Details

Time bar (total: 59.7s)

sample78.0ms

Algorithm
intervals
Results
40.0ms256×body80valid

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
done5000
42165
3512
2154
162
029

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.7b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.8b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
24.9b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
104×add-sqr-sqrt *-un-lft-identity
72×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×add-cbrt-cube add-exp-log associate-/r/
6×div-inv associate-/l*
5×flip3-- flip--
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
Counts
4 → 163
Calls
4 calls:
0.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
11.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
19.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series631.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
52.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
143.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
387.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify2.5s

Counts
175 → 175
Iterations
IterNodes
done5000
23509
1701
0296

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize90.0ms

Local error

Found 4 expressions with local error:

16.2b
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
16.2b
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
16.2b
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
24.9b
(/ (fma x (fma x (* (* (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416)) (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))) (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
89×add-sqr-sqrt *-un-lft-identity
65×add-cube-cbrt
21×associate-/r*
12×distribute-lft-out-- difference-of-squares
9×cbrt-prod add-cbrt-cube add-exp-log associate-/r/
5×div-inv
4×expm1-log1p-u pow1 flip3-- log1p-expm1-u flip-- add-log-exp
3×cbrt-undiv pow1/3 div-exp associate-/l*
1×clear-num frac-2neg
Counts
4 → 143
Calls
4 calls:
1.0ms
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
1.0ms
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
1.0ms
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
15.0ms
(/ (fma x (fma x (* (* (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416)) (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))) (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
214.0ms
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
193.0ms
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
195.0ms
(cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))
440.0ms
(/ (fma x (fma x (* (* (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416)) (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))) (cbrt (fma x (fma x 4.16438922228 78.6994924154) 137.519416416))) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify2.2s

Counts
155 → 155
Iterations
IterNodes
done5000
23380
1744
0309

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
15.2b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
15.4b
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
21.8b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

rewrite655.0ms

Algorithm
rewrite-expression-head
Rules
9324×times-frac
4496×add-sqr-sqrt
4495×*-un-lft-identity
3617×add-cube-cbrt
2136×sqrt-prod
439×distribute-lft-out-- difference-of-squares
227×div-inv
185×associate-/r/
80×associate-/l*
73×flip3-- flip--
63×associate-/r*
41×add-exp-log
32×add-cbrt-cube
28×div-exp
19×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg 1-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 2872
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
10.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
127.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
19.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

series1.6s

Counts
4 → 12
Calls
4 calls:
121.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
202.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
411.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
841.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

simplify5.3s

Counts
2884 → 2884
Iterations
IterNodes
done5000
03077

prune23.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize116.0ms

Local error

Found 4 expressions with local error:

15.2b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
15.4b
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (cbrt (* (* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))))
21.0b
(cbrt (* (* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))
21.8b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
1052×times-frac
494×add-sqr-sqrt *-un-lft-identity
480×add-cube-cbrt
189×sqrt-prod
80×associate-/l*
73×cbrt-prod
31×associate-/r*
27×div-inv
25×add-exp-log
17×add-cbrt-cube
15×div-exp associate-/r/
14×cbrt-div
10×frac-times cbrt-undiv associate-*l/
7×distribute-lft-out-- difference-of-squares
6×associate-*r/
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×1-exp
1×flip3-- pow1/3 pow3 rem-cbrt-cube flip-- associate-/l/
Counts
4 → 571
Calls
4 calls:
18.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
36.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (cbrt (* (* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))))
120.0ms
(cbrt (* (* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))
9.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

series1.4s

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
517.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (cbrt (* (* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))))
189.0ms
(cbrt (* (* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))
530.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

simplify3.5s

Counts
583 → 583
Iterations
IterNodes
done5001
12361
0899

prune7.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes576.0ms

Accuracy

98% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 24.7b

bsearch502.0ms

Steps
ItersRangePoint
9
1.4589432968901477e+64
1.6249510797319983e+72
3.780764592174215e+68
10
-2.1456788011981848e+77
-2.0853333964574043e+66
-1.0406092101249711e+67

simplify13.0ms

Iterations
IterNodes
done41
141
036

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.8s8008×body80valid