Details

Time bar (total: 27.9s)

sample67.0ms

Algorithm
intervals
Results
49.0ms463×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2.0 3.0) (* (* (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)))))
1.0b
(sqrt PI)

rewrite3.4s

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:
1.1s
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
63.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.2s
(* (/ 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)))))
3.0ms
(sqrt PI)

series611.0ms

Counts
4 → 10
Calls
4 calls:
77.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
60.0ms
(* (/ 2.0 3.0) (* (* (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)))))
0.0ms
(sqrt PI)

simplify804.0ms

Counts
173 → 173
Iterations

Useful iterations: done (786.0ms)

IterNodesCost
03508160
111365868
done50004750

prune1.3s

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)))))
0.0b
(* 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))))))

rewrite90.0ms

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))))
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)))))
20.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
66.0ms
(* (* 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:
224.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
296.0ms
(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)))))
107.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
494.0ms
(* (* 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 (255.0ms)

IterNodesCost
01301864
12781791
210081543
done50001543

prune486.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 3.0 (pow (fabs x) 3))
0.3b
(/ 2.0 (/ 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))
1.0b
(sqrt PI)

rewrite91.0ms

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:
25.0ms
(/ 3.0 (pow (fabs x) 3))
17.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
12.0ms
(/ (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))
2.0ms
(sqrt PI)

series606.0ms

Counts
4 → 10
Calls
4 calls:
39.0ms
(/ 3.0 (pow (fabs x) 3))
79.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
487.0ms
(/ (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))
0.0ms
(sqrt PI)

simplify2.9s

Counts
382 → 382
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
054410863
110709979
238099589
done50009589

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
0.3b
(* (sqrt PI) (* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))))))
1.0b
(sqrt PI)
29.1b
(/ (* (fma (fma 5.0 (fma 2.0 (* 2.0 (* (fabs x) (fabs x))) (- (* (* (pow (fabs x) (* 2 3)) (/ 2.0 3.0)) (/ 2.0 3.0)))) (* (* (* (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) 1.0) (fabs x)) (pow (fabs x) (+ 3 1)))) 21.0 (* (* (* (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))) 1.0) (fabs x)) (pow (fabs x) (* 2 3)))) 1.0) (* (sqrt PI) (* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))))

rewrite473.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log add-cbrt-cube
48×distribute-rgt-in distribute-lft-in
25×prod-exp cbrt-unprod
19×pow1
16×associate-*r/
12×sub-neg prod-diff
9×add-sqr-sqrt associate-*l* pow-prod-down
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp
6×sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-- flip--
2×associate-*r* associate-/r/ *-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l*
Counts
4 → 134
Calls
4 calls:
63.0ms
(* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
228.0ms
(* (sqrt PI) (* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))))))
3.0ms
(sqrt PI)
173.0ms
(/ (* (fma (fma 5.0 (fma 2.0 (* 2.0 (* (fabs x) (fabs x))) (- (* (* (pow (fabs x) (* 2 3)) (/ 2.0 3.0)) (/ 2.0 3.0)))) (* (* (* (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) 1.0) (fabs x)) (pow (fabs x) (+ 3 1)))) 21.0 (* (* (* (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))) 1.0) (fabs x)) (pow (fabs x) (* 2 3)))) 1.0) (* (sqrt PI) (* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))))

series1.4s

Counts
4 → 10
Calls
4 calls:
111.0ms
(* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
190.0ms
(* (sqrt PI) (* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))))))
0.0ms
(sqrt PI)
1.1s
(/ (* (fma (fma 5.0 (fma 2.0 (* 2.0 (* (fabs x) (fabs x))) (- (* (* (pow (fabs x) (* 2 3)) (/ 2.0 3.0)) (/ 2.0 3.0)))) (* (* (* (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) 1.0) (fabs x)) (pow (fabs x) (+ 3 1)))) 21.0 (* (* (* (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))) 1.0) (fabs x)) (pow (fabs x) (* 2 3)))) 1.0) (* (sqrt PI) (* 21.0 (* 5.0 (- (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))))

simplify2.2s

Counts
144 → 144
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02608001
16927529
233635547
done50015473

prune1.1s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes341.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02430
12930
done2930

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.4s14085×body80valid