
(/ (+ (fma 2.0 (fabs x) (* (pow (fabs x) 3) (/ 2.0 3.0))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))) (sqrt PI))
2.0ms
(sqrt PI)

series550.0ms

Counts
4 → 10
Calls
4 calls:
77.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
70.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
403.0ms
(/ (+ (fma 2.0 (fabs x) (* (pow (fabs x) 3) (/ 2.0 3.0))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify2.9s

Counts
166 → 166
Iterations

Useful iterations: 2 (889.0ms)

IterNodesCost
02884328
17213710
239463432
done50003432

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (expm1 (log1p (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
(expm1 (log1p (sqrt PI)))
1.0b
(sqrt PI)

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
26×add-sqr-sqrt associate-*l*
20×add-cube-cbrt *-un-lft-identity
19×times-frac
16×pow1
14×associate-*l/ prod-exp cbrt-unprod
12×frac-add
7×pow-prod-down
6×frac-times flip3-+ associate-*r/ flip-+
4×cbrt-undiv expm1-log1p-u div-exp associate-*r* log1p-expm1-u add-log-exp
3×sqrt-prod
2×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square expm1-log1p distribute-lft-in sqrt-pow1 pow1/2 expm1-udef
Counts
4 → 114
Calls
4 calls:
1.8s
(* (/ 1.0 (expm1 (log1p (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)))))
126.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(expm1 (log1p (sqrt PI)))
3.0ms
(sqrt PI)

series867.0ms

Counts
4 → 8
Calls
4 calls:
819.0ms
(* (/ 1.0 (expm1 (log1p (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)))))
47.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(expm1 (log1p (sqrt PI)))
0.0ms
(sqrt PI)

simplify788.0ms

Counts
122 → 122
Iterations

Useful iterations: done (781.0ms)

IterNodesCost
02776133
19574326
done50013556

prune923.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes317.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02430
12930
done2930

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.4s14049×body80valid