Details

Time bar (total: 5.0s)

analyze8.0ms (0.2%)

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

sample43.0ms (0.9%)

Algorithm
1×intervals
Results
34.0ms256×body80valid

simplify77.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
0493873
1493873

prune16.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.9b

Counts
2 → 2

localize47.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.1b
(* 0.0424060604 (pow x 4))
0.1b
(* x (* x 0.7715471019))
13.5b
(* 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))))))))))
30.3b
(/ (+ 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)))))))))

rewrite95.0ms (1.9%)

Algorithm
1×rewrite-expression-head
Rules
97×*-un-lft-identity
41×times-frac
40×add-sqr-sqrt
38×distribute-lft-out
34×associate-*r*
30×add-cube-cbrt
21×add-exp-log
18×add-cbrt-cube
11×pow1
9×associate-*l*
8×prod-exp
6×cbrt-unprod
5×associate-/r* unswap-sqr
4×unpow-prod-down pow-prod-down associate-/r/ associate-/l* add-log-exp
3×flip3-+ *-commutative flip-+
2×cbrt-undiv div-exp div-inv associate-/l/ sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-exp clear-num
Counts
4 → 133
Calls

4 calls:

43.0ms
(* 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))))))))))
36.0ms
(/ (+ 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
(* 0.0424060604 (pow x 4))
5.0ms
(* x (* x 0.7715471019))

series55.0ms (1.1%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(* 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))))))))))
21.0ms
(/ (+ 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)))))))))
7.0ms
(* 0.0424060604 (pow x 4))
3.0ms
(* x (* x 0.7715471019))

simplify90.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
055877626

prune1.5s (30.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1423145
Fresh101
Picked101
Done000
Total1443147

Merged error: 0b

Counts
147 → 3

localize44.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.1b
(* 0.1049934947 (* x x))
0.1b
(* 0.0424060604 (pow x 4))
0.1b
(* x (* x 0.7715471019))
30.4b
(* (* 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 (+ 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))))))))))

rewrite60.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
41×add-exp-log
33×*-un-lft-identity
30×associate-*r*
28×add-cbrt-cube
24×add-sqr-sqrt
21×prod-exp
19×pow1
18×add-cube-cbrt
15×times-frac
13×cbrt-unprod
10×associate-*l*
9×pow-prod-down distribute-lft-out
5×associate-*r/
4×unpow-prod-down div-exp *-commutative add-log-exp unswap-sqr
3×flip3-+ flip-+
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ associate-/r/ sqr-pow
1×pow-to-exp pow-exp un-div-inv div-inv
Counts
4 → 112
Calls

4 calls:

40.0ms
(* (* 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 (+ 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
(* 0.1049934947 (* x x))
5.0ms
(* 0.0424060604 (pow x 4))
5.0ms
(* x (* x 0.7715471019))

series34.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(* (* 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 (+ 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))))))))))
4.0ms
(* 0.0424060604 (pow x 4))
3.0ms
(* x (* x 0.7715471019))
3.0ms
(* 0.1049934947 (* x x))

simplify67.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050384018

prune1.0s (20.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1240124
Fresh022
Picked011
Done000
Total1243127

Merged error: 0b

Counts
127 → 3

localize10.0ms (0.2%)

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))
0.6b
(/ 0.2514179000665375 (pow x 3))

rewrite51.0ms (1%)

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:

37.0ms
(+ (/ 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))

series13.0ms (0.3%)

Counts
3 → 9
Calls

3 calls:

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

simplify36.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
051591498

prune295.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1380138
Fresh011
Picked011
Done011
Total1383141

Merged error: 0b

Counts
141 → 3

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
0.1b
(* (pow x 4) 0.265709700396151)
0.1b
(* x (* x 0.6665536072))
12.0b
(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))

rewrite24.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
17×add-sqr-sqrt
16×add-exp-log
13×associate-*l* add-cbrt-cube
12×*-un-lft-identity
11×pow1
10×add-cube-cbrt
8×associate-*r*
7×prod-exp
6×add-log-exp
5×cbrt-unprod
4×unpow-prod-down pow-prod-down unswap-sqr
3×*-commutative
2×associate-*r/ sqr-pow
1×distribute-rgt-in pow-to-exp sub-neg flip3-- distribute-lft-in flip3-+ diff-log pow-exp flip-- flip-+ distribute-lft-out
Counts
4 → 77
Calls

4 calls:

8.0ms
(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
5.0ms
(* (pow x 4) 0.265709700396151)
5.0ms
(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))
5.0ms
(* x (* x 0.6665536072))

series25.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

10.0ms
(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))
8.0ms
(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
4.0ms
(* (pow x 4) 0.265709700396151)
3.0ms
(* x (* x 0.6665536072))

simplify66.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
04944942
14944942

prune160.0ms (3.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New89089
Fresh000
Picked011
Done022
Total89392

Merged error: 0b

Counts
92 → 3

regimes49.0ms (1%)

Accuracy

Total 0.0b remaining (65.6%)

Threshold costs 0.0b (65.6%)

bsearch73.0ms (1.4%)

Steps
ItersRangePoint
9
0.006277777667856217
1682886.7166918893
756.1667267563336
10
-1.9941737845059043e+31
-6.5355947410292e+19
-7.312697197229387e+22

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010299
110299

end0.0ms (0%)

sample1.1s (21%)

Algorithm
1×intervals
Results
954.0ms8000×body80valid

Profiling

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