Details

Time bar (total: 7.1s)

analyze8.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
50%50%0%5
81.2%18.7%0%6
100%0%0%7

sample37.0ms (0.5%)

Algorithm
1×intervals
Results
29.0ms256×body80valid

simplify86.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
0493873
1493873

prune15.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.1b

Counts
2 → 2

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b
(* 0.0001789971 (pow x 10))
0.2b
(* (pow x 10) 0.0008327945)
14.3b
(* x (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))
26.6b
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))

rewrite79.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
41×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×associate-*r*
21×add-exp-log
19×times-frac
15×add-cbrt-cube
13×associate-*l*
8×unpow-prod-down prod-exp unswap-sqr
6×pow1
4×associate-/r/ cbrt-unprod add-log-exp sqr-pow
3×flip3-+ associate-/r* *-commutative flip-+ associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp div-inv associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num
Counts
4 → 115
Calls

4 calls:

33.0ms
(* x (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))
32.0ms
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))
5.0ms
(* 0.0001789971 (pow x 10))
5.0ms
(* (pow x 10) 0.0008327945)

series55.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

22.0ms
(* x (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))
19.0ms
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))
9.0ms
(* 0.0001789971 (pow x 10))
5.0ms
(* (pow x 10) 0.0008327945)

simplify48.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
050126112

prune1.2s (16.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1243127
Fresh101
Picked101
Done000
Total1263129

Merged error: 0b

Counts
129 → 3

localize52.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.9b
(sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))
14.3b
(* x (* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))) (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))))
21.1b
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))
24.7b
(* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))) (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))))

rewrite177.0ms (2.5%)

Algorithm
1×rewrite-expression-head
Rules
94×add-sqr-sqrt
76×times-frac
60×add-exp-log
53×*-un-lft-identity
47×add-cube-cbrt
44×sqrt-prod
36×add-cbrt-cube
27×associate-*l*
25×associate-*r* prod-exp
17×div-exp
15×unswap-sqr
13×cbrt-unprod
12×pow1
9×cbrt-undiv
8×sqrt-div
6×associate-/r* associate-/r/
5×flip3-+ associate-*r/ flip-+
4×rec-exp 1-exp pow-prod-down add-log-exp
3×div-inv associate-/l*
2×frac-times associate-*l/ *-commutative associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 176
Calls

4 calls:

63.0ms
(* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))) (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))))
55.0ms
(* x (* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))) (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))))
35.0ms
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))
16.0ms
(sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))

series88.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

29.0ms
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))
24.0ms
(* x (* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))) (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12)))))))
22.0ms
(* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))) (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (pow x 4))) (* 0.0072644182 (pow x 6))) (* 0.0005064034 (pow x 8))) (* 0.0001789971 (pow x 10))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))))
13.0ms
(sqrt (+ (+ (+ (+ (+ (+ 1.0 (* (* x x) 0.7715471019)) (* (pow x 4) 0.2909738639)) (* (pow x 6) 0.0694555761)) (* (pow x 8) 0.0140005442)) (* (pow x 10) 0.0008327945)) (* (* 0.0001789971 2.0) (pow x 12))))

simplify139.0ms (2%)

Algorithm
1×egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
0495018231
1495018231

prune3.1s (44%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1880188
Fresh022
Picked011
Done000
Total1883191

Merged error: 0b

Counts
191 → 3

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
0.2b
(/ 0.15298196345929327 (pow x 5))
0.3b
(/ 0.2514179000665375 (pow x 3))

rewrite46.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
60×times-frac
55×*-un-lft-identity
44×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
13×add-exp-log
12×cube-prod
8×add-log-exp sqr-pow
7×add-cbrt-cube
6×div-exp associate-/l*
5×distribute-lft-out
4×cube-mult unpow3 frac-add
3×pow1 sum-log
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ pow-exp clear-num flip-+ div-inv
1×+-commutative associate-+r+
Counts
3 → 129
Calls

3 calls:

32.0ms
(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
5.0ms
(/ 0.2514179000665375 (pow x 3))
4.0ms
(/ 0.15298196345929327 (pow x 5))

series15.0ms (0.2%)

Counts
3 → 9
Calls

3 calls:

6.0ms
(/ 0.2514179000665375 (pow x 3))
5.0ms
(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
4.0ms
(/ 0.15298196345929327 (pow x 5))

simplify32.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
051591498

prune288.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1380138
Fresh011
Picked011
Done011
Total1383141

Merged error: 0b

Counts
141 → 3

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(/ 0.15298196345929327 (pow x 6))
0.0b
(/ 0.2514179000665375 (pow x 4))
0.4b
(/ 0.5 (* x x))
15.5b
(* x (+ (/ 0.15298196345929327 (pow x 6)) (+ (/ 0.5 (* x x)) (/ 0.2514179000665375 (pow x 4)))))

rewrite43.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
45×*-un-lft-identity times-frac
42×add-sqr-sqrt
40×add-cube-cbrt
24×unpow-prod-down
21×add-exp-log
15×associate-/r* add-cbrt-cube
9×associate-/l*
8×div-exp sqr-pow
6×pow1
5×associate-*r/ associate-*r*
4×cbrt-undiv frac-add add-log-exp
3×frac-2neg associate-*l* clear-num div-inv distribute-lft-out
2×pow-to-exp flip3-+ pow-exp prod-exp cbrt-unprod flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 138
Calls

4 calls:

26.0ms
(* x (+ (/ 0.15298196345929327 (pow x 6)) (+ (/ 0.5 (* x x)) (/ 0.2514179000665375 (pow x 4)))))
4.0ms
(/ 0.2514179000665375 (pow x 4))
4.0ms
(/ 0.5 (* x x))
4.0ms
(/ 0.15298196345929327 (pow x 6))

series20.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

10.0ms
(* x (+ (/ 0.15298196345929327 (pow x 6)) (+ (/ 0.5 (* x x)) (/ 0.2514179000665375 (pow x 4)))))
4.0ms
(/ 0.15298196345929327 (pow x 6))
3.0ms
(/ 0.2514179000665375 (pow x 4))
3.0ms
(/ 0.5 (* x x))

simplify37.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
055991599

prune318.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1500150
Fresh000
Picked011
Done022
Total1503153

Merged error: 0b

Counts
153 → 3

regimes50.0ms (0.7%)

Accuracy

Total 0.0b remaining (18%)

Threshold costs 0.0b (18%)

bsearch70.0ms (1%)

Steps
ItersRangePoint
10
4869182.832930685
1.4482933346023836e+21
39879067.879498824
8
-2059.9896197063636
-0.17031860657869693
-1972.1349771299758

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0102141
1102141

end0.0ms (0%)

sample1.0s (14.3%)

Algorithm
1×intervals
Results
924.0ms8000×body80valid

Profiling

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