Details

Time bar (total: 19.5s)

sample47.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213837
344837
4153737
done500037

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize37.0ms

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) 137.519416416) x) y) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
23.4b
(/ (* (- 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))

rewrite467.0ms

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)
133.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
48.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
201.0ms
(/ (* (- 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))

series557.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
105.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
49.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
338.0ms
(/ (* (- 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))

simplify2.3s

Counts
103 → 103
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02312728
16712670
228752324
done50002312

prune662.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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) 137.519416416) x) y) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
22.4b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite457.0ms

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:
75.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
133.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
61.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
185.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series461.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
78.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
46.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
276.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify1.4s

Counts
103 → 103
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02162753
15622703
219932443
done50002431

prune635.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.2b
(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
22.7b
(* (+ (* (+ (* (+ (* (+ (* 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)))

rewrite792.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
25×*-un-lft-identity
24×add-cube-cbrt
21×add-exp-log associate-*r*
20×times-frac
15×add-cbrt-cube
11×pow1
9×associate-*l*
6×flip3-+ associate-*l/ prod-exp flip-+
5×unswap-sqr
4×div-exp associate-/r/ cbrt-unprod add-log-exp
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv frac-times rec-exp 1-exp div-inv
1×pow-flip frac-2neg associate-*r/ clear-num un-div-inv inv-pow
Counts
4 → 115
Calls
4 calls:
145.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
88.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
93.0ms
(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
459.0ms
(* (+ (* (+ (* (+ (* (+ (* 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)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
61.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
100.0ms
(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
282.0ms
(* (+ (* (+ (* (+ (* (+ (* 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)))

simplify1.9s

Counts
127 → 127
Iterations

Useful iterations: 2 (699.0ms)

IterNodesCost
02453635
16413443
221783075
done50003075

prune840.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

7.3b
(sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
7.3b
(sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
14.1b
(* (* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
19.5b
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
52×add-sqr-sqrt
42×times-frac
38×*-un-lft-identity
36×associate-*r*
35×add-cube-cbrt
17×sqrt-div
15×pow1
11×add-exp-log frac-times associate-*l/ add-cbrt-cube
10×flip3-+ flip-+
8×associate-/r/
6×rem-sqrt-square sqrt-pow1
4×associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod div-inv add-log-exp unswap-sqr
2×pow-flip pow1/2 *-commutative inv-pow
Counts
4 → 145
Calls
4 calls:
81.0ms
(sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
64.0ms
(sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
595.0ms
(* (* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
459.0ms
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

series946.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
142.0ms
(sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
270.0ms
(* (* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
415.0ms
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

simplify1.2s

Counts
157 → 157
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02456815
15815982
216155321
done50015246

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes393.0ms

Accuracy

96.7% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 25.1b

bsearch350.0ms

Steps
ItersRangePoint
9
2.0544205719112106e+24
3.3351947746546834e+30
2.501382024595969e+30
7
-2.6008056194933348e+29
-3.829260934998948e+27
-3.298674557903701e+28

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
04683
16473
done6473

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s8009×body80valid