Details

Time bar (total: 13.2s)

sample33.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213737
333037
4101737
5399837
done500037

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
23.2b
(/ (* (- 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))

rewrite121.0ms

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:
34.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
19.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
10.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
54.0ms
(/ (* (- 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))

series406.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
42.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
64.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
229.0ms
(/ (* (- 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))

simplify967.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (363.0ms)

IterNodesCost
02272664
16552592
225872274
done50012274

prune456.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

6.1b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
14.8b
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.0b
(* (/ (- x 2.0) (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 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
19.3b
(/ (+ (* (+ (* (+ (* (+ (* 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)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
108×times-frac
95×*-un-lft-identity
69×add-cube-cbrt
63×sqrt-prod
36×associate-*l*
24×associate-*r*
20×add-exp-log add-cbrt-cube
13×distribute-lft-out-- difference-of-squares
12×associate-/r*
10×sqrt-div
9×unswap-sqr
8×associate-/r/ associate-/l*
7×pow1
6×cbrt-undiv flip3-+ div-exp flip-+
4×prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp
2×frac-2neg clear-num
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 205
Calls
4 calls:
18.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
25.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
156.0ms
(* (/ (- x 2.0) (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 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
51.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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)))

series756.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
121.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
242.0ms
(* (/ (- x 2.0) (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 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
322.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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)))

simplify1.1s

Counts
217 → 217
Iterations

Useful iterations: done (1.1s)

IterNodesCost
032711178
189610694
228899609
done50019483

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
23.4b
(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
21×associate-*r*
18×times-frac
16×frac-times associate-*l/
14×pow1 prod-exp
10×flip3-+ flip-+
8×cbrt-unprod
7×associate-*l*
6×flip3-- div-exp flip--
5×associate-*r/ pow-prod-down
4×associate-/r/ add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-/r* *-commutative associate-/l*
2×div-inv unswap-sqr
1×pow-flip frac-2neg clear-num un-div-inv inv-pow
Counts
4 → 129
Calls
4 calls:
21.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
10.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
24.0ms
(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
144.0ms
(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
63.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
52.0ms
(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
223.0ms
(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify1.2s

Counts
141 → 141
Iterations

Useful iterations: 2 (509.0ms)

IterNodesCost
02924567
19114339
234893819
done50013819

prune501.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

16.0b
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.0b
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.0b
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.6b
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (cbrt (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))) (* (cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
18×cbrt-prod sqrt-div
16×add-exp-log
15×flip3-+ flip-+
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×sqrt-prod
8×frac-times associate-/r/ add-cbrt-cube associate-/l/
4×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp
3×pow1/3
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 85
Calls
4 calls:
12.0ms
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
12.0ms
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
12.0ms
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
95.0ms
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (cbrt (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))) (* (cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
125.0ms
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
123.0ms
(cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
281.0ms
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (cbrt (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))) (* (cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (cbrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

simplify1.5s

Counts
97 → 97
Iterations

Useful iterations: 3 (631.0ms)

IterNodesCost
02175352
15495055
214844433
346524080
done50004080

prune632.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes203.0ms

Accuracy

96.2% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 24.5b

bsearch268.0ms

Steps
ItersRangePoint
10
3.1558492924628487e+21
2.0877402634697386e+37
2.3371063637595438e+32
8
-2.701315959983062e+27
-5.080993971428125e+22
-6.759357258045804e+26

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04469
16659
done6659

end0.0ms

sample701.0ms

Algorithm
intervals
Results
523.0ms8009×body80valid