Details

Time bar (total: 47.0s)

sample84.0ms

Algorithm
intervals
Results
42.0ms256×body80valid

simplify1.1s

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.7b

localize41.0ms

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)))
3.6b
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
23.1b
(* (/ (- 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))

rewrite210.0ms

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:
25.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
25.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
45.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
108.0ms
(* (/ (- 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))

series563.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
80.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
77.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
335.0ms
(* (/ (- 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
24710
1939
0274

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite245.0ms

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:
72.0ms
(* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x)
60.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
32.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
78.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

series546.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x)
55.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
99.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
316.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

simplify1.6s

Counts
103 → 103
Iterations
IterNodes
done5000
22951
1564
0207

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize102.0ms

Local error

Found 4 expressions with local error:

14.0b
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
14.0b
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
14.0b
(cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
23.1b
(* (/ (/ (/ (- x 2.0) (cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))) (cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))) (cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

rewrite908.0ms

Algorithm
rewrite-expression-head
Rules
3742×times-frac
1999×add-sqr-sqrt
1935×*-un-lft-identity
1880×cbrt-prod
1503×add-cube-cbrt
1338×associate-*l*
216×distribute-lft-out-- difference-of-squares
92×cbrt-div
86×associate-/r/
48×flip3-+ flip-+
43×div-inv
18×add-exp-log
15×unswap-sqr
12×add-cbrt-cube
6×pow1 cbrt-undiv div-exp
4×prod-exp cbrt-unprod add-log-exp
3×pow1/3 associate-*r*
2×frac-times associate-*r/
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ *-commutative
Counts
4 → 1419
Calls
4 calls:
4.0ms
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
5.0ms
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
12.0ms
(cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
656.0ms
(* (/ (/ (/ (- x 2.0) (cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))) (cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))) (cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))) (+ (* (+ y (* (+ (* x (+ 78.6994924154 (* 4.16438922228 x))) 137.519416416) x)) x) z))

series1.4s

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
157.0ms
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
178.0ms
(cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
899.0ms
(* (/ (/ (/ (- x 2.0) (cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))) (cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))) (cbrt (+ (* 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
1431 → 1431
Iterations
IterNodes
done5002
14896
01048

prune23.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
14.5b
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
14.5b
(cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))
17.3b
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z)) (cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))) (/ (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* (+ 43.3400022514 x) x))))) 47.066876606) (cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
33×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-prod
24×associate-/r*
22×cbrt-div
16×add-exp-log
11×flip3-+ flip-+
10×add-cbrt-cube
8×associate-/l/
6×cbrt-undiv div-exp
5×associate-/r/
4×frac-times pow1 add-log-exp
3×pow1/3 div-inv
2×associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×clear-num frac-2neg associate-/l*
Counts
4 → 115
Calls
4 calls:
41.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
29.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
2.0ms
(cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))
179.0ms
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z)) (cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))) (/ (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* (+ 43.3400022514 x) x))))) 47.066876606) (cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
282.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
238.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
1.3s
(cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))
479.0ms
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z)) (cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))) (/ (+ (* x (+ 313.399215894 (* x (+ 263.505074721 (* (+ 43.3400022514 x) x))))) 47.066876606) (cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))))

simplify622.0ms

Counts
127 → 127
Iterations
IterNodes
done5000
1924
0338

prune1.7s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes518.0ms

Accuracy

97.9% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 25.2b

bsearch544.0ms

Steps
ItersRangePoint
9
1.951333632833995e+45
4.94862611632601e+50
2.1235665282408094e+49
10
-4.472020465331658e+63
-1.3194991668433843e+53
-3.441930889845368e+61

simplify14.0ms

Iterations
IterNodes
done60
160
040

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.8s8004×body80valid