Details

Time bar (total: 14.1s)

sample45.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (198.0ms)

IterNodesCost
044173
1132173
2502109
3204079
done500079

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.2909738639 (* x x))
0.4b
(* (* x x) 0.0008327945)
0.4b
(* (* x x) 0.0001789971)
28.4b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log add-cbrt-cube
19×pow1
12×add-sqr-sqrt
10×flip3-+ prod-exp cbrt-unprod flip-+
9×add-cube-cbrt *-un-lft-identity pow-prod-down
8×associate-*r/ frac-add
7×associate-*r*
6×associate-*l/ associate-/r/ associate-/l/
5×associate-*l*
4×add-log-exp
3×times-frac associate-/r* *-commutative unswap-sqr
2×cbrt-undiv div-exp
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
6.0ms
(* 0.2909738639 (* x x))
7.0ms
(* (* x x) 0.0008327945)
8.0ms
(* (* x x) 0.0001789971)
456.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 0.2909738639 (* x x))
24.0ms
(* (* x x) 0.0008327945)
30.0ms
(* (* x x) 0.0001789971)
263.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: 2 (514.0ms)

IterNodesCost
02534390
18364190
241623558
done50003558

prune852.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (sqrt 0.0001789971))
0.3b
(* x (sqrt 0.0001789971))
0.4b
(* (* x x) 0.0008327945)
28.4b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x (sqrt 0.0001789971)) (* x (sqrt 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

rewrite468.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
18×add-exp-log add-cbrt-cube
15×associate-*r*
13×pow1 add-cube-cbrt *-un-lft-identity
10×flip3-+ flip-+
8×associate-*r/ frac-add sqrt-prod
7×associate-*l*
6×associate-*l/ prod-exp associate-/r/ cbrt-unprod associate-/l/
5×pow-prod-down unswap-sqr
4×add-log-exp
3×times-frac associate-/r* *-commutative
2×cbrt-undiv div-exp
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 96
Calls
4 calls:
6.0ms
(* x (sqrt 0.0001789971))
4.0ms
(* x (sqrt 0.0001789971))
7.0ms
(* (* x x) 0.0008327945)
447.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x (sqrt 0.0001789971)) (* x (sqrt 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* x (sqrt 0.0001789971))
43.0ms
(* x (sqrt 0.0001789971))
24.0ms
(* (* x x) 0.0008327945)
334.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x (sqrt 0.0001789971)) (* x (sqrt 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

simplify1.2s

Counts
108 → 108
Iterations

Useful iterations: 2 (338.0ms)

IterNodesCost
02504605
18154217
239393601
done50003601

prune674.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (sqrt 0.0001789971))
0.4b
(* (* x x) 0.0008327945)
28.4b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (cbrt (pow (* x (sqrt 0.0001789971)) 3)) (* x (sqrt 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))
40.4b
(cbrt (pow (* x (sqrt 0.0001789971)) 3))

rewrite466.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-sqr-sqrt add-cbrt-cube
11×pow1 add-cube-cbrt *-un-lft-identity
10×flip3-+ flip-+
9×associate-*r*
8×cbrt-prod associate-*r/ frac-add
6×associate-*l/ associate-/r/ associate-/l/
5×prod-exp cbrt-unprod
4×associate-*l* pow-prod-down sqrt-prod add-log-exp
3×times-frac associate-/r* unswap-sqr
2×cbrt-undiv div-exp *-commutative
1×cube-mult unpow-prod-down frac-2neg pow1/3 unpow3 cube-prod clear-num rem-cbrt-cube div-inv associate-/l* sqr-pow
Counts
4 → 91
Calls
4 calls:
6.0ms
(* x (sqrt 0.0001789971))
7.0ms
(* (* x x) 0.0008327945)
448.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (cbrt (pow (* x (sqrt 0.0001789971)) 3)) (* x (sqrt 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))
1.0ms
(cbrt (pow (* x (sqrt 0.0001789971)) 3))

series493.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* x (sqrt 0.0001789971))
24.0ms
(* (* x x) 0.0008327945)
373.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (cbrt (pow (* x (sqrt 0.0001789971)) 3)) (* x (sqrt 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))
52.0ms
(cbrt (pow (* x (sqrt 0.0001789971)) 3))

simplify1.3s

Counts
103 → 103
Iterations

Useful iterations: 2 (364.0ms)

IterNodesCost
02854800
18964213
242023609
done50003609

prune721.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 x) (* 0.265709700396151 (pow x 5)))
0.0b
(* 0.265709700396151 (pow x 5))
0.1b
(* 0.6665536072 (pow x 3))
18.9b
(- (+ (* 1.0 x) (* 0.265709700396151 (pow x 5))) (* 0.6665536072 (pow x 3)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sqr-pow
2×pow-to-exp diff-log pow-exp sum-log *-commutative cbrt-unprod
1×+-commutative cube-mult sub-neg flip3-- flip3-+ unpow3 associate--l+ flip-- flip-+
Counts
4 → 81
Calls
4 calls:
2.0ms
(+ (* 1.0 x) (* 0.265709700396151 (pow x 5)))
5.0ms
(* 0.265709700396151 (pow x 5))
6.0ms
(* 0.6665536072 (pow x 3))
16.0ms
(- (+ (* 1.0 x) (* 0.265709700396151 (pow x 5))) (* 0.6665536072 (pow x 3)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(+ (* 1.0 x) (* 0.265709700396151 (pow x 5)))
50.0ms
(* 0.265709700396151 (pow x 5))
36.0ms
(* 0.6665536072 (pow x 3))
64.0ms
(- (+ (* 1.0 x) (* 0.265709700396151 (pow x 5))) (* 0.6665536072 (pow x 3)))

simplify2.1s

Counts
93 → 93
Iterations

Useful iterations: 3 (513.0ms)

IterNodesCost
01371067
1340957
21039907
34936897
done5000897

prune187.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.0b

bsearch404.0ms

Steps
ItersRangePoint
7
25.411711264148785
868.4016055832647
572.1454395333247
10
-155084744.97222546
-0.0009113054925467739
-857599.9443123471

simplify13.0ms

Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
078178
1113137
done113137

end0.0ms

sample799.0ms

Algorithm
intervals
Results
697.0ms8000×body80valid