Details

Time bar (total: 28.4s)

sample85.0ms

Algorithm
intervals
Results
53.0ms456×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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)))))
0.1b
(* (/ 1.0 5.0) (* (* (* (* (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)

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 163
Calls
4 calls:
1.9s
(* (/ 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)))))
1.0s
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
87.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series598.0ms

Counts
4 → 10
Calls
4 calls:
433.0ms
(* (/ 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)))))
83.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
82.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify791.0ms

Counts
173 → 173
Iterations

Useful iterations: done (781.0ms)

IterNodesCost
03508160
111365868
done50014750

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
48×associate-*l*
45×times-frac
38×add-cube-cbrt *-un-lft-identity
35×add-exp-log
22×associate-*r*
19×add-cbrt-cube
17×unswap-sqr
14×prod-exp
13×sqrt-prod
10×unpow-prod-down
7×pow1 div-exp
6×cbrt-unprod sqr-pow
5×cube-prod
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*l/ *-commutative div-inv
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down
Counts
4 → 162
Calls
4 calls:
36.0ms
(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
58.0ms
(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))))
23.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0ms
(sqrt PI)

series604.0ms

Counts
4 → 10
Calls
4 calls:
90.0ms
(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
453.0ms
(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))))))
61.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)

simplify2.4s

Counts
172 → 172
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03074308
18763725
235603374
done50013367

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (* (pow (fabs x) 6) (/ 1.0 (sqrt 21.0))))))))
0.2b
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b
(sqrt PI)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
48×associate-*l*
45×times-frac
38×add-cube-cbrt *-un-lft-identity
35×add-exp-log
23×associate-*r*
19×add-cbrt-cube
17×unswap-sqr
14×prod-exp
13×sqrt-prod
10×unpow-prod-down
7×pow1 div-exp
6×cbrt-unprod sqr-pow
5×cube-prod
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*l/ *-commutative div-inv
2×frac-times flip3-+ associate-*r/ flip-+
1×unpow-prod-up distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down
Counts
4 → 163
Calls
4 calls:
48.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
46.0ms
(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (* (pow (fabs x) 6) (/ 1.0 (sqrt 21.0))))))))
25.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
2.0ms
(sqrt PI)

series876.0ms

Counts
4 → 10
Calls
4 calls:
73.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
740.0ms
(* (/ 1.0 (sqrt PI)) (+ (fma 2.0 (fabs x) (* (/ 2.0 3.0) (pow (fabs x) 3))) (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (* (pow (fabs x) 6) (/ 1.0 (sqrt 21.0))))))))
62.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)

simplify2.6s

Counts
173 → 173
Iterations

Useful iterations: 2 (881.0ms)

IterNodesCost
03184595
19114144
236503622
done50003622

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize48.0ms

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)

rewrite99.0ms

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:
17.0ms
(/ 3.0 (pow (fabs x) 3))
24.0ms
(/ (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))
25.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms
(sqrt PI)

series567.0ms

Counts
4 → 10
Calls
4 calls:
63.0ms
(/ 3.0 (pow (fabs x) 3))
450.0ms
(/ (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))
54.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify2.8s

Counts
382 → 382
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
054410863
110739979
237939589
done50009589

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes332.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03247
14445
done4445

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.1s13874×body80valid