Details

Time bar (total: 15.2s)

sample49.0ms

Algorithm
intervals
Results
31.0ms472×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
02867
16967
222148
378137
4253037
done500137

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (pow (fabs x) 6) (/ 1.0 21.0))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
0.2b
(* (pow (fabs x) 6) (/ 1.0 21.0))
0.5b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
296×times-frac
179×add-sqr-sqrt
157×add-cube-cbrt *-un-lft-identity
41×unpow-prod-down
40×associate-/r*
36×cube-prod
32×add-exp-log
29×associate-*l*
19×add-cbrt-cube
16×associate-*r*
15×sqr-pow
13×sqrt-prod
12×cube-mult unpow3
11×div-exp
9×associate-*r/ unswap-sqr
8×prod-exp
7×pow1 div-inv
5×cbrt-undiv
4×frac-times flip3-+ frac-add cbrt-unprod flip-+ add-log-exp
3×pow-to-exp pow-exp associate-/l*
2×*-commutative
1×distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r/
Counts
4 → 288
Calls
4 calls:
201.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (pow (fabs x) 6) (/ 1.0 21.0))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
10.0ms
(* (pow (fabs x) 6) (/ 1.0 21.0))
11.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms
(sqrt PI)

series445.0ms

Counts
4 → 10
Calls
4 calls:
333.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (pow (fabs x) 6) (/ 1.0 21.0))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
66.0ms
(* (pow (fabs x) 6) (/ 1.0 21.0))
46.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify662.0ms

Counts
298 → 298
Iterations

Useful iterations: done (650.0ms)

IterNodesCost
05316858
114366159
done50006080

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 4) (/ 1.0 5.0))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (* (pow (fabs x) 6) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0))) (/ (cbrt 1.0) (sqrt 21.0)))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
0.5b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
296×times-frac
179×add-sqr-sqrt
157×add-cube-cbrt *-un-lft-identity
41×unpow-prod-down
40×associate-/r*
36×cube-prod
32×add-exp-log
29×associate-*l*
19×add-cbrt-cube
16×associate-*r*
15×sqr-pow
13×sqrt-prod
12×cube-mult unpow3
11×div-exp
9×associate-*r/ unswap-sqr
8×prod-exp
7×pow1 div-inv
5×cbrt-undiv
4×frac-times flip3-+ frac-add cbrt-unprod flip-+ add-log-exp
3×pow-to-exp pow-exp associate-/l*
2×*-commutative
1×distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r/
Counts
4 → 288
Calls
4 calls:
10.0ms
(* (pow (fabs x) 4) (/ 1.0 5.0))
199.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (* (pow (fabs x) 6) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0))) (/ (cbrt 1.0) (sqrt 21.0)))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
11.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms
(sqrt PI)

series823.0ms

Counts
4 → 10
Calls
4 calls:
46.0ms
(* (pow (fabs x) 4) (/ 1.0 5.0))
724.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ 2.0 (+ (* (pow (fabs x) 4) (/ 1.0 5.0)) (* (* (pow (fabs x) 6) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0))) (/ (cbrt 1.0) (sqrt 21.0)))))) (/ 2.0 (/ 3.0 (pow (fabs x) 3)))))
52.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify635.0ms

Counts
298 → 298
Iterations

Useful iterations: done (623.0ms)

IterNodesCost
05387740
114667008
done50016929

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 (/ 3.0 (pow (fabs x) 3))) (/ 1.0 (sqrt PI)))
0.5b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
549×times-frac
329×add-sqr-sqrt
255×add-cube-cbrt *-un-lft-identity
125×associate-*l*
66×unpow-prod-down cube-prod
51×add-exp-log
40×associate-/r*
30×add-cbrt-cube
26×div-exp
24×sqr-pow
22×associate-*r*
21×cube-mult unpow3 sqrt-prod
18×unswap-sqr
12×cbrt-undiv
10×prod-exp div-inv
8×pow1
6×cbrt-unprod
4×add-log-exp
3×pow-to-exp pow-exp associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 399
Calls
4 calls:
86.0ms
(* (/ 2.0 (/ 3.0 (pow (fabs x) 3))) (/ 1.0 (sqrt PI)))
11.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series177.0ms

Counts
4 → 8
Calls
4 calls:
124.0ms
(* (/ 2.0 (/ 3.0 (pow (fabs x) 3))) (/ 1.0 (sqrt PI)))
52.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify960.0ms

Counts
407 → 407
Iterations

Useful iterations: done (946.0ms)

IterNodesCost
05127005
114736238
done50005909

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 7) (pow (sqrt 21.0) 2))
0.1b
(* 0.2 (pow (fabs x) 5))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 1.0 (/ (pow (fabs x) 7) (pow (sqrt 21.0) 2))) (+ (* 0.2 (pow (fabs x) 5)) (* 2.0 (fabs x))))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
92×unpow-prod-down
89×add-sqr-sqrt
88×times-frac
69×*-un-lft-identity
68×add-cube-cbrt
40×sqrt-prod
28×add-exp-log
24×sqr-pow
22×associate-*r* associate-*l*
12×add-cbrt-cube
11×associate-/r* unswap-sqr
9×div-exp
8×pow-to-exp pow-exp unpow2
7×prod-exp associate-/l*
6×pow1
4×cube-prod add-log-exp
3×sqrt-div *-commutative cbrt-unprod
2×frac-times flip3-+ associate-*r/ flip-+ div-inv
1×cbrt-undiv distribute-rgt-in cube-mult frac-2neg distribute-lft-in unpow3 pow-prod-down associate-*l/ clear-num
Counts
4 → 212
Calls
4 calls:
8.0ms
(/ (pow (fabs x) 7) (pow (sqrt 21.0) 2))
5.0ms
(* 0.2 (pow (fabs x) 5))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
184.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 1.0 (/ (pow (fabs x) 7) (pow (sqrt 21.0) 2))) (+ (* 0.2 (pow (fabs x) 5)) (* 2.0 (fabs x))))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (pow (fabs x) 7) (pow (sqrt 21.0) 2))
58.0ms
(* 0.2 (pow (fabs x) 5))
51.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
432.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 1.0 (/ (pow (fabs x) 7) (pow (sqrt 21.0) 2))) (+ (* 0.2 (pow (fabs x) 5)) (* 2.0 (fabs x))))))

simplify1.1s

Counts
224 → 224
Iterations

Useful iterations: 2 (456.0ms)

IterNodesCost
03654829
17984484
229263683
done50003683

prune804.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03453
14353
done4353

end0.0ms

sample1.1s

Algorithm
intervals
Results
951.0ms14200×body80valid