Details

Time bar (total: 18.6s)

sample70.0ms

Algorithm
intervals
Results
35.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213837
346037
4192437
done500137

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize30.0ms

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)
29.0b
(/ (* (- 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))

rewrite365.0ms

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:
52.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
93.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
30.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
187.0ms
(/ (* (- 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))

series577.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
87.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
91.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
361.0ms
(/ (* (- 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))

simplify2.2s

Counts
103 → 103
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02282606
16932570
242582232
done50002228

prune642.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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)
26.1b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite423.0ms

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:
59.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
131.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
45.0ms
(* (+ (* x 4.16438922228) 78.6994924154) 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))

series544.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
105.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
102.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
290.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify1.7s

Counts
103 → 103
Iterations

Useful iterations: 2 (484.0ms)

IterNodesCost
02132631
15812603
230432349
done50022349

prune629.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

22.7b
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
22.7b
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
22.7b
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
26.1b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (* (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) 313.399215894) x) 47.066876606))

rewrite475.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log cbrt-div associate-*l/ add-cbrt-cube
5×flip3-+ flip-+
4×pow1 add-log-exp
3×cbrt-prod pow1/3 associate-/r* associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 64
Calls
4 calls:
21.0ms
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
22.0ms
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
22.0ms
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
407.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (* (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) 313.399215894) x) 47.066876606))

series823.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
146.0ms
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
149.0ms
(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
372.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (* (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) 313.399215894) x) 47.066876606))

simplify816.0ms

Counts
76 → 76
Iterations

Useful iterations: done (810.0ms)

IterNodesCost
01653492
14143473
216452299
done50022153

prune534.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

7.3b
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))
7.3b
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))
17.9b
(* (/ 1 (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))))
22.6b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x))))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 160
Calls
4 calls:
5.0ms
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))
5.0ms
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))
130.0ms
(* (/ 1 (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))))
109.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x))))

series874.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))
89.0ms
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))
279.0ms
(* (/ 1 (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x)))))
416.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) x))))

simplify3.2s

Counts
172 → 172
Iterations

Useful iterations: 2 (691.0ms)

IterNodesCost
02549513
17389074
248188303
done50018303

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

98.4% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 25.0b

bsearch325.0ms

Steps
ItersRangePoint
8
3.7740427348779304e+65
4.0812815848014643e+68
4.733154227916775e+67
8
-2.5023847974189304e+56
-1.5843314335962344e+52
-8.446602559927393e+55

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04375
16461
done6461

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8006×body80valid