Details

Time bar (total: 8.2s)

sample9.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
057
176
done76

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize7.0ms

Local error

Found 1 expressions with local error:

15.6b
(/ x (fma x x 1.0))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
2.0ms
(/ x (fma x x 1.0))

series65.0ms

Counts
1 → 3
Calls
1 calls:
64.0ms
(/ x (fma x x 1.0))

simplify1.5s

Counts
32 → 32
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
068377
1132362
2323332
3775332
41942332
done5001332

prune67.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (fma x x 1.0))
15.4b
(* x (/ 1 (fma x x 1.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log
13×associate-*r*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u rec-exp 1-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 71
Calls
2 calls:
2.0ms
(/ 1 (fma x x 1.0))
8.0ms
(* x (/ 1 (fma x x 1.0)))

series121.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(/ 1 (fma x x 1.0))
71.0ms
(* x (/ 1 (fma x x 1.0)))

simplify1.8s

Counts
77 → 77
Iterations

Useful iterations: 3 (427.0ms)

IterNodesCost
0122880
1278729
2617643
31768642
done5000642

prune106.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
3.9b
(/ (cbrt x) (fma x x 1.0))
11.5b
(* (* (cbrt x) (cbrt x)) (/ (cbrt x) (fma x x 1.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
34×add-cube-cbrt *-un-lft-identity
28×cbrt-prod
22×associate-*r*
18×add-exp-log
11×add-cbrt-cube
9×pow1
6×prod-exp cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp pow-prod-down associate-/r* unswap-sqr
2×pow1/3 div-inv
1×frac-2neg associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 114
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
3.0ms
(/ (cbrt x) (fma x x 1.0))
21.0ms
(* (* (cbrt x) (cbrt x)) (/ (cbrt x) (fma x x 1.0)))

series561.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt x)
177.0ms
(cbrt x)
128.0ms
(/ (cbrt x) (fma x x 1.0))
83.0ms
(* (* (cbrt x) (cbrt x)) (/ (cbrt x) (fma x x 1.0)))

simplify887.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (314.0ms)

IterNodesCost
01821643
14811561
217331325
done50001325

prune287.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ 1.0 (pow x 5)))
0.2b
(/ 1.0 (pow x 5))
0.2b
(/ 1.0 (pow x 3))
19.2b
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
532×*-un-lft-identity
373×times-frac
240×prod-diff
238×add-sqr-sqrt
225×add-cube-cbrt
129×distribute-lft-out
79×unpow-prod-down
67×cube-prod
52×div-inv
27×sqr-pow
22×cube-mult unpow3
19×associate-/r*
14×add-exp-log
13×fma-def
11×add-log-exp
8×add-cbrt-cube
6×fma-neg div-exp associate-/l*
5×difference-of-squares
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×frac-sub
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ diff-log frac-add pow-exp clear-num sum-log flip-+
1×+-commutative sub-neg flip3-- associate--l+ flip--
Counts
4 → 418
Calls
4 calls:
26.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
5.0ms
(/ 1.0 (pow x 5))
4.0ms
(/ 1.0 (pow x 3))
291.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
53.0ms
(/ 1.0 (pow x 5))
37.0ms
(/ 1.0 (pow x 3))
49.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

simplify1.4s

Counts
430 → 430
Iterations

Useful iterations: done (1.4s)

IterNodesCost
048017448
1106214593
230689867
done50009090

prune452.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch67.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
2168.5227801871383
10
-5.276190702543451e+18
-14583263.309321204
-62379821099783.21

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02146
12832
done2832

end0.0ms

sample216.0ms

Algorithm
intervals
Results
134.0ms8000×body80valid