Details

Time bar (total: 14.7s)

sample59.0ms

Algorithm
intervals
Results
34.0ms256×body80valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
01821
13818
27218
316417
433917
559617
681917
792617
8119217
9163317
10169717
11169817
done169817

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b
(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.1b
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.2b
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms
(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
5.0ms
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series388.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
44.0ms
(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
83.0ms
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
225.0ms
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0129985
1246962
2572857
31554852
done5000849

prune330.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b
(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
4.1b
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.2b
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
1.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
1.0ms
(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
9.0ms
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series389.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
31.0ms
(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
112.0ms
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
216.0ms
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify1.2s

Counts
71 → 71
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0129985
1246962
2572857
31554852
done5000849

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
0.1b
(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
5.5b
(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.3b
(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-*l/ associate-/r/ *-commutative associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-in fma-def frac-2neg distribute-lft-in clear-num sum-log div-inv associate-/l*
Counts
4 → 87
Calls
4 calls:
17.0ms
(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
31.0ms
(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
75.0ms
(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
87.0ms
(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series404.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
102.0ms
(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
82.0ms
(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
187.0ms
(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.5s

Counts
99 → 99
Iterations

Useful iterations: 2 (524.0ms)

IterNodesCost
01811622
15091377
218341191
done50001191

prune459.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
16.1b
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
16.1b
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
16.2b
(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
66×times-frac
47×add-cube-cbrt *-un-lft-identity
42×sqrt-prod
22×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
9×unswap-sqr
8×pow1
6×associate-/r*
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 146
Calls
4 calls:
44.0ms
(* (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
2.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
7.0ms
(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
55.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
69.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
200.0ms
(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

simplify1.5s

Counts
158 → 158
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02354085
16013864
219173375
done50003342

prune560.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes176.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 16.3b

bsearch169.0ms

Steps
ItersRangePoint
10
7.432584257913239e-20
1.2374180015220204e-09
1.221975873940991e-09
10
-5.626223438004971e+37
-8.917676564026456e+18
-9.058164115916726e+18

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02847
14039
done4039

end0.0ms

sample1.1s

Algorithm
intervals
Results
809.0ms8000×body80valid