Details

Time bar (total: 14.9s)

sample51.0ms

Algorithm
intervals
Results
30.0ms256×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 3 (246.0ms)

IterNodesCost
044173
1132173
2502109
3204079
done500179

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.2909738639 (* x x))
0.1b
(* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))
0.1b
(* (* x x) 0.0001789971)
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

rewrite496.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log add-cbrt-cube
19×pow1
12×add-sqr-sqrt
11×flip3-+ flip-+
10×associate-*r/ prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity pow-prod-down
8×frac-add
7×associate-*r*
6×associate-*l/ associate-/r/ associate-/l/
5×associate-*l*
4×add-log-exp
3×times-frac associate-/r* *-commutative unswap-sqr
2×cbrt-undiv div-exp
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv associate-/l*
Counts
4 → 94
Calls
4 calls:
6.0ms
(* 0.2909738639 (* x x))
12.0ms
(* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))
9.0ms
(* (* x x) 0.0001789971)
466.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* 0.2909738639 (* x x))
91.0ms
(* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))
25.0ms
(* (* x x) 0.0001789971)
260.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)))))

simplify1.6s

Counts
106 → 106
Iterations

Useful iterations: 2 (609.0ms)

IterNodesCost
02684626
19084406
245643746
done50003746

prune699.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3)))
0.1b
(/ 0.15298196345929327 (pow x 5))
0.2b
(/ 0.2514179000665375 (pow x 3))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
59×times-frac
50×*-un-lft-identity
44×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
13×add-exp-log
12×cube-prod
8×sqr-pow
7×add-cbrt-cube
6×div-exp associate-/l*
5×add-log-exp
4×cube-mult unpow3
3×pow1
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv distribute-lft-out
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
3 → 124
Calls
3 calls:
58.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3)))
3.0ms
(/ 0.15298196345929327 (pow x 5))
4.0ms
(/ 0.2514179000665375 (pow x 3))

series215.0ms

Counts
3 → 9
Calls
3 calls:
127.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3)))
52.0ms
(/ 0.15298196345929327 (pow x 5))
36.0ms
(/ 0.2514179000665375 (pow x 3))

simplify510.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (164.0ms)

IterNodesCost
01971536
13921320
210661262
done50011262

prune286.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))) (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)))))
34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

rewrite816.0ms

Algorithm
rewrite-expression-head
Rules
14×associate-*r/
13×flip3-+ flip-+
9×add-exp-log add-cbrt-cube
8×frac-add
6×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity associate-*l/ associate-/r/ associate-/l/
4×pow1 add-log-exp
3×cbrt-prod times-frac pow1/3 associate-/r*
2×cbrt-undiv div-exp
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 66
Calls
4 calls:
791.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))) (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)))))
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

series919.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (+ (* (pow x 6) 0.0694555761) (+ (* (* (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))) (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) (cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)))))
217.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
220.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
216.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

simplify1.2s

Counts
78 → 78
Iterations

Useful iterations: 2 (340.0ms)

IterNodesCost
02676619
18926394
241414423
done50004423

prune829.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
34.0b
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-div associate-*r/
4×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 44
Calls
4 calls:
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
7.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

series893.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
225.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
218.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))
225.0ms
(cbrt (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

simplify1.8s

Counts
56 → 56
Iterations

Useful iterations: 3 (688.0ms)

IterNodesCost
0971684
12541628
28851488
346261248
done50001248

prune834.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch513.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
683.8811236483473
8
-14583263.309321204
-1162.6651869185068
-519755.0885507373

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
077191
1113177
done113177

end0.0ms

sample839.0ms

Algorithm
intervals
Results
737.0ms8000×body80valid