Details

Time bar (total: 13.5s)

sample50.0ms

Algorithm
intervals
Results
29.0ms256×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: done (1.4s)

IterNodesCost
044173
1132173
2535109
3233079
done500073

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.0072644182 (* x x))
0.1b
(* 0.1049934947 (* x x))
14.7b
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
28.1b
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

rewrite573.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
28×frac-add
27×flip3-+ flip-+
25×associate-*l*
22×add-cube-cbrt *-un-lft-identity
21×add-exp-log add-cbrt-cube
20×associate-*r/
19×times-frac
16×pow1
14×associate-/l/
12×associate-/r/
8×prod-exp cbrt-unprod
7×pow-prod-down
5×associate-*r*
4×add-log-exp unswap-sqr
3×associate-/r* *-commutative associate-/l*
2×cbrt-undiv div-exp div-inv
1×frac-2neg associate-*l/ clear-num
Counts
4 → 123
Calls
4 calls:
16.0ms
(* 0.0072644182 (* x x))
17.0ms
(* 0.1049934947 (* x x))
296.0ms
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
238.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

series527.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* 0.0072644182 (* x x))
25.0ms
(* 0.1049934947 (* x x))
268.0ms
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
203.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

simplify503.0ms

Counts
135 → 135
Iterations

Useful iterations: done (495.0ms)

IterNodesCost
03228929
110328593
done50007811

prune971.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) 0.0140005442)
0.1b
(* 0.0072644182 (* x x))
0.1b
(* 0.1049934947 (* x x))
28.2b
(* (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (/ x (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
44×frac-add
39×flip3-+ flip-+
29×associate-*r/
24×add-exp-log associate-*r* add-cbrt-cube
23×add-sqr-sqrt
21×pow1
15×add-cube-cbrt *-un-lft-identity
14×frac-times associate-*l/
11×prod-exp cbrt-unprod
10×times-frac associate-*l* pow-prod-down
6×associate-/r/
5×unswap-sqr
4×*-commutative add-log-exp
1×cbrt-undiv div-exp div-inv
Counts
4 → 123
Calls
4 calls:
18.0ms
(* (* x x) 0.0140005442)
17.0ms
(* 0.0072644182 (* x x))
16.0ms
(* 0.1049934947 (* x x))
342.0ms
(* (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (/ x (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (* x x) 0.0140005442)
30.0ms
(* 0.0072644182 (* x x))
25.0ms
(* 0.1049934947 (* x x))
272.0ms
(* (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (/ x (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))))

simplify639.0ms

Counts
135 → 135
Iterations

Useful iterations: done (631.0ms)

IterNodesCost
04099660
114949006
done50008458

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.1049934947 (* x x))
9.2b
(cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3))
14.7b
(* (cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3)) x)
28.1b
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

rewrite973.0ms

Algorithm
rewrite-expression-head
Rules
94×cbrt-prod
61×add-sqr-sqrt
50×associate-*l*
47×times-frac
45×add-cube-cbrt *-un-lft-identity
42×flip3-+ flip-+
40×unpow-prod-down cube-prod frac-add
32×associate-*r/
30×associate-/r/
14×associate-/l/
13×add-exp-log
12×add-cbrt-cube
11×pow1
8×unswap-sqr
5×div-inv
4×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×associate-/r* associate-/l* sqr-pow
2×cube-div cube-mult cbrt-div unpow3 *-commutative
1×cbrt-undiv frac-2neg pow1/3 div-exp associate-*l/ clear-num rem-cbrt-cube
Counts
4 → 189
Calls
4 calls:
17.0ms
(* 0.1049934947 (* x x))
138.0ms
(cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3))
568.0ms
(* (cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3)) x)
239.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

series718.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* 0.1049934947 (* x x))
208.0ms
(cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3))
275.0ms
(* (cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3)) x)
209.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

simplify796.0ms

Counts
201 → 201
Iterations

Useful iterations: done (775.0ms)

IterNodesCost
039619805
1126518136
done500017150

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 0.15298196345929327 (pow x 5))
0.3b
(/ 0.2514179000665375 (pow x 3))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
57×times-frac
43×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
19×associate-/r*
12×add-exp-log cube-prod
8×sqr-pow
6×div-exp add-cbrt-cube associate-/l*
4×cube-mult unpow3
2×pow1 cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv add-log-exp
Counts
2 → 110
Calls
2 calls:
7.0ms
(/ 0.15298196345929327 (pow x 5))
11.0ms
(/ 0.2514179000665375 (pow x 3))

series89.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ 0.15298196345929327 (pow x 5))
37.0ms
(/ 0.2514179000665375 (pow x 3))

simplify1.5s

Counts
116 → 116
Iterations

Useful iterations: 2 (130.0ms)

IterNodesCost
01731234
12981045
27931013
335031013
done50011013

prune231.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 28.7b

bsearch418.0ms

Steps
ItersRangePoint
10
0.0001820196720056695
1126179.5725289274
781.2761340127653
9
-5463081689.944393
-76786.820650899
-289825.49522047787

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
063114
192100
done92100

end0.0ms

sample844.0ms

Algorithm
intervals
Results
712.0ms8000×body80valid