Details

Time bar (total: 18.3s)

sample46.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
done32
332
226
116
011

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize25.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma y y (fma x x (* z z))) 3.0)
36.0b
(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
4×add-cbrt-cube add-exp-log
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
2 → 56
Calls
2 calls:
4.0ms
(/ (fma y y (fma x x (* z z))) 3.0)
3.0ms
(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series334.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(/ (fma y y (fma x x (* z z))) 3.0)
257.0ms
(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.2s

Counts
62 → 62
Iterations
IterNodes
done5007
42661
3787
2323
1167
0101

prune492.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
35.9b
(sqrt (fma y y (fma x x (* z z))))
35.9b
(sqrt (fma y y (fma x x (* z z))))
36.0b
(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×times-frac
38×*-un-lft-identity
36×sqrt-prod
32×add-cube-cbrt
22×associate-*r* associate-*l*
21×add-exp-log
16×add-cbrt-cube
15×unswap-sqr
11×pow1
7×div-exp
6×prod-exp
4×expm1-log1p-u cbrt-undiv sqrt-pow1 cbrt-unprod log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×frac-times rem-sqrt-square 1-exp pow-prod-down associate-*l/ associate-*r/ div-inv
1×*-commutative
Counts
4 → 129
Calls
4 calls:
55.0ms
(* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
2.0ms
(sqrt (fma y y (fma x x (* z z))))
2.0ms
(sqrt (fma y y (fma x x (* z z))))
20.0ms
(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))

series692.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
156.0ms
(sqrt (fma y y (fma x x (* z z))))
167.0ms
(sqrt (fma y y (fma x x (* z z))))
273.0ms
(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))

simplify2.6s

Counts
141 → 141
Iterations
IterNodes
done5000
33144
21017
1492
0168

prune828.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 20.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma y y (fma x x (* z z)))) (cbrt 3.0))
35.9b
(sqrt (fma y y (fma x x (* z z))))
35.9b
(sqrt (fma y y (fma x x (* z z))))
36.0b
(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma y y (fma x x (* z z)))) (cbrt 3.0))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×*-un-lft-identity add-cube-cbrt
28×sqrt-prod
21×cbrt-prod
9×pow1
6×associate-/r* add-exp-log associate-/l*
5×add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×rem-sqrt-square
1×frac-times cbrt-undiv clear-num frac-2neg div-exp pow-prod-down associate-*l/ associate-*r/ div-inv
Counts
4 → 108
Calls
4 calls:
6.0ms
(/ (sqrt (fma y y (fma x x (* z z)))) (cbrt 3.0))
1.0ms
(sqrt (fma y y (fma x x (* z z))))
1.0ms
(sqrt (fma y y (fma x x (* z z))))
38.0ms
(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma y y (fma x x (* z z)))) (cbrt 3.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
324.0ms
(/ (sqrt (fma y y (fma x x (* z z)))) (cbrt 3.0))
164.0ms
(sqrt (fma y y (fma x x (* z z))))
189.0ms
(sqrt (fma y y (fma x x (* z z))))
530.0ms
(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma y y (fma x x (* z z)))) (cbrt 3.0))))

simplify2.4s

Counts
120 → 120
Iterations
IterNodes
done5001
41523
3559
2296
1197
0132

prune837.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 20.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (fma y y (fma x x (* z z))) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))
35.9b
(sqrt (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
75×times-frac sqrt-prod
52×*-un-lft-identity
48×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
8×pow1
7×add-exp-log
6×associate-/r* add-cbrt-cube
5×sqrt-div
4×div-inv
3×expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u associate-/l* add-log-exp
1×frac-times cbrt-undiv clear-num frac-2neg sqrt-unprod div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
3 → 148
Calls
3 calls:
10.0ms
(/ (fma y y (fma x x (* z z))) (cbrt 3.0))
97.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))
5.0ms
(sqrt (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))

series1.2s

Counts
3 → 9
Calls
3 calls:
195.0ms
(/ (fma y y (fma x x (* z z))) (cbrt 3.0))
457.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))
541.0ms
(sqrt (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))

simplify2.2s

Counts
157 → 157
Iterations
IterNodes
done5000
32237
2787
1341
0201

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.7b

regimes525.0ms

Accuracy

61.9% (7.5b remaining)

Error of 26.0b against oracle of 18.5b and baseline of 38.2b

bsearch94.0ms

Steps
ItersRangePoint
7
5.523479031932673e+71
9.923697228955153e+72
9.809026589055476e+72
8
-9.423127371740811e+115
-6.705095497870994e+112
-1.494510111118953e+114

simplify10.0ms

Iterations
IterNodes
done45
245
140
029

end0.0ms

sample1.0s

Algorithm
intervals
Results
812.0ms8000×body80valid