Details

Time bar (total: 18.9s)

sample54.0ms

Algorithm
intervals
Results
27.0ms256×body80valid

simplify30.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01114
11613
22612
33312
done3312

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
35.8b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×rem-sqrt-square div-inv
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num fma-udef
Counts
3 → 66
Calls
3 calls:
1.0ms
(fma z z (fma x x (* y y)))
10.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
9.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series579.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(fma z z (fma x x (* y y)))
126.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
358.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify2.2s

Counts
75 → 75
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
01071274
11751215
24761106
325441106
done50011106

prune672.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.1b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
35.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 72
Calls
3 calls:
1.0ms
(fma z z (fma x x (* y y)))
55.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series671.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(fma z z (fma x x (* y y)))
351.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
223.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.2s

Counts
81 → 81
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01111348
11981242
26871164
done50001162

prune614.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.1b
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
35.7b
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/l*
1×cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod fma-udef
Counts
4 → 158
Calls
4 calls:
1.0ms
(fma z z (fma x x (* y y)))
13.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
162.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
14.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
102.0ms
(fma z z (fma x x (* y y)))
267.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
647.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
715.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

simplify1.4s

Counts
170 → 170
Iterations

Useful iterations: 2 (320.0ms)

IterNodesCost
02094025
13523854
212553648
done50003648

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num fma-udef div-inv
Counts
3 → 88
Calls
3 calls:
1.0ms
(fma z z (fma x x (* y y)))
17.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series769.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(fma z z (fma x x (* y y)))
462.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
219.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.6s

Counts
97 → 97
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01161917
11831741
26041678
337051678
done50001676

prune617.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.0b

regimes727.0ms

Accuracy

62.8% (7.3b remaining)

Error of 25.8b against oracle of 18.4b and baseline of 38.1b

bsearch118.0ms

Steps
ItersRangePoint
5
1.7705603877136343e+107
6.026839760300236e+107
5.8656034904665116e+107
10
-8.04593412009165e+152
-1.7585685694369138e+134
-6.31568496964865e+142

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02432
13032
done3032

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.3s8000×body80valid