Details

Time bar (total: 21.2s)

sample40.0ms

Algorithm
intervals
Results
20.0ms257×body80valid

simplify1.1s

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: 26.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
25.3b
(/ (* (- 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))

rewrite339.0ms

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:
27.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
43.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
54.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
212.0ms
(/ (* (- 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))

series467.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
52.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
45.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
279.0ms
(/ (* (- 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))

simplify1.8s

Counts
103 → 103
Iterations

Useful iterations: 2 (598.0ms)

IterNodesCost
02262502
16822452
241822138
done50012138

prune875.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
13.9b
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
14.0b
(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
21.5b
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
108×times-frac
95×*-un-lft-identity
69×add-cube-cbrt
63×sqrt-prod
36×associate-*l*
24×associate-*r*
20×add-exp-log add-cbrt-cube
13×distribute-lft-out-- difference-of-squares
12×associate-/r*
10×sqrt-div
9×unswap-sqr
8×associate-/r/ associate-/l*
7×pow1
6×cbrt-undiv flip3-+ div-exp flip-+
4×prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp
2×frac-2neg clear-num
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 205
Calls
4 calls:
57.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
74.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
356.0ms
(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
127.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series1.0s

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
163.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
308.0ms
(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
439.0ms
(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify2.1s

Counts
217 → 217
Iterations

Useful iterations: 2 (805.0ms)

IterNodesCost
032711178
192710694
2451110015
done500110015

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

13.9b
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
14.0b
(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ 1 (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))))
16.3b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.3b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite618.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
68×add-sqr-sqrt *-un-lft-identity
60×times-frac
47×add-cbrt-cube
42×add-cube-cbrt
36×associate-*l*
34×prod-exp
33×sqrt-prod
26×div-exp
18×cbrt-unprod
14×cbrt-undiv
13×distribute-lft-out-- difference-of-squares
9×pow1
6×cbrt-prod associate-/r*
5×frac-times associate-*r/ associate-/l*
4×rec-exp cbrt-div flip3-+ sqrt-div 1-exp associate-/r/ flip-+ add-log-exp
3×pow-prod-down associate-*l/
2×pow1/3 div-inv associate-/l/
1×flip3-- frac-2neg div-sub associate-*r* clear-num *-commutative flip--
Counts
4 → 166
Calls
4 calls:
78.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
440.0ms
(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ 1 (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))))
43.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
42.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series1.8s

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
1.3s
(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ 1 (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))))
176.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
198.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify635.0ms

Counts
178 → 178
Iterations

Useful iterations: done (614.0ms)

IterNodesCost
038311315
1113310879
done50009104

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

16.3b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.3b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.3b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.3b
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
35.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
34.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
50.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
48.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series812.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
196.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
179.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
220.0ms
(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify2.0s

Counts
64 → 64
Iterations

Useful iterations: 3 (673.0ms)

IterNodesCost
0771864
11811820
25671692
333611612
done50001612

prune821.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes441.0ms

Accuracy

96.4% (0.9b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 24.7b

bsearch438.0ms

Steps
ItersRangePoint
9
7.873908159948502e+26
4.819176892787514e+35
4.345734830617796e+35
9
-8.7601795446176e+47
-5.3805723331774746e+42
-1.786591216703896e+47

simplify23.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
04485
16375
26575
36775
done6775

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.8s8008×body80valid