Details

Time bar (total: 24.0s)

sample52.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213837
346037
4192437
done500137

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
26.9b
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
8×associate-*l/ associate-/l/
7×flip3-+ flip-+
4×frac-times prod-exp cbrt-unprod add-log-exp
3×flip3-- times-frac pow-prod-down associate-/r* *-commutative flip-- unswap-sqr
2×cbrt-undiv associate-*r/ div-exp associate-/r/
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 91
Calls
4 calls:
89.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
38.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
58.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
198.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series513.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
81.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
41.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
305.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify2.3s

Counts
103 → 103
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02282606
16932570
242762234
done50022230

prune753.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b
(* 4.16438922228 (pow x 2))
26.9b
(/ (* (- x 2.0) (+ (* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite419.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×add-exp-log
15×add-cbrt-cube
14×associate-*r*
13×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×pow1 associate-/l/
6×flip3-+ associate-*l/ prod-exp flip-+ unswap-sqr
4×frac-times unpow-prod-down cbrt-unprod add-log-exp
3×flip3-- times-frac associate-/r* *-commutative flip--
2×cbrt-undiv associate-*r/ div-exp pow-prod-down associate-/r/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num div-inv associate-/l*
Counts
4 → 98
Calls
4 calls:
186.0ms
(* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x)
53.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
21.0ms
(* 4.16438922228 (pow x 2))
153.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series520.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x)
51.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
35.0ms
(* 4.16438922228 (pow x 2))
316.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify2.7s

Counts
110 → 110
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02372735
16932681
240362316
done50022310

prune647.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (+ x 43.3400022514) x) 263.505074721)
14.4b
(+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721)))
26.9b
(/ (* (- x 2.0) (+ (* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x) z)) (+ (* (+ (/ (* (+ (pow (* (+ x 43.3400022514) x) 3) (pow 263.505074721 3)) x) (+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721)))) 313.399215894) x) 47.066876606))
26.9b
(/ (* (+ (pow (* (+ x 43.3400022514) x) 3) (pow 263.505074721 3)) x) (+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
64×associate-*l/
32×flip3-+ frac-add flip-+
20×frac-times associate-/r/
19×add-exp-log flip3-- add-cbrt-cube flip--
10×associate-*r/ associate-/l/
9×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
6×times-frac associate-/r*
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×associate-*r* pow-prod-down
2×associate-+r+ frac-2neg clear-num sum-log div-inv associate-/l*
1×+-commutative associate-+r- sub-neg diff-log associate-*l* *-commutative
Counts
4 → 123
Calls
4 calls:
42.0ms
(* (* (+ x 43.3400022514) x) 263.505074721)
84.0ms
(+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721)))
775.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x) z)) (+ (* (+ (/ (* (+ (pow (* (+ x 43.3400022514) x) 3) (pow 263.505074721 3)) x) (+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721)))) 313.399215894) x) 47.066876606))
147.0ms
(/ (* (+ (pow (* (+ x 43.3400022514) x) 3) (pow 263.505074721 3)) x) (+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721))))

series1.5s

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (* (+ x 43.3400022514) x) 263.505074721)
59.0ms
(+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721)))
1.1s
(/ (* (- x 2.0) (+ (* (+ (* (+ (+ (* 4.16438922228 (pow x 2)) (* 78.6994924154 x)) 137.519416416) x) y) x) z)) (+ (* (+ (/ (* (+ (pow (* (+ x 43.3400022514) x) 3) (pow 263.505074721 3)) x) (+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721)))) 313.399215894) x) 47.066876606))
180.0ms
(/ (* (+ (pow (* (+ x 43.3400022514) x) 3) (pow 263.505074721 3)) x) (+ (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (- (* 263.505074721 263.505074721) (* (* (+ x 43.3400022514) x) 263.505074721))))

simplify653.0ms

Counts
135 → 135
Iterations

Useful iterations: done (641.0ms)

IterNodesCost
03588115
112757311
done50006643

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x))
21.2b
(+ (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)) (- (* 47.066876606 47.066876606) (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
29.1b
(* (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (pow (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 3) (pow 47.066876606 3))) (+ (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)) (- (* 47.066876606 47.066876606) (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
29.3b
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (pow (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 3) (pow 47.066876606 3)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
101×associate-*l/
50×frac-times flip3-+ flip-+
48×frac-add
45×pow1
34×associate-*r/
30×add-exp-log add-cbrt-cube
27×flip3-- flip--
18×pow-prod-down
15×*-un-lft-identity
13×prod-exp cbrt-unprod
12×associate-*l*
11×add-sqr-sqrt
10×times-frac
9×add-cube-cbrt add-log-exp
8×associate-/l/
5×associate-/r*
4×cbrt-undiv div-exp associate-*r* associate-/r/ pow-sqr pow-prod-up
3×sum-cubes distribute-lft-out
2×associate-+r+ pow-plus sum-log *-commutative div-inv
1×+-commutative pow2 distribute-rgt-in associate-+r- sub-neg frac-2neg distribute-lft-in diff-log swap-sqr clear-num associate-/l* unswap-sqr
Counts
4 → 177
Calls
4 calls:
294.0ms
(* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x))
225.0ms
(+ (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)) (- (* 47.066876606 47.066876606) (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
1.1s
(* (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (pow (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 3) (pow 47.066876606 3))) (+ (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)) (- (* 47.066876606 47.066876606) (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
146.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (pow (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 3) (pow 47.066876606 3)))

series1.6s

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x))
101.0ms
(+ (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)) (- (* 47.066876606 47.066876606) (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
830.0ms
(* (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (pow (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 3) (pow 47.066876606 3))) (+ (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)) (- (* 47.066876606 47.066876606) (* (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
580.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (pow (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 3) (pow 47.066876606 3)))

simplify1.2s

Counts
189 → 189
Iterations

Useful iterations: done (1.2s)

IterNodesCost
040719821
1173017919
done500116691

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes399.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 27.7b

bsearch441.0ms

Steps
ItersRangePoint
9
8.375463895322616e+20
3.7617724825378538e+28
2.9239076483770014e+28
8
-1.4530194792501984e+40
-4.885693272806499e+37
-3.1485706152712823e+38

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
05197
17487
done7487

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.5s8007×body80valid