Details

Time bar (total: 28.9s)

sample90.0ms

Algorithm
intervals
Results
65.0ms426×body80valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.0s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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:
1.8s
(* (/ 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)))))
1.1s
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
96.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series647.0ms

Counts
4 → 10
Calls
4 calls:
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)))))
79.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
73.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify848.0ms

Counts
173 → 173
Iterations

Useful iterations: done (837.0ms)

IterNodesCost
03508160
111365868
done50014750

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(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
(* (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))))) (sqrt (/ 1 PI)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×associate-*r*
17×*-un-lft-identity
16×add-cube-cbrt sqrt-prod
11×add-exp-log times-frac
8×add-cbrt-cube
7×unswap-sqr
6×pow1 associate-*l*
4×expm1-log1p-u unpow-prod-down prod-exp log1p-expm1-u add-log-exp
2×*-commutative cbrt-unprod fma-udef sqr-pow
1×pow-to-exp sqrt-div associate-*r/ pow-prod-down pow-exp div-inv
Counts
4 → 84
Calls
4 calls:
1.0ms
(fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))
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)))))
25.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
48.0ms
(* (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))))) (sqrt (/ 1 PI)))

series948.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))
264.0ms
(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)))))
89.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
449.0ms
(* (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))))) (sqrt (/ 1 PI)))

simplify3.8s

Counts
96 → 96
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01552173
12862066
28421887
346291883
done50001883

prune619.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
66×associate-*l*
65×times-frac
50×add-cube-cbrt *-un-lft-identity
35×add-exp-log
23×associate-*r* sqrt-prod
20×cbrt-prod
19×unswap-sqr
18×add-cbrt-cube
14×prod-exp
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 → 183
Calls
4 calls:
53.0ms
(* (/ (cbrt 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)))))))
30.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
38.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0ms
(sqrt PI)

series671.0ms

Counts
4 → 10
Calls
4 calls:
504.0ms
(* (/ (cbrt 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)))))))
86.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
80.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)

simplify2.9s

Counts
193 → 193
Iterations

Useful iterations: 2 (818.0ms)

IterNodesCost
03245364
19344676
237524291
done50014291

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (pow (fabs x) 7)) (cbrt (pow (fabs x) 7)))
15.7b
(cbrt (pow (fabs x) 7))
15.7b
(cbrt (pow (fabs x) 7))
15.7b
(cbrt (pow (fabs x) 7))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
73×cbrt-prod
46×add-sqr-sqrt
29×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
16×unswap-sqr
15×sqr-pow
11×pow1
10×swap-sqr associate-*r* associate-*l*
9×pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 117
Calls
4 calls:
35.0ms
(* (cbrt (pow (fabs x) 7)) (cbrt (pow (fabs x) 7)))
2.0ms
(cbrt (pow (fabs x) 7))
2.0ms
(cbrt (pow (fabs x) 7))
4.0ms
(cbrt (pow (fabs x) 7))

series1.0s

Counts
4 → 12
Calls
4 calls:
271.0ms
(* (cbrt (pow (fabs x) 7)) (cbrt (pow (fabs x) 7)))
250.0ms
(cbrt (pow (fabs x) 7))
305.0ms
(cbrt (pow (fabs x) 7))
219.0ms
(cbrt (pow (fabs x) 7))

simplify2.9s

Counts
129 → 129
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0911700
11431523
23881349
312081317
done50001291

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02430
12930
done2930

end0.0ms

sample3.3s

Algorithm
intervals
Results
3.0s13797×body80valid