Details

Time bar (total: 50.1s)

sample124.0ms

Algorithm
intervals
Results
84.0ms711×body80valid

simplify13.0s

Counts
1 → 1
Iterations
IterNodes
done5000
54325
41662
3511
2171
153
018

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b b (* a a))
0.1b
(* (- 1.0 a) (* a a))
0.1b
(fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))
0.3b
(pow (fma b b (* a a)) 2.0)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
7×add-cube-cbrt
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow pow-prod-down prod-exp cbrt-unprod
2×associate-*l/ fma-udef
1×pow-to-exp flip3-- pow-pow associate-*r* pow-exp *-commutative flip-- distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 64
Calls
4 calls:
1.0ms
(fma b b (* a a))
68.0ms
(* (- 1.0 a) (* a a))
1.0ms
(fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))
6.0ms
(pow (fma b b (* a a)) 2.0)

series833.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(fma b b (* a a))
452.0ms
(* (- 1.0 a) (* a a))
80.0ms
(fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))
223.0ms
(pow (fma b b (* a a)) 2.0)

simplify7.5s

Counts
76 → 76
Iterations
IterNodes
done5004
33585
2818
1274
0120

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))) (cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))))
8.8b
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))
8.8b
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))
8.8b
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
17.0ms
(* (cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))) (cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))))
2.0ms
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))
2.0ms
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))
2.0ms
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))

series1.3s

Counts
4 → 12
Calls
4 calls:
232.0ms
(* (cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))) (cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a)))))
243.0ms
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))
376.0ms
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))
405.0ms
(cbrt (fma (+ 3.0 a) (* b b) (* (- 1.0 a) (* a a))))

simplify4.5s

Counts
93 → 93
Iterations
IterNodes
done5001
31537
2577
1253
0112

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize116.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0)))
18.0b
(cbrt (pow (fma b b (* a a)) 2.0))
18.0b
(cbrt (pow (fma b b (* a a)) 2.0))
18.0b
(cbrt (pow (fma b b (* a a)) 2.0))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
73×cbrt-prod
46×add-sqr-sqrt
29×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
16×unswap-sqr
15×sqr-pow
11×pow1
10×swap-sqr associate-*r* associate-*l*
9×pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 117
Calls
4 calls:
48.0ms
(* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0)))
4.0ms
(cbrt (pow (fma b b (* a a)) 2.0))
4.0ms
(cbrt (pow (fma b b (* a a)) 2.0))
4.0ms
(cbrt (pow (fma b b (* a a)) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
312.0ms
(* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0)))
346.0ms
(cbrt (pow (fma b b (* a a)) 2.0))
312.0ms
(cbrt (pow (fma b b (* a a)) 2.0))
406.0ms
(cbrt (pow (fma b b (* a a)) 2.0))

simplify5.5s

Counts
129 → 129
Iterations
IterNodes
done5001
43125
31071
2522
1236
0122

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize153.0ms

Local error

Found 4 expressions with local error:

11.4b
(sqrt (pow (fma b b (* a a)) 2.0))
11.4b
(sqrt (pow (fma b b (* a a)) 2.0))
18.0b
(cbrt (pow (fma b b (* a a)) 2.0))
18.0b
(cbrt (pow (fma b b (* a a)) 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×cbrt-prod unpow-prod-down sqrt-prod
12×add-cube-cbrt *-un-lft-identity
6×rem-sqrt-square sqr-pow
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2 pow1/3
Counts
4 → 76
Calls
4 calls:
7.0ms
(sqrt (pow (fma b b (* a a)) 2.0))
7.0ms
(sqrt (pow (fma b b (* a a)) 2.0))
4.0ms
(cbrt (pow (fma b b (* a a)) 2.0))
5.0ms
(cbrt (pow (fma b b (* a a)) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
308.0ms
(sqrt (pow (fma b b (* a a)) 2.0))
297.0ms
(sqrt (pow (fma b b (* a a)) 2.0))
318.0ms
(cbrt (pow (fma b b (* a a)) 2.0))
313.0ms
(cbrt (pow (fma b b (* a a)) 2.0))

simplify3.3s

Counts
88 → 88
Iterations
IterNodes
done5000
41733
3683
2286
1142
082

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes406.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done22
122
019

end0.0ms

sample4.8s

Algorithm
intervals
Results
4.1s20252×body80valid