Details

Time bar (total: 5.2s)

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

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0497773
1497773

prune16.0ms

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: 28.6b

Counts
2 → 2

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (* x 0.7715471019))
0.2b
(* 0.0072644182 (pow x 6))
13.2b
(* 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))))))))))
28.6b
(/ (+ 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)))))))))

rewrite89.0ms

Algorithm
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:
5.0ms
(* x (* x 0.7715471019))
5.0ms
(* 0.0072644182 (pow x 6))
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))))))) (+ 1.0 (+ (+ (* 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))))))))))
34.0ms
(/ (+ 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
(* x (* x 0.7715471019))
8.0ms
(* 0.0072644182 (pow x 6))
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)))))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
050097623

prune863.0ms

Filtered
87 candidates to 145 candidates (-66.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1423145
Fresh101
Picked101
Done000
Total1443147

Merged error: 0b

Counts
147 → 3

localize45.0ms

Local error

Found 4 expressions with local error:

3.5b
(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))))))))
3.5b
(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))))))))
26.3b
(/ (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)))))))))
26.6b
(* (* x (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))))))))) (/ (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))))))))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
145×*-un-lft-identity
70×times-frac
58×distribute-lft-out
52×sqrt-prod
46×add-sqr-sqrt
44×add-cube-cbrt
41×associate-*r*
18×add-exp-log add-cbrt-cube
11×pow1
10×sqrt-div
7×flip3-+ flip-+ associate-/l*
6×prod-exp cbrt-unprod
5×associate-*r/ associate-/r*
4×associate-/r/ add-log-exp
3×cbrt-undiv div-exp pow-prod-down
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ div-inv associate-/l/
1×frac-2neg associate-*l* clear-num *-commutative
Counts
4 → 160
Calls
4 calls:
15.0ms
(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))))))))
20.0ms
(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))))))))
33.0ms
(/ (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)))))))))
58.0ms
(* (* x (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))))))))) (/ (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))))))))))

series75.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(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))))))))
12.0ms
(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))))))))
27.0ms
(/ (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)))))))))
24.0ms
(* (* x (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))))))))) (/ (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))))))))))

simplify115.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0539713504

prune1.8s

Filtered
101 candidates to 172 candidates (-70.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1720172
Fresh022
Picked011
Done000
Total1723175

Merged error: 0b

Counts
175 → 3

localize12.0ms

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))
11.8b
(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))

rewrite23.0ms

Algorithm
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)
4.0ms
(* x (* x 0.6665536072))
5.0ms
(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))

series22.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
3.0ms
(* (pow x 4) 0.265709700396151)
3.0ms
(* x (* x 0.6665536072))
9.0ms
(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))

simplify63.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04933942
14933942

prune123.0ms

Filtered
57 candidates to 89 candidates (-56.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New89089
Fresh011
Picked011
Done011
Total89392

Merged error: 0b

Counts
92 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
0.0b
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
0.2b
(/ 0.15298196345929327 (pow x 5))
0.7b
(/ 0.2514179000665375 (pow x 3))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity times-frac
45×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
14×add-exp-log
12×cube-prod
11×add-log-exp
8×add-cbrt-cube sqr-pow
7×distribute-lft-out
6×div-exp associate-/l*
5×frac-add
4×pow1 cube-mult unpow3 sum-log
3×flip3-+ flip-+
2×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num div-inv
1×associate-+r+
Counts
4 → 143
Calls
4 calls:
36.0ms
(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
18.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
4.0ms
(/ 0.15298196345929327 (pow x 5))
5.0ms
(/ 0.2514179000665375 (pow x 3))

series22.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
9.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
4.0ms
(/ 0.15298196345929327 (pow x 5))
3.0ms
(/ 0.2514179000665375 (pow x 3))

simplify55.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051131711

prune233.0ms

Filtered
97 candidates to 155 candidates (-59.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1550155
Fresh000
Picked011
Done022
Total1553158

Merged error: 0b

Counts
158 → 3

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 28.4b

bsearch55.0ms

Steps
ItersRangePoint
8
141.79014047600597
1480414.495896021
700.6170713655624
6
-2778096879157123.0
-481768560180643.2
-877563645586482.5

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0237131
1237131

end0.0ms

sample1.1s

Algorithm
intervals
Results
971.0ms8000×body80valid

Profiling

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