Details

Time bar (total: 47.3s)

sample63.0ms

Algorithm
intervals
Results
32.0ms256×body80valid

simplify1.0s

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

localize50.0ms

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))

rewrite201.0ms

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:
24.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
23.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
28.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
121.0ms
(* (/ (- 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))

series565.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (+ 263.505074721 (* x (+ 43.3400022514 x))) x)
97.0ms
(* x (+ 78.6994924154 (* 4.16438922228 x)))
89.0ms
(/ (- x 2.0) (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
331.0ms
(* (/ (- 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

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize76.0ms

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)))

rewrite279.0ms

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:
56.0ms
(* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x)
36.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
43.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
142.0ms
(/ (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z) (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))

series561.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x)
52.0ms
(* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)
128.0ms
(* (+ (* 4.16438922228 x) 78.6994924154) x)
299.0ms
(/ (+ (* (+ (* (+ (* (+ (* 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

prune857.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize118.0ms

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))

rewrite945.0ms

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:
5.0ms
(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)))
20.0ms
(cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
694.0ms
(* (/ (/ (/ (- 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:
178.0ms
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
188.0ms
(cbrt (+ 47.066876606 (* (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x)) x)))
163.0ms
(cbrt (+ (* x (+ 313.399215894 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))) 47.066876606))
867.0ms
(* (/ (/ (/ (- 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))

simplify3.0s

Counts
1431 → 1431
Iterations
IterNodes
done5002
14896
01048

prune24.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize83.0ms

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)))))

rewrite334.0ms

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:
56.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
57.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
5.0ms
(cbrt (+ z (* (+ (* x (+ 137.519416416 (* (+ (* 4.16438922228 x) 78.6994924154) x))) y) x)))
209.0ms
(/ (* (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:
268.0ms
(cbrt (+ (* (+ (* (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416) x) y) x) z))
263.0ms
(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)))
493.0ms
(/ (* (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)))))

simplify696.0ms

Counts
127 → 127
Iterations
IterNodes
done5000
1924
0338

prune1.7s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes467.0ms

Accuracy

97.9% (0.5b remaining)

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

bsearch488.0ms

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

simplify13.0ms

Iterations
IterNodes
done60
160
040

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s8004×body80valid