Details

Time bar (total: 10.5s)

sample66.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
16.0ms261×body80nan

simplify68.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
01114
12212
24411
36411
46911
57011
done7011

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (+ y z))
1.0b
(fma y z (* x (+ y z)))
18.8b
(sqrt (fma y z (* x (+ y z))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cube-cbrt
5×add-exp-log add-cbrt-cube
4×associate-*r*
3×expm1-log1p-u associate-*l* sqrt-prod log1p-expm1-u add-log-exp
2×associate-*r/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ fma-udef distribute-lft-out unswap-sqr
Counts
3 → 50
Calls
3 calls:
29.0ms
(* x (+ y z))
0.0ms
(fma y z (* x (+ y z)))
2.0ms
(sqrt (fma y z (* x (+ y z))))

series233.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* x (+ y z))
33.0ms
(fma y z (* x (+ y z)))
157.0ms
(sqrt (fma y z (* x (+ y z))))

simplify598.0ms

Counts
59 → 59
Iterations

Useful iterations: done (596.0ms)

IterNodesCost
091581
1235532
2851485
done5001479

prune231.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* y (+ z x))
0.5b
(fma x z (* y (+ z x)))
18.8b
(sqrt (fma x z (* y (+ z x))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cube-cbrt
5×add-exp-log add-cbrt-cube
4×associate-*r*
3×expm1-log1p-u associate-*l* sqrt-prod log1p-expm1-u add-log-exp
2×associate-*r/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ fma-udef distribute-lft-out unswap-sqr
Counts
3 → 50
Calls
3 calls:
23.0ms
(* y (+ z x))
0.0ms
(fma x z (* y (+ z x)))
2.0ms
(sqrt (fma x z (* y (+ z x))))

series240.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(* y (+ z x))
48.0ms
(fma x z (* y (+ z x)))
158.0ms
(sqrt (fma x z (* y (+ z x))))

simplify483.0ms

Counts
59 → 59
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
089581
1229532
2791483
done5001479

prune176.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma x z (* y (+ z x)))
0.5b
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
18.8b
(sqrt (fma x z (* y (+ z x))))
18.8b
(sqrt (fma x z (* y (+ z x))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod fma-udef
Counts
4 → 117
Calls
4 calls:
0.0ms
(fma x z (* y (+ z x)))
29.0ms
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
2.0ms
(sqrt (fma x z (* y (+ z x))))
2.0ms
(sqrt (fma x z (* y (+ z x))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(fma x z (* y (+ z x)))
141.0ms
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
141.0ms
(sqrt (fma x z (* y (+ z x))))
165.0ms
(sqrt (fma x z (* y (+ z x))))

simplify1.6s

Counts
129 → 129
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01092711
12301656
210971506
done50011476

prune487.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
18.8b
(sqrt (fma x z (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
2.0ms
(sqrt (fma x z (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
313.0ms
(cbrt y)
310.0ms
(cbrt y)
267.0ms
(cbrt y)
199.0ms
(sqrt (fma x z (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

simplify1.7s

Counts
66 → 66
Iterations

Useful iterations: done (1.7s)

IterNodesCost
065570
1138515
2393417
32114359
done5001356

prune305.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.8b

regimes140.0ms

Accuracy

0% (0.3b remaining)

Error of 19.6b against oracle of 19.2b and baseline of 19.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01123
11423
done1423

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.0s8000×body80valid
615.0ms7896×body80nan