Details

Time bar (total: 19.5s)

sample35.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify4.9s

Counts
1 → 1
Iterations
IterNodes
done5000
103779
92852
82267
71902
61547
5966
4418
3167
272
138
018

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b
(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.1b
(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
15.6b
(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms
(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.0ms
(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
9.0ms
(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series319.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(fma (+ z 6.012459259764103) z 3.350343815022304)
44.0ms
(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
149.0ms
(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
92.0ms
(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify1.5s

Counts
71 → 71
Iterations
IterNodes
done5002
32290
2606
1229
0118

prune522.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) y x)
15.0b
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.0b
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.0b
(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma (/ (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) y x)
1.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
5.0ms
(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(fma (/ (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) y x)
91.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
75.0ms
(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
193.0ms
(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
done5000
33916
2996
1332
0161

prune763.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.1b
(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))) y x)
0.5b
(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
15.7b
(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
17×add-exp-log
16×associate-/r*
11×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
5×pow1
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp fma-udef
1×associate-/r/ pow-flip inv-pow
Counts
4 → 127
Calls
4 calls:
0.0ms
(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
1.0ms
(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))) y x)
17.0ms
(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
4.0ms
(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

series414.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
180.0ms
(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))) y x)
89.0ms
(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
97.0ms
(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

simplify1.5s

Counts
139 → 139
Iterations
IterNodes
done5001
22085
1504
0222

prune942.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))
0.5b
(/ 101.23733352003816 (* z z))
0.5b
(/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))))
0.8b
(fma (/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z)))) y x)

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
115×*-un-lft-identity
103×add-sqr-sqrt
93×add-cube-cbrt
91×prod-diff
23×div-inv
13×add-exp-log
11×add-cbrt-cube
8×distribute-lft-out
7×fma-neg
6×associate-/r* associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u div-exp log1p-expm1-u difference-of-squares
3×cbrt-undiv
2×clear-num frac-2neg associate-/r/
1×rec-exp sub-neg flip3-+ flip3-- diff-log 1-exp prod-exp frac-sub cbrt-unprod flip-+ fma-udef pow-flip flip-- inv-pow
Counts
4 → 194
Calls
4 calls:
47.0ms
(- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))
6.0ms
(/ 101.23733352003816 (* z z))
125.0ms
(/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))))
0.0ms
(fma (/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z)))) y x)

series288.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))
49.0ms
(/ 101.23733352003816 (* z z))
62.0ms
(/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))))
83.0ms
(fma (/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z)))) y x)

simplify2.5s

Counts
206 → 206
Iterations
IterNodes
done5000
23819
1814
0342

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes388.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.5b

bsearch179.0ms

Steps
ItersRangePoint
8
1875.4132169206714
595377.2589799166
453539.71708965226
8
-3.1196064285525156e+19
-2.342337183003078e+16
-2.37889685483777e+16

simplify26.0ms

Iterations
IterNodes
done50
150
035

end0.0ms

sample1.2s

Algorithm
intervals
Results
936.0ms8000×body80valid