Details

Time bar (total: 24.1s)

sample81.0ms

Algorithm
intervals
Results
41.0ms256×body80valid

simplify1.3s

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: 25.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
24.2b
(/ (* (- 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))

rewrite416.0ms

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:
61.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
105.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
51.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
196.0ms
(/ (* (- 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))

series601.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
87.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
101.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
347.0ms
(/ (* (- 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))

simplify2.1s

Counts
103 → 103
Iterations

Useful iterations: 2 (662.0ms)

IterNodesCost
02282606
16702570
228992212
done50002212

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.3b
(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
22.5b
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
110×add-sqr-sqrt
106×*-un-lft-identity
74×add-cube-cbrt
18×associate-/r*
16×distribute-lft-out-- difference-of-squares
15×add-exp-log associate-/r/ add-cbrt-cube
10×flip3-+ flip-+
8×pow1 div-inv associate-/l*
6×associate-*r* associate-*l*
4×cbrt-undiv div-exp associate-*l/ associate-/l/ add-log-exp
2×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
1×flip3-- div-sub flip--
Counts
4 → 184
Calls
4 calls:
140.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
39.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
170.0ms
(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
202.0ms
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series710.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
98.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
362.0ms
(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
168.0ms
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.4s

Counts
196 → 196
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03489979
19599813
234879379
done50009369

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
13.1b
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
13.3b
(* (/ (- 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))))
19.8b
(/ (+ (* (+ (* (+ (* (+ (* 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)))

rewrite880.0ms

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:
65.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
116.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
461.0ms
(* (/ (- 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))))
228.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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)))

series990.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
137.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
382.0ms
(* (/ (- 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))))
387.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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)))

simplify1.8s

Counts
217 → 217
Iterations

Useful iterations: 2 (813.0ms)

IterNodesCost
032711178
188410694
228419609
done50029609

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

13.0b
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
13.0b
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
13.3b
(* (/ 1 (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (* (/ (- x 2.0) (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 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))
19.8b
(/ (+ (* (+ (* (+ (* (+ (* 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)))

rewrite784.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
59×sqrt-prod
47×add-cbrt-cube
46×add-sqr-sqrt
45×times-frac
42×add-cube-cbrt *-un-lft-identity
36×prod-exp
33×associate-*l*
27×div-exp
18×cbrt-unprod
14×cbrt-undiv sqrt-div
13×pow1
8×sqrt-pow1
6×associate-/r*
5×frac-times rec-exp flip3-+ 1-exp associate-*r/ flip-+
4×rem-sqrt-square pow1/2 associate-/r/ add-log-exp
3×pow-prod-down associate-*l/ associate-/l*
2×div-inv associate-/l/
1×frac-2neg associate-*r* clear-num *-commutative
Counts
4 → 166
Calls
4 calls:
67.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
59.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
503.0ms
(* (/ 1 (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (* (/ (- x 2.0) (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 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))
141.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
144.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
157.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
425.0ms
(* (/ 1 (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (* (/ (- x 2.0) (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 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))
438.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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)))

simplify2.0s

Counts
178 → 178
Iterations

Useful iterations: done (2.0s)

IterNodesCost
031511529
178210757
227727796
done50007775

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes349.0ms

Accuracy

97.5% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 25.2b

bsearch540.0ms

Steps
ItersRangePoint
10
2.6969245666033035e+35
4.264445276026206e+51
4.185814178876574e+51
9
-5.504247016617868e+37
-3.1641101034949086e+31
-4.1468195884167556e+37

simplify12.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
04267
16057
done6057

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.9s8011×body80valid