Details

Time bar (total: 32.8s)

sample97.0ms

Algorithm
intervals
Results
58.0ms256×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: done (2.2s)

IterNodesCost
044173
1132173
2547109
3278179
done500173

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.0001789971 (pow x 6))
0.3b
(* 0.1049934947 (* x x))
12.6b
(* (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) x)
27.4b
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
44×associate-*r/ frac-add
39×flip3-+ flip-+
35×add-sqr-sqrt
33×associate-*l*
28×associate-/r/
24×add-cube-cbrt *-un-lft-identity
21×add-exp-log
19×times-frac
18×add-cbrt-cube
11×pow1 associate-*r*
8×prod-exp
6×cbrt-unprod associate-/l/ unswap-sqr
4×unpow-prod-down pow-prod-down add-log-exp
3×associate-/r* *-commutative associate-/l*
2×cbrt-undiv div-exp div-inv sqr-pow
1×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num
Counts
4 → 137
Calls
4 calls:
18.0ms
(* 0.0001789971 (pow x 6))
35.0ms
(* 0.1049934947 (* x x))
766.0ms
(* (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) x)
540.0ms
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))

series842.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* 0.0001789971 (pow x 6))
49.0ms
(* 0.1049934947 (* x x))
392.0ms
(* (/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) x)
326.0ms
(/ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))

simplify869.0ms

Counts
149 → 149
Iterations

Useful iterations: done (852.0ms)

IterNodesCost
039710356
113339808
done50009040

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.0001789971 (pow x 6))
0.3b
(* 0.1049934947 (* x x))
0.5b
(/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))
26.9b
(* (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))

rewrite955.0ms

Algorithm
rewrite-expression-head
Rules
49×associate-*r/
48×frac-add
44×flip3-+ flip-+
35×add-sqr-sqrt associate-*r*
28×associate-/r/
24×add-cube-cbrt *-un-lft-identity
21×add-exp-log
19×times-frac
18×add-cbrt-cube
11×pow1
9×associate-*l*
8×prod-exp
6×frac-times associate-*l/ cbrt-unprod unswap-sqr
4×unpow-prod-down pow-prod-down add-log-exp
3×associate-/r* *-commutative associate-/l*
2×cbrt-undiv div-exp div-inv sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num
Counts
4 → 143
Calls
4 calls:
18.0ms
(* 0.0001789971 (pow x 6))
19.0ms
(* 0.1049934947 (* x x))
172.0ms
(/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))
737.0ms
(* (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))

series690.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* 0.0001789971 (pow x 6))
33.0ms
(* 0.1049934947 (* x x))
208.0ms
(/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442)))))))
379.0ms
(* (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))) (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))))

simplify856.0ms

Counts
155 → 155
Iterations

Useful iterations: done (837.0ms)

IterNodesCost
042811554
1148310868
done500210190

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize121.0ms

Local error

Found 4 expressions with local error:

25.4b
(- (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6))))))
26.2b
(* (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) (- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6))))))))
26.9b
(/ (* (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) (- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))) (- (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))
27.9b
(- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
640×associate-*r/
505×flip3-+ flip-+
452×frac-times
328×frac-sub
162×associate-*l/
133×associate-/l/
27×associate-*l*
20×frac-add associate-/r/
19×add-sqr-sqrt
18×add-exp-log add-cbrt-cube
15×add-log-exp
14×add-cube-cbrt *-un-lft-identity
13×times-frac
12×distribute-rgt-in distribute-lft-in
7×flip3-- associate--l+ flip--
6×pow1 associate--r+
5×cbrt-undiv div-exp
4×sub-neg diff-log prod-exp cbrt-unprod
3×associate-*r* associate-/r* sum-log
2×div-inv unswap-sqr
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 451
Calls
4 calls:
154.0ms
(- (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6))))))
846.0ms
(* (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) (- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6))))))))
566.0ms
(/ (* (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) (- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))) (- (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))
122.0ms
(- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
155.0ms
(- (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6))))))
488.0ms
(* (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) (- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6))))))))
714.0ms
(/ (* (/ x (+ (* (pow x 6) (+ (* (pow x 6) (* 2.0 0.0001789971)) 0.0694555761)) (+ (+ 1.0 (* 0.7715471019 (* x x))) (* (pow x 4) (+ 0.2909738639 (+ (* (pow x 6) 0.0008327945) (* (pow x 4) 0.0140005442))))))) (- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))) (- (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (* (pow x 4) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))
228.0ms
(- (* (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182)) (+ (+ 1.0 (* 0.1049934947 (* x x))) (* (pow x 6) 0.0072644182))) (* (pow x (* 2 4)) (* (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))) (+ 0.0424060604 (+ (* (pow x 4) 0.0005064034) (* 0.0001789971 (pow x 6)))))))

simplify1.6s

Counts
463 → 463
Iterations

Useful iterations: done (1.4s)

IterNodesCost
086483540
1282476196
done500073922

prune9.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 0.2514179000665373 (pow x 3)) (/ 0.1529819634592937 (pow x 5)))
0.0b
(+ (+ (/ 0.2514179000665373 (pow x 3)) (/ 0.1529819634592937 (pow x 5))) (/ 0.5 x))
0.2b
(/ 0.1529819634592937 (pow x 5))
0.3b
(/ 0.2514179000665373 (pow x 3))

rewrite831.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity times-frac
45×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
14×add-exp-log
12×cube-prod
11×add-log-exp
8×add-cbrt-cube sqr-pow
7×distribute-lft-out
6×div-exp associate-/l*
5×frac-add
4×pow1 cube-mult unpow3 sum-log
3×flip3-+ flip-+
2×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num div-inv
1×associate-+l+
Counts
4 → 143
Calls
4 calls:
117.0ms
(+ (/ 0.2514179000665373 (pow x 3)) (/ 0.1529819634592937 (pow x 5)))
670.0ms
(+ (+ (/ 0.2514179000665373 (pow x 3)) (/ 0.1529819634592937 (pow x 5))) (/ 0.5 x))
23.0ms
(/ 0.1529819634592937 (pow x 5))
10.0ms
(/ 0.2514179000665373 (pow x 3))

series380.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(+ (/ 0.2514179000665373 (pow x 3)) (/ 0.1529819634592937 (pow x 5)))
81.0ms
(+ (+ (/ 0.2514179000665373 (pow x 3)) (/ 0.1529819634592937 (pow x 5))) (/ 0.5 x))
71.0ms
(/ 0.1529819634592937 (pow x 5))
67.0ms
(/ 0.2514179000665373 (pow x 3))

simplify1.4s

Counts
155 → 155
Iterations

Useful iterations: 2 (555.0ms)

IterNodesCost
02352136
15311879
224451787
done50001787

prune412.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.6b

bsearch809.0ms

Steps
ItersRangePoint
10
15.006088268796836
293663098603.6372
786.2107275504625
8
-28361.394281441724
-101.50163225226844
-17675.050466169654

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
069173
1100157
done100157

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.6s8000×body80valid