Details

Time bar (total: 17.5s)

sample52.0ms

Algorithm
intervals
Results
34.0ms452×body80valid

simplify107.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142
done500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.2b
(* (/ 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)

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
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:
608.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
57.0ms
(* (/ 2.0 3.0) (* (* (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) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0ms
(sqrt PI)

series429.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
43.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
325.0ms
(* (/ 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)

simplify58.0ms

Counts
165 → 165
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011964518
150013737
done50013737

prune662.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×add-cbrt-cube
4×pow1 times-frac associate-/r* add-log-exp
3×pow1/3
2×cbrt-undiv div-exp sqrt-prod
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
20.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt PI) (cbrt PI))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt PI) (cbrt PI))))

simplify71.0ms

Counts
60 → 60
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0191516
1726476
22896456
35002452
done5002452

prune344.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (sqrt (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)))))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (* (/ 1.0 (sqrt (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)
1.0b
(sqrt PI)

rewrite4.1s

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
62×associate-*l*
58×add-sqr-sqrt
57×times-frac
48×add-exp-log
45×add-cube-cbrt *-un-lft-identity
40×associate-*l/
36×frac-add
31×frac-times associate-*r/
30×add-cbrt-cube
22×prod-exp
18×flip3-+ flip-+
13×pow1
12×cbrt-unprod
11×div-exp
6×cbrt-undiv
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down add-log-exp unswap-sqr
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
Counts
4 → 183
Calls
4 calls:
1.2s
(* (/ 1.0 (sqrt (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)))))
2.9s
(* (/ 1 (sqrt (sqrt PI))) (* (/ 1.0 (sqrt (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))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series831.0ms

Counts
4 → 8
Calls
4 calls:
504.0ms
(* (/ 1.0 (sqrt (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)))))
326.0ms
(* (/ 1 (sqrt (sqrt PI))) (* (/ 1.0 (sqrt (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)
0.0ms
(sqrt PI)

simplify103.0ms

Counts
191 → 191
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0116910366
150018570
done50018570

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (* 1 1.0) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))) (sqrt (sqrt PI)))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (/ (* (* 1 1.0) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite4.6s

Algorithm
rewrite-expression-head
Rules
93×add-exp-log
66×sqrt-prod
54×add-sqr-sqrt
51×times-frac
45×prod-exp add-cbrt-cube
38×*-un-lft-identity
35×add-cube-cbrt
31×associate-*l*
30×div-exp
17×cbrt-unprod
13×cbrt-undiv associate-*r/ associate-*r*
10×1-exp
9×associate-/r*
8×pow1
7×unswap-sqr
6×frac-add associate-/l/
5×rec-exp
4×add-log-exp
3×flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 159
Calls
4 calls:
1.7s
(/ (* (* 1 1.0) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))) (sqrt (sqrt PI)))
2.9s
(* (/ 1 (sqrt (sqrt PI))) (/ (* (* 1 1.0) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series840.0ms

Counts
4 → 8
Calls
4 calls:
511.0ms
(/ (* (* 1 1.0) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))) (sqrt (sqrt PI)))
329.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (* (* 1 1.0) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify149.0ms

Counts
167 → 167
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08446136
147055114
250024912
done50024912

prune793.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes212.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04142
14142
done4142

end0.0ms

sample1.2s

Algorithm
intervals
Results
970.0ms13844×body80valid