Details

Time bar (total: 19.2s)

sample48.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify818.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.0b

localize71.0ms

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)))
2.2b
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
23.3b
(* (/ (- 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))

rewrite128.0ms

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:
13.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
13.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
24.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
75.0ms
(* (/ (- 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))

series513.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
95.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
85.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
282.0ms
(* (/ (- 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))

simplify2.1s

Counts
140 → 140
Iterations
IterNodes
done5000
24710
1939
0274

prune993.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)
0.1b
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
0.1b
(* (+ (* 4.16438922228 x) 78.6994924154) x)
23.2b
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

rewrite135.0ms

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:
13.0ms
(* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)
35.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
21.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
65.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)
54.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
97.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
270.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

simplify1.4s

Counts
103 → 103
Iterations
IterNodes
done5001
22971
1565
0210

prune978.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize116.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606))
7.0b
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
15.0b
(/ (/ (+ z (* (+ (* x (+ (* x (+ (* 4.16438922228 x) 78.6994924154)) 137.519416416)) y) x)) (sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606))) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x))))
20.2b
(/ (+ z (* (+ (* x (+ (* x (+ (* 4.16438922228 x) 78.6994924154)) 137.519416416)) y) x)) (sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r* flip3-+ flip-+
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 264
Calls
4 calls:
27.0ms
(sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606))
4.0ms
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
100.0ms
(/ (/ (+ z (* (+ (* x (+ (* x (+ (* 4.16438922228 x) 78.6994924154)) 137.519416416)) y) x)) (sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606))) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x))))
52.0ms
(/ (+ z (* (+ (* x (+ (* x (+ (* 4.16438922228 x) 78.6994924154)) 137.519416416)) y) x)) (sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606)))

series1.5s

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606))
89.0ms
(sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
725.0ms
(/ (/ (+ z (* (+ (* x (+ (* x (+ (* 4.16438922228 x) 78.6994924154)) 137.519416416)) y) x)) (sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606))) (sqrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x))))
594.0ms
(/ (+ z (* (+ (* x (+ (* x (+ (* 4.16438922228 x) 78.6994924154)) 137.519416416)) y) x)) (sqrt (+ (* x (+ (* (+ 263.505074721 (* x (+ x 43.3400022514))) x) 313.399215894)) 47.066876606)))

simplify1.7s

Counts
276 → 276
Iterations
IterNodes
done5000
24903
1989
0404

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* x (+ x 43.3400022514)) 263.505074721) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.2b
(/ 1 (+ 47.066876606 (* x (+ (* (+ (* x (+ x 43.3400022514)) 263.505074721) x) 313.399215894))))
23.3b
(* (+ (* x (+ y (* (+ 137.519416416 (* (+ (* x 4.16438922228) 78.6994924154) x)) x))) z) (/ 1 (+ 47.066876606 (* x (+ (* (+ (* x (+ x 43.3400022514)) 263.505074721) x) 313.399215894)))))

rewrite163.0ms

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:
61.0ms
(* (+ (* x (+ x 43.3400022514)) 263.505074721) x)
39.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
8.0ms
(/ 1 (+ 47.066876606 (* x (+ (* (+ (* x (+ x 43.3400022514)) 263.505074721) x) 313.399215894))))
49.0ms
(* (+ (* x (+ y (* (+ 137.519416416 (* (+ (* x 4.16438922228) 78.6994924154) x)) x))) z) (/ 1 (+ 47.066876606 (* x (+ (* (+ (* x (+ x 43.3400022514)) 263.505074721) x) 313.399215894)))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (+ (* x (+ x 43.3400022514)) 263.505074721) x)
107.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
70.0ms
(/ 1 (+ 47.066876606 (* x (+ (* (+ (* x (+ x 43.3400022514)) 263.505074721) x) 313.399215894))))
260.0ms
(* (+ (* x (+ y (* (+ 137.519416416 (* (+ (* x 4.16438922228) 78.6994924154) x)) x))) z) (/ 1 (+ 47.066876606 (* x (+ (* (+ (* x (+ x 43.3400022514)) 263.505074721) x) 313.399215894)))))

simplify494.0ms

Counts
127 → 127
Iterations
IterNodes
done5000
1684
0240

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes532.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.4b

bsearch404.0ms

Steps
ItersRangePoint
9
3.0455316621450604e+53
6.601528886642014e+60
2.375361050611562e+59
7
-3.5539660008838154e+52
-7.123290046831777e+50
-1.486655794493064e+52

simplify41.0ms

Iterations
IterNodes
done76
376
274
172
051

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s8007×body80valid