Details

Time bar (total: 30.8s)

sample107.0ms

Algorithm
intervals
Results
59.0ms256×body80valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: done (2.4s)

IterNodesCost
044173
1132173
2547109
3278179
done500173

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow x 4) 0.0140005442)
0.3b
(* (pow x 4) 0.0005064034)
13.2b
(* (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) x)
28.8b
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
44×associate-*r/ frac-add
41×add-sqr-sqrt associate-*l*
39×flip3-+ flip-+
28×associate-/r/
26×add-cube-cbrt *-un-lft-identity
21×add-exp-log
19×times-frac
15×add-cbrt-cube
9×associate-*r*
8×unpow-prod-down prod-exp unswap-sqr
6×pow1 associate-/l/
4×cbrt-unprod add-log-exp sqr-pow
3×associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp div-inv
1×frac-2neg pow-prod-down associate-*l/ clear-num
Counts
4 → 143
Calls
4 calls:
25.0ms
(* (pow x 4) 0.0140005442)
25.0ms
(* (pow x 4) 0.0005064034)
728.0ms
(* (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) x)
484.0ms
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))

series852.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (pow x 4) 0.0140005442)
47.0ms
(* (pow x 4) 0.0005064034)
396.0ms
(* (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) x)
343.0ms
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))

simplify807.0ms

Counts
155 → 155
Iterations

Useful iterations: done (792.0ms)

IterNodesCost
039710409
113069953
done50009140

prune2.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize93.0ms

Local error

Found 4 expressions with local error:

2.1b
(sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))
13.2b
(* (/ (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) x)
23.9b
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))
26.6b
(/ (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
694×times-frac
362×add-sqr-sqrt
356×sqrt-prod
344×associate-*r/ frac-add
337×add-cube-cbrt *-un-lft-identity
294×flip3-+ flip-+
238×sqrt-div
234×associate-*l*
224×associate-/r/
39×associate-/l*
20×add-exp-log add-cbrt-cube
16×div-inv
12×associate-/r*
7×pow1 cbrt-undiv div-exp associate-/l/ unswap-sqr
4×add-log-exp
3×associate-*r* prod-exp cbrt-unprod
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 633
Calls
4 calls:
176.0ms
(sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))
1.5s
(* (/ (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) x)
572.0ms
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))
769.0ms
(/ (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
212.0ms
(sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))
391.0ms
(* (/ (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) x)
519.0ms
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))
330.0ms
(/ (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))) (sqrt (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))

simplify1.9s

Counts
645 → 645
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0881110471
12491100219
done500096229

prune10.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 0.15298196345929327 (pow x 5))
0.4b
(/ 0.2514179000665375 (pow x 3))

rewrite53.0ms

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:
27.0ms
(/ 0.15298196345929327 (pow x 5))
16.0ms
(/ 0.2514179000665375 (pow x 3))

series175.0ms

Counts
2 → 6
Calls
2 calls:
101.0ms
(/ 0.15298196345929327 (pow x 5))
74.0ms
(/ 0.2514179000665375 (pow x 3))

simplify981.0ms

Counts
116 → 116
Iterations

Useful iterations: done (973.0ms)

IterNodesCost
01731234
13421045
214191015
done50001013

prune333.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.0b

bsearch779.0ms

Steps
ItersRangePoint
11
0.022891638200552334
5.118117448855024e+31
673.5332051604527
9
-31601356937510816.0
-2823503834.9923654
-4052405089.3470764

simplify434.0ms

Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
063153
192139
done92139

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.8s8000×body80valid