Details

Time bar (total: 23.2s)

sample55.0ms

Algorithm
intervals
Results
29.0ms258×body80valid

simplify1.4s

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.4b

localize111.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (+ 78.6994924154 (* 4.16438922228 x)))
0.1b
(* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x)
3.2b
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
21.0b
(* (/ (- 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))

rewrite193.0ms

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:
18.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
13.0ms
(* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x)
22.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
132.0ms
(* (/ (- 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))

series709.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
122.0ms
(* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x)
113.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
372.0ms
(* (/ (- 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))

simplify2.6s

Counts
140 → 140
Iterations
IterNodes
done5000
24611
1936
0276

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize215.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
7.7b
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
11.7b
(/ (- x 2.0) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))
21.0b
(* (* (/ 1 (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))) (/ (- x 2.0) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
40×*-un-lft-identity
38×add-exp-log
30×times-frac
26×add-cube-cbrt
24×add-cbrt-cube sqrt-prod
17×prod-exp
11×pow1
9×frac-times div-exp cbrt-unprod
7×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
6×associate-/r* sqrt-div associate-*l/
5×cbrt-undiv associate-*r/ associate-/l*
4×add-log-exp
3×associate-*r* pow-prod-down
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/r/ associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in flip3-- div-sub associate-*l* *-commutative div-inv flip--
Counts
4 → 129
Calls
4 calls:
8.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
8.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
23.0ms
(/ (- x 2.0) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))
129.0ms
(* (* (/ 1 (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))) (/ (- x 2.0) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

series829.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
110.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
180.0ms
(/ (- x 2.0) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))
409.0ms
(* (* (/ 1 (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))) (/ (- x 2.0) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

simplify2.5s

Counts
141 → 141
Iterations
IterNodes
done5001
24852
1866
0287

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize237.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))
11.7b
(sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))
11.7b
(/ (- x 2.0) (* (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606))) (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))))
21.0b
(* (* (/ 1 (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))) (/ (- x 2.0) (* (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606))) (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

rewrite541.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
38×add-cbrt-cube
32×sqrt-div
30×prod-exp
20×sqrt-prod
19×add-sqr-sqrt
16×div-exp cbrt-unprod
15×*-un-lft-identity
13×frac-times pow1
12×flip3-+ flip-+
11×add-cube-cbrt
9×cbrt-undiv
8×sqrt-pow1 associate-*l/ associate-/r/
7×associate-*r/
5×times-frac associate-/l*
4×rem-sqrt-square pow1/2 add-log-exp
3×rec-exp 1-exp associate-*r* pow-prod-down
2×distribute-lft-out-- difference-of-squares associate-/l/
1×distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in flip3-- div-sub associate-*l* *-commutative div-inv flip--
Counts
4 → 125
Calls
4 calls:
13.0ms
(sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))
15.0ms
(sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))
53.0ms
(/ (- x 2.0) (* (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606))) (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))))
456.0ms
(* (* (/ 1 (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))) (/ (- x 2.0) (* (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606))) (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

series1.3s

Counts
4 → 12
Calls
4 calls:
163.0ms
(sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))
181.0ms
(sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))
203.0ms
(/ (- x 2.0) (* (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606))) (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))))
716.0ms
(* (* (/ 1 (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))) (/ (- x 2.0) (* (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606))) (sqrt (sqrt (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* x (+ 43.3400022514 x)))))) 47.066876606)))))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

simplify610.0ms

Counts
137 → 137
Iterations
IterNodes
done5001
11029
0329

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize176.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))
7.7b
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
7.7b
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
22.1b
(/ (* (- x 2.0) (+ (* (+ y (* x (+ 137.519416416 (* (+ 78.6994924154 (* x 4.16438922228)) x)))) x) z)) (* (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt sqrt-div
24×sqrt-prod
21×pow1
18×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
14×*-un-lft-identity add-cube-cbrt
12×frac-times
10×sqrt-pow1 pow1/2
8×swap-sqr associate-/r/ associate-/l/
6×associate-*r* associate-*l* associate-*l/ associate-*r/
5×prod-exp pow-prod-up cbrt-unprod
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×flip3-- pow-prod-down pow-sqr flip--
2×rem-sqrt-square
1×pow2 clear-num associate-/r* rem-square-sqrt frac-2neg times-frac pow-plus sqrt-unprod *-commutative div-inv associate-/l*
Counts
4 → 124
Calls
4 calls:
32.0ms
(* (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))
8.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
8.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
69.0ms
(/ (* (- x 2.0) (+ (* (+ y (* x (+ 137.519416416 (* (+ 78.6994924154 (* x 4.16438922228)) x)))) x) z)) (* (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))))

series707.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))))
89.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
106.0ms
(sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
435.0ms
(/ (* (- x 2.0) (+ (* (+ y (* x (+ 137.519416416 (* (+ 78.6994924154 (* x 4.16438922228)) x)))) x) z)) (* (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))) (sqrt (+ 47.066876606 (* x (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))))

simplify1.9s

Counts
136 → 136
Iterations
IterNodes
done5000
24046
1658
0215

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes516.0ms

Accuracy

94.8% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 25.3b

bsearch303.0ms

Steps
ItersRangePoint
9
488997712.5877659
631776370996477.2
620615997107907.6
3
-6.376815652518718e+28
-5.267362834597857e+28
-6.307474851398664e+28

simplify5.0ms

Iterations
IterNodes
done62
162
043

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.9s8010×body80valid