Details

Time bar (total: 6.0s)

analyze8.0ms

Algorithm
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

Algorithm
intervals
Results
35.0ms256×body80valid

simplify74.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0493873
1493873

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.9b

Counts
2 → 2

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.1049934947 (* x x))
0.3b
(* 0.0424060604 (pow x 4))
14.0b
(* 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))))))))))
27.4b
(/ (+ 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)))))))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
97×*-un-lft-identity
41×add-sqr-sqrt times-frac
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 unswap-sqr
5×associate-/r*
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 → 134
Calls
4 calls:
5.0ms
(* 0.1049934947 (* x x))
5.0ms
(* 0.0424060604 (pow x 4))
37.0ms
(* 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))))))))))
30.0ms
(/ (+ 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)))))))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 0.1049934947 (* x x))
4.0ms
(* 0.0424060604 (pow x 4))
23.0ms
(* 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)))))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
052957635

prune864.0ms

Filtered
88 candidates to 146 candidates (-65.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1433146
Fresh101
Picked101
Done000
Total1453148

Merged error: 0b

Counts
148 → 3

localize61.0ms

Local error

Found 4 expressions with local error:

13.9b
(sqrt (/ (+ 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))))))))))
13.9b
(sqrt (/ (+ 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)))))))))))
27.4b
(/ (+ 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))))))))))
27.4b
(/ (+ 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)))))))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
147×*-un-lft-identity
74×times-frac
56×distribute-lft-out
50×add-sqr-sqrt
48×sqrt-prod
44×add-cube-cbrt
9×associate-/r*
8×add-exp-log associate-/r/ add-cbrt-cube associate-/l*
6×pow1 flip3-+ flip-+
4×rem-sqrt-square div-inv associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 157
Calls
4 calls:
28.0ms
(sqrt (/ (+ 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))))))))))
28.0ms
(sqrt (/ (+ 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)))))))))))
37.0ms
(/ (+ 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))))))))))
30.0ms
(/ (+ 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)))))))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(sqrt (/ (+ 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))))))))))
23.0ms
(sqrt (/ (+ 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))))))))))
23.0ms
(/ (+ 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)))))))))

simplify114.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0501715396

prune2.5s

Filtered
110 candidates to 169 candidates (-53.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1690169
Fresh022
Picked011
Done000
Total1693172

Merged error: 0b

Counts
172 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
59×times-frac
50×*-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×sqr-pow
7×add-cbrt-cube
6×div-exp associate-/l*
5×add-log-exp
4×cube-mult unpow3
3×pow1
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv distribute-lft-out
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
3 → 124
Calls
3 calls:
17.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
4.0ms
(/ 0.15298196345929327 (pow x 5))
5.0ms
(/ 0.2514179000665375 (pow x 3))

series18.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
4.0ms
(/ 0.15298196345929327 (pow x 5))
4.0ms
(/ 0.2514179000665375 (pow x 3))

simplify52.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052101220

prune183.0ms

Filtered
82 candidates to 133 candidates (-62.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1330133
Fresh011
Picked011
Done011
Total1333136

Merged error: 0b

Counts
136 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.15298196345929327 (pow x 6))
0.3b
(/ 0.2514179000665375 (pow x 4))
0.3b
(/ 0.5 (* x x))
14.5b
(* x (+ (/ 0.15298196345929327 (pow x 6)) (+ (/ 0.5 (* x x)) (/ 0.2514179000665375 (pow x 4)))))

rewrite43.0ms

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

series21.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ 0.15298196345929327 (pow x 6))
4.0ms
(/ 0.2514179000665375 (pow x 4))
3.0ms
(/ 0.5 (* x x))
7.0ms
(* x (+ (/ 0.15298196345929327 (pow x 6)) (+ (/ 0.5 (* x x)) (/ 0.2514179000665375 (pow x 4)))))

simplify37.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
050231599

prune217.0ms

Filtered
95 candidates to 150 candidates (-57.9%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1500150
Fresh000
Picked011
Done022
Total1503153

Merged error: 0b

Counts
153 → 3

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.8b

bsearch97.0ms

Steps
ItersRangePoint
8
1.1024660446669612
9121.48111632846
679.4541649262793
9
-817538837.9468343
-1.6466316905262575
-29997.69344674242

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0109171
1109171

end0.0ms

analyze8.0ms

Algorithm
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

sample1.1s

Algorithm
intervals
Results
982.0ms8000×body80valid

Profiling

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