Details

Time bar (total: 21.0s)

sample81.0ms

Algorithm
intervals
Results
61.0ms426×body80valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02867
16967
222848
386437
4308737
done500033

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

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)

rewrite2.9s

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×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 → 155
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)))))
1.0s
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
92.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series585.0ms

Counts
4 → 10
Calls
4 calls:
444.0ms
(* (/ 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)))))
78.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
62.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify834.0ms

Counts
165 → 165
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
03427956
111065828
done50004727

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
29×associate-*r*
25×associate-*l*
24×*-un-lft-identity
23×add-cube-cbrt
21×add-exp-log
16×sqrt-prod
14×unswap-sqr
12×unpow-prod-down add-cbrt-cube
11×times-frac
10×prod-exp
6×pow1 sqr-pow
4×cube-prod *-commutative cbrt-unprod add-log-exp
3×pow-to-exp sqrt-div pow-exp
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
24.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
22.0ms
(* 0.2 (pow (fabs x) 5))
13.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
257.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

series657.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
99.0ms
(* 0.2 (pow (fabs x) 5))
62.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
410.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify1.2s

Counts
134 → 134
Iterations

Useful iterations: 2 (439.0ms)

IterNodesCost
02282601
15942449
219642292
done50002292

prune823.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite342.0ms

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*
20×associate-*r/
19×add-cbrt-cube
17×unswap-sqr
16×frac-add
14×prod-exp
13×sqrt-prod
12×flip3-+ flip-+
11×associate-*l/
10×unpow-prod-down
8×frac-times
7×pow1 div-exp
6×cbrt-unprod sqr-pow
5×cube-prod
4×pow-to-exp pow-exp add-log-exp
3×cbrt-undiv *-commutative div-inv
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 → 167
Calls
4 calls:
248.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
25.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
54.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
2.0ms
(sqrt PI)

series566.0ms

Counts
4 → 10
Calls
4 calls:
411.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
68.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
86.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)

simplify764.0ms

Counts
177 → 177
Iterations

Useful iterations: done (752.0ms)

IterNodesCost
03696028
112535140
done50004817

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* (cbrt PI) (cbrt PI)))
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 52
Calls
4 calls:
15.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify1.5s

Counts
56 → 56
Iterations

Useful iterations: 3 (332.0ms)

IterNodesCost
064476
1131385
2321349
31082340
done5000340

prune560.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02733
13833
done3833

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.7s13797×body80valid