Details

Time bar (total: 23.0s)

sample61.0ms

Algorithm
intervals
Results
30.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213837
344837
4153737
done500037

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
27.3b
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite424.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
8×associate-*l/ associate-/l/
7×flip3-+ flip-+
4×frac-times prod-exp cbrt-unprod add-log-exp
3×flip3-- times-frac pow-prod-down associate-/r* *-commutative flip-- unswap-sqr
2×cbrt-undiv associate-*r/ div-exp associate-/r/
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 91
Calls
4 calls:
82.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
71.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
34.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
233.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series441.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
39.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
71.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
284.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify1.7s

Counts
103 → 103
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02262502
16602452
228452124
done50022112

prune507.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
24.9b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
12×add-exp-log add-cbrt-cube
10×pow1
9×times-frac associate-*r* associate-*l*
6×associate-*l/
5×flip3-+ flip-+
4×add-log-exp
3×pow-prod-down prod-exp associate-/r* *-commutative cbrt-unprod associate-/l* unswap-sqr
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 91
Calls
4 calls:
64.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
51.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
28.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
194.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series358.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
38.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
65.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
208.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify1.1s

Counts
103 → 103
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02112527
15522485
219542243
done50012231

prune587.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
6.6b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.7b
(/ (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
21.8b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite600.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 264
Calls
4 calls:
71.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
63.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
253.0ms
(/ (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
189.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series795.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
81.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
246.0ms
(/ (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
362.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify1.4s

Counts
276 → 276
Iterations

Useful iterations: done (1.3s)

IterNodesCost
036221587
183319839
2184118761
done500017974

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

14.2b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.8b
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.8b
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
18.1b
(* (/ (/ 1 (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
1143×times-frac
1013×add-sqr-sqrt
893×sqrt-prod
422×*-un-lft-identity
383×add-cube-cbrt
303×associate-*r*
130×unswap-sqr
123×associate-*l*
114×cbrt-prod
64×add-exp-log
40×add-cbrt-cube
34×sqrt-div
33×div-exp
22×associate-/r/
20×cbrt-div div-inv
18×cbrt-undiv
15×prod-exp
14×flip3-+ flip-+
10×pow1
9×cbrt-unprod
8×sqrt-pow1
4×rem-sqrt-square pow1/2 add-log-exp
3×rec-exp 1-exp
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 647
Calls
4 calls:
30.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
61.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
69.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
1.2s
(* (/ (/ 1 (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
166.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
181.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
998.0ms
(* (/ (/ 1 (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

simplify2.1s

Counts
659 → 659
Iterations

Useful iterations: done (2.0s)

IterNodesCost
089672325
1287369415
done500167561

prune4.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes437.0ms

Accuracy

96.7% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.7b

bsearch382.0ms

Steps
ItersRangePoint
6
7.769509167694276e+22
1.0155484648794991e+24
9.98303336278828e+23
10
-2.0172170472211408e+39
-1.6030899885608685e+28
-3.947481332209468e+38

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05487
17187
done7187

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.8s8009×body80valid