Details

Time bar (total: 7.0s)

sample21.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (17.0ms)

IterNodesCost
01821
13818
27118
314017
426217
543317
664217
777217
895517
9108817
10114817
11114917
done114917

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize12.0ms

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)
3.2b
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite4.0ms

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)
2.0ms
(/ 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)

series255.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
35.0ms
(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
58.0ms
(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
133.0ms
(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify578.0ms

Counts
71 → 71
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
0129985
1246962
2588854
31652849
done5000842

prune248.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b
(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
3.2b
(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
14.6b
(log (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b
(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×log-prod times-frac
15×exp-sum
6×pow1 add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u exp-prod log1p-expm1-u add-log-exp
3×associate-/l*
2×log-pow
1×cbrt-undiv frac-2neg div-exp rem-log-exp clear-num fma-udef div-inv rem-exp-log
Counts
4 → 82
Calls
4 calls:
4.0ms
(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
4.0ms
(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms
(log (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms
(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series278.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
61.0ms
(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
67.0ms
(log (fma (+ z 6.012459259764103) z 3.350343815022304))
131.0ms
(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify805.0ms

Counts
94 → 94
Iterations

Useful iterations: 3 (361.0ms)

IterNodesCost
01801536
13521313
27971155
321091148
done50001148

prune301.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3)
3.2b
(/ y (cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3)))
8.3b
(cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3))
14.7b
(fma (/ y (cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-prod
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×unpow-prod-down cube-prod
15×associate-/r*
7×add-exp-log
6×cube-mult unpow3 add-cbrt-cube sqr-pow
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/l*
1×cbrt-undiv pow-to-exp pow-pow frac-2neg pow1/3 div-exp pow-exp clear-num rem-cbrt-cube fma-udef div-inv rem-cube-cbrt
Counts
4 → 135
Calls
4 calls:
1.0ms
(pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3)
5.0ms
(/ y (cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3)))
1.0ms
(cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3))
1.0ms
(fma (/ y (cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series264.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3)
64.0ms
(/ y (cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3)))
20.0ms
(cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3))
138.0ms
(fma (/ y (cbrt (pow (fma (+ z 6.012459259764103) z 3.350343815022304) 3))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify556.0ms

Counts
147 → 147
Iterations

Useful iterations: done (546.0ms)

IterNodesCost
02122751
13932201
210311962
done50001955

prune375.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ z 6.012459259764103) z)
0.1b
(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.3b
(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.8b
(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
14×*-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
5×flip3-+ flip-+
4×expm1-log1p-u associate-*r/ associate-*l/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×times-frac pow-prod-down associate-/r* *-commutative unswap-sqr
2×cbrt-undiv div-exp associate-/r/ associate-/l/
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv distribute-lft-out associate-/l*
Counts
4 → 96
Calls
4 calls:
9.0ms
(* (+ z 6.012459259764103) z)
10.0ms
(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
22.0ms
(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0ms
(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series291.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (+ z 6.012459259764103) z)
68.0ms
(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
56.0ms
(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
124.0ms
(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify668.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (188.0ms)

IterNodesCost
01981630
15471386
219271207
done50001207

prune323.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes164.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.4b

bsearch127.0ms

Steps
ItersRangePoint
7
2942.2625356967415
64063.92193037696
63485.56364381746
7
-3.5710064929965375e+19
-4.5045000713410016e+17
-1.9637172304780186e+19

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02544
13136
done3136

end0.0ms

sample492.0ms

Algorithm
intervals
Results
319.0ms8000×body80valid