Details

Time bar (total: 27.4s)

sample121.0ms

Algorithm
intervals
Results
86.0ms473×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02867
16967
222848
386437
4308737
done500033

prune27.0ms

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

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 135
Calls
4 calls:
21.0ms
(* (* (fabs x) (fabs x)) (fabs x))
2.0s
(* (/ 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)))))
92.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series565.0ms

Counts
4 → 10
Calls
4 calls:
30.0ms
(* (* (fabs x) (fabs x)) (fabs x))
475.0ms
(* (/ 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)))))
61.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.3s

Counts
145 → 145
Iterations

Useful iterations: done (3.3s)

IterNodesCost
02836867
19365041
244943885
done50013849

prune984.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* 0.2 (pow (fabs x) 5))
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))))))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))

rewrite448.0ms

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:
26.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
25.0ms
(* 0.2 (pow (fabs x) 5))
354.0ms
(* (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))))))
37.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

series650.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
106.0ms
(* 0.2 (pow (fabs x) 5))
392.0ms
(* (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))))))
63.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

simplify1.3s

Counts
134 → 134
Iterations

Useful iterations: 2 (464.0ms)

IterNodesCost
02282601
15942449
219642292
done50002292

prune800.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 135
Calls
4 calls:
29.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.1s
(* (/ 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) (* (* (* (* (pow (fabs x) 3) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
139.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series579.0ms

Counts
4 → 10
Calls
4 calls:
40.0ms
(* (* (fabs x) (fabs x)) (fabs x))
489.0ms
(* (/ 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) (* (* (* (* (pow (fabs x) 3) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
50.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.8s

Counts
145 → 145
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02856579
19414792
244993811
done50003737

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 (pow (fabs x) 5)) 5.0)
0.1b
(* (/ (sqrt 1.0) (sqrt PI)) (+ (+ (* (pow (fabs x) 3) (/ 2.0 3.0)) (* 2.0 (fabs x))) (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (/ (pow (fabs x) (+ 6 1)) (/ 21.0 1.0)))))
0.2b
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0b
(sqrt PI)

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
56×times-frac
52×associate-*l*
48×*-un-lft-identity
43×add-cube-cbrt sqrt-prod
32×add-exp-log
19×add-cbrt-cube
18×associate-*r*
16×frac-add
13×unswap-sqr
12×flip3-+ flip-+
11×prod-exp
9×associate-*r/
8×frac-times div-exp
7×pow1
5×unpow-prod-down cube-prod cbrt-unprod
4×cbrt-undiv add-log-exp
3×pow-to-exp pow-exp associate-/r* div-inv distribute-lft-out sqr-pow
2×*-commutative
1×distribute-rgt-in cube-mult rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down associate-*l/ clear-num associate-/l*
Counts
4 → 168
Calls
4 calls:
18.0ms
(/ (* 1.0 (pow (fabs x) 5)) 5.0)
1.3s
(* (/ (sqrt 1.0) (sqrt PI)) (+ (+ (* (pow (fabs x) 3) (/ 2.0 3.0)) (* 2.0 (fabs x))) (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (/ (pow (fabs x) (+ 6 1)) (/ 21.0 1.0)))))
47.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)

series629.0ms

Counts
4 → 10
Calls
4 calls:
103.0ms
(/ (* 1.0 (pow (fabs x) 5)) 5.0)
468.0ms
(* (/ (sqrt 1.0) (sqrt PI)) (+ (+ (* (pow (fabs x) 3) (/ 2.0 3.0)) (* 2.0 (fabs x))) (+ (/ (* 1.0 (pow (fabs x) 5)) 5.0) (/ (pow (fabs x) (+ 6 1)) (/ 21.0 1.0)))))
58.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)

simplify774.0ms

Counts
178 → 178
Iterations

Useful iterations: done (763.0ms)

IterNodesCost
03446229
111675652
done50005340

prune1.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: done (8.0ms)

IterNodesCost
03446
14643
done4641

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.1s14065×body80valid