Details

Time bar (total: 24.7s)

sample83.0ms

Algorithm
intervals
Results
49.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done5000
41945
3460
2138
155
029

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
0.1b
(* x (+ 78.6994924154 (* 4.16438922228 x)))
3.4b
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
22.7b
(* (/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606)) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
42×*-un-lft-identity
31×times-frac
28×add-cube-cbrt
27×associate-*l*
15×add-cbrt-cube add-exp-log
10×pow1
9×associate-*r*
7×distribute-lft-out-- difference-of-squares
6×flip3-+ flip-+
5×associate-/l*
4×prod-exp associate-*r/ associate-/r/ cbrt-unprod add-log-exp unswap-sqr
3×associate-/r* pow-prod-down associate-*l/ *-commutative
2×distribute-rgt-in frac-times cbrt-undiv distribute-lft-in div-exp div-inv associate-/l/
1×clear-num frac-2neg flip3-- div-sub flip--
Counts
4 → 128
Calls
4 calls:
26.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
24.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
45.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
113.0ms
(* (/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606)) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

series651.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
101.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
99.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
385.0ms
(* (/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606)) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

simplify2.7s

Counts
140 → 140
Iterations
IterNodes
done5000
24710
1939
0274

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
12×add-cbrt-cube add-exp-log
10×pow1
9×times-frac associate-*r* associate-*l*
6×associate-*l/
5×flip3-+ flip-+
4×add-log-exp
3×associate-/r* pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l* unswap-sqr
2×associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 91
Calls
4 calls:
70.0ms
(* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x)
33.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
53.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
87.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x)
88.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
56.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
298.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

simplify1.5s

Counts
103 → 103
Iterations
IterNodes
done5002
22987
1564
0207

prune806.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
0.6b
(/ (/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)) (- 47.066876606 (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)))))
22.3b
(* (/ (/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)) (- 47.066876606 (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))))) (- 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
22.7b
(/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
107×add-sqr-sqrt
96×*-un-lft-identity add-cube-cbrt
54×associate-*l*
22×add-cbrt-cube add-exp-log
20×associate-/r/
18×associate-/l*
10×flip3-+ flip-+ div-inv
8×pow1
7×cbrt-undiv div-exp
6×associate-/r* associate-*r*
4×flip3-- prod-exp cbrt-unprod flip-- add-log-exp unswap-sqr
3×associate-*l/ associate-/l/
2×distribute-rgt-in frac-times clear-num sub-neg frac-2neg distribute-lft-in pow-prod-down associate-*r/ *-commutative
Counts
4 → 212
Calls
4 calls:
66.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
103.0ms
(/ (/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)) (- 47.066876606 (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)))))
106.0ms
(* (/ (/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)) (- 47.066876606 (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))))) (- 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
68.0ms
(/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606))

series2.3s

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
1.0s
(/ (/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)) (- 47.066876606 (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)))))
599.0ms
(* (/ (/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)) (- 47.066876606 (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))))) (- 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
599.0ms
(/ (+ z (* (+ (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x) y) x)) (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606))

simplify746.0ms

Counts
224 → 224
Iterations
IterNodes
done5001
11150
0394

prune3.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
0.1b
(* (+ (* 4.16438922228 x) 78.6994924154) x)
0.4b
(/ 1 (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606))
22.9b
(* (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (/ 1 (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
25×*-un-lft-identity
24×add-cube-cbrt
21×associate-*r* add-exp-log
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×associate-/r* pow-prod-down *-commutative associate-/l*
2×frac-times cbrt-undiv rec-exp 1-exp div-inv
1×clear-num frac-2neg associate-*r/ un-div-inv pow-flip inv-pow
Counts
4 → 115
Calls
4 calls:
45.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
28.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
29.0ms
(/ 1 (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606))
222.0ms
(* (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (/ 1 (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
116.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
81.0ms
(/ 1 (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606))
293.0ms
(* (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (/ 1 (+ (* x (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))) 47.066876606)))

simplify4.1s

Counts
127 → 127
Iterations
IterNodes
done5001
24916
1676
0240

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes409.0ms

Accuracy

96.5% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.3b

bsearch378.0ms

Steps
ItersRangePoint
8
4.3244295128648204e+19
5.507951260787393e+23
5.4273741753551194e+23
7
-9.327061863251967e+32
-5.947023803583033e+30
-9.142892062834603e+32

simplify9.0ms

Iterations
IterNodes
done70
270
169
048

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.4s8007×body80valid