Details

Time bar (total: 40.2s)

sample95.0ms

Algorithm
intervals
Results
62.0ms422×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: done (3.3s)

IterNodesCost
02867
16967
222848
386437
4308737
done500033

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (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)

rewrite15.9s

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×add-cube-cbrt *-un-lft-identity
15×associate-*l/
13×sqrt-prod
12×frac-add
11×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 → 165
Calls
4 calls:
14.0s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
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)))))
76.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series592.0ms

Counts
4 → 10
Calls
4 calls:
109.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
428.0ms
(* (/ 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)))))
56.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.4s

Counts
175 → 175
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03768848
112026296
done50004869

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize53.0ms

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
(* (/ 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)))) (/ (* (pow (fabs x) (* 2 3)) (* (fabs x) 1.0)) 21.0)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite1.8s

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
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
7×associate-*l/
6×frac-times flip3-+ associate-*r/ associate-*r* flip-+
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 distribute-lft-out
Counts
4 → 156
Calls
4 calls:
880.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
787.0ms
(* (/ 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)))) (/ (* (pow (fabs x) (* 2 3)) (* (fabs x) 1.0)) 21.0)))
126.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series622.0ms

Counts
4 → 10
Calls
4 calls:
78.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
476.0ms
(* (/ 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)))) (/ (* (pow (fabs x) (* 2 3)) (* (fabs x) 1.0)) 21.0)))
67.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.0s

Counts
166 → 166
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03427170
111065363
248814313
done50014193

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize44.0ms

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)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0)) (* (* (/ (cbrt 1.0) (sqrt 21.0)) (fabs x)) (pow (fabs x) (* 2 3))))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.2b
(* (/ (cbrt 1.0) (sqrt 21.0)) (fabs x))
1.0b
(sqrt PI)

rewrite923.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt associate-*l*
69×times-frac
55×associate-*l/
52×add-cube-cbrt *-un-lft-identity
36×frac-add
35×add-exp-log
34×add-cbrt-cube
33×sqrt-prod
22×frac-times associate-*r/
20×cbrt-prod
18×pow1
16×prod-exp cbrt-unprod
14×flip3-+ flip-+
8×pow-prod-down unswap-sqr
7×associate-*r*
5×cbrt-undiv div-exp
4×add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 185
Calls
4 calls:
758.0ms
(* (/ 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)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0)) (* (* (/ (cbrt 1.0) (sqrt 21.0)) (fabs x)) (pow (fabs x) (* 2 3))))))
113.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
37.0ms
(* (/ (cbrt 1.0) (sqrt 21.0)) (fabs x))
1.0ms
(sqrt PI)

series955.0ms

Counts
4 → 10
Calls
4 calls:
774.0ms
(* (/ 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)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0)) (* (* (/ (cbrt 1.0) (sqrt 21.0)) (fabs x)) (pow (fabs x) (* 2 3))))))
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
131.0ms
(* (/ (cbrt 1.0) (sqrt 21.0)) (fabs x))
0.0ms
(sqrt PI)

simplify924.0ms

Counts
195 → 195
Iterations

Useful iterations: done (915.0ms)

IterNodesCost
039910280
113298119
done50007520

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (fabs x) (cbrt 1.0)) (sqrt 21.0))
0.4b
(* (fabs x) (/ 1.0 5.0))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×times-frac
14×add-exp-log
13×associate-*r* add-cbrt-cube
12×sqrt-prod
8×pow1
6×associate-/r*
4×add-log-exp
3×cbrt-undiv div-exp associate-*l* prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 85
Calls
4 calls:
14.0ms
(/ (* (fabs x) (cbrt 1.0)) (sqrt 21.0))
14.0ms
(* (fabs x) (/ 1.0 5.0))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series178.0ms

Counts
4 → 8
Calls
4 calls:
147.0ms
(/ (* (fabs x) (cbrt 1.0)) (sqrt 21.0))
32.0ms
(* (fabs x) (/ 1.0 5.0))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.4s

Counts
93 → 93
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0159878
1354798
21293734
done5001726

prune831.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
03156
14554
done4554

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.1s14061×body80valid